Integrating Large Language Models into a Novel Intuitionistic Fuzzy PROBID Method for Multi-Criteria Decision-Making Problems

Abstract

As vision and mission statements embody the directions set forth by an organization, their connection to the Sustainable Development Goals (SDGs) must be made explicit to guide overall decision-making in taking strides toward the sustainability agenda. The semantic alignment of these strategic statements with the SDGs is investigated in a previous study, although several limitations need further exploration. Thus, this study aims to advance two contributions: (1) utilizing the capabilities of LLMs (Large Language Models) in text semantic analysis and (2) integrating fuzziness into the problem domain by using a novel intuitionistic fuzzy set extension of the PROBID (Preference Ranking On the Basis of Ideal-average Distance) method. First, a systematic approach evaluates the semantic alignment of organizational strategic statements with the SDGs by leveraging the use of LLMs in semantic similarity and relatedness tasks. Second, viewing it as a multi-criteria decision-making (MCDM) problem and recognizing the limitations of LLMs, the evaluations are represented as intuitionistic fuzzy sets (IFSs), which prompted the development of an IF extension of the PROBID method. The proposed IF-PROBID method was then deployed to evaluate the 47 top Philippine corporations. Utilizing ChatGPT 3.5, 7990 prompts with repetitions generated the membership, non-membership, and hesitance scores for each evaluation. Also, we developed a cohort-dependent SDG–vision–mission matrix that categorizes corporations into four distinct classifications. Findings suggest that “highly-aligned” corporations belong to the private and technology sectors, with some in the industrial and real estate sectors. Meanwhile, “weakly-aligned” corporations come from the manufacturing and private sectors. In addition, case-specific insights are presented in this work. The comparative analysis yields a high agreement between the results and those generated by other IF-MCDM extensions. This paper is the first to demonstrate two methodological advances: (1) the integration of LLMs in MCDM problems and (2) the development of the IF-PROBID method that handles the resulting inherently imprecise evaluations.

1. Introduction

In a significant global shift, the United Nations transitioned from the Millennium Development Goals to the 2030 Agenda for Sustainable Development. This transition, designed to meet unfulfilled targets and address new challenges, leveraged the knowledge gained from implementing the previous goals [1]. The 2030 Agenda for Sustainable Development, which focuses on sustainability and the interdependence of environmental, social, and economic aspects, has become a global beacon for development, health, education, and inequality reduction [2]. This global ambition directly influences national policies and strategies, with governments setting their own targets to ensure effective planning and strategy implementation [1]. The UN Statistical Commission has agreed on a comprehensive global indicator framework for the Sustainable Development Goals (SDGs), comprising 241 indicators to monitor global progress [2]. The SDGs, along with their targets and indicators, underscore the necessity for countries to set their own goals, targets, and priorities for implementation based on their unique conditions and capabilities [3], highlighting the global significance of the UN SDGs.

Since its implementation, the SDGs have been integrated into national-level development policy planning [4], with each country adopting its unique and diverse approach. West African states prioritize agriculture in their Nationally Determined Contribution [5]. Wales focuses on health and well-being [6]. The Russian Federation emphasizes high-quality education aligned with SDGs [7]. European countries are adopting the SDGs and the European Green Deal frameworks, linking them to national recommendations for achieving climate objectives while enhancing EU recovery plans [8]. Montenegro has developed the “National Strategy for Sustainable Development” for implementing the SDGs [9]. Developing nations, such as Albania [10], Tanzania [11], and Ukraine [12], have also designed frameworks for SDG deployment. At the sectoral level, public and private sector participation is critical to tackling global challenges while enhancing organizational performance [13,14]. Organizations have broadened their understanding of operational performance, environmental perception, and the notion of sustainability, achieving social and economic significance [15]. Those who place value on equity and the importance of social and ecological systems are found to possess a competitive advantage, with recent empirical support from developing economies [16,17,18].

The impending climate crisis has increasingly drawn more organizations to pay attention to the SDGs and the sustainability agenda [19]. Many recognize that environmental responsibility and social impact are now central to competitiveness and long-term value creation [19]. This broader view links operational performance with environmental stewardship, offering measurable benefits in market positioning, organizational performance, and stakeholder trust [16,17,18]. However, balancing economic success, social development, and environmental concerns has become challenging for industrial organizations. This paved the way for initiatives such as corporate social responsibility, corporate social performance, and environmental management, which are paradigms established to support corporate sustainability [20]. In addition, business excellence models now incorporate SDGs into traditional operations [21,22]. These models integrate the application of quality methods and tools into organizations, focusing on organizational needs, capabilities, policies, and strategic direction, as well as consumers, suppliers, human resources, procedures, and performance [23]. Bocken et al. [24] identified potential approaches for business model innovation, including eco-efficiency improvements (e.g., lean production, cleaner production, and eco-design), visions for a new economy (e.g., blue economy), waste value creation (e.g., recycling), product-service systems, and social enterprise solutions. Meanwhile, environmentally friendly methods include using organic and natural materials to build buildings, implementing tighter emissions controls, sourcing supplies responsibly, and developing organizations and processes to utilize resources efficiently and economically [25]. Essentially, organizations have addressed the SDGs in various ways [26]. Some organizations incorporated the SDGs into their organizational sustainability training and development programs, as well as performance evaluations and incentives, which are designed to promote sustainable practices, increase employee satisfaction and productivity, reduce environmental impact, and enhance organizational reputation [27]. Some organizations also channeled their alignment of SDGs by integrating their corporate strategies and new technologies [28].

Although these initiatives respond to the need for organizations to address the SDGs, a more integrative direction that coordinates activities at the operational level is pivotal to effectively bringing organizations to the forefront of the SDGs. Sanchez-Planelles et al. [21] found that organizations with formal structures for sustainability tend to integrate sustainable practices more effectively than those with fragmented, “siloed” approaches. In this regard, strategic planning is crucial for integrating sustainability into organizational strategies, priorities, and service delivery models, thereby achieving social, economic, and environmental benefits [29,30,31]. Developing efficient strategic management procedures is crucial to ensuring sustainability across all levels of an organization [32]. The strategic direction of an organization is shaped by its history, development, resources, and environment, outlining future goals and actions [33]. These strategic directions are formally encapsulated in mission and vision statements. A mission statement is a powerful tool for establishing clear strategic directions [34,35] and guiding organizations to make sound decisions that align with their goals and values [36]. The mission and vision statements are closely linked as they share a common purpose of guiding an organization toward its goals and objectives [37]. The mission sets the stage for the organization’s future growth, while the vision provides a sense of perspective and ensures continual advancement [38]. In the context of the SDGs, organizations consider social and environmental factors, as well as cost and quality considerations, when defining their business strategies. Organizations assess how their operations impact various dimensions of sustainability, including efforts aimed at minimizing harm and maximizing societal benefits, which can also affect profitability [39]. As vision and mission statements embody the directions set by an organization, their link to SDGs must be made explicit to guide overall decision-making in its operations.

1.1. Motivation of the Study

While national policies worldwide have integrated the SDGs into various frameworks, the main challenge exists not only at the country level but also within organizations, where they convert these global goals into practical initiatives. Increasingly, organizations are expected to perform beyond mere compliance as they are anticipated to embed sustainability into their operations, governance, and long-term strategic planning. Mission and vision statements are crucial tools that organizations use to show their commitment to the SDGs. They shape decision-making, resource allocation, and accountability processes. Understanding how these strategic statements align with sustainability goals offers essential insights into an organization’s capacity to balance profitability with social and environmental responsibilities. Such an agenda was demonstrated in the recent work of Encenzo et al. [40], which evaluates the semantic alignment between mission statements and the explicit statements of the SDGs. The contribution of such an agenda is to gain insights into how mission statements fit with the underlying directions of the SDGs, given that mission statements guide the overall strategic initiatives of organizations. Encenzo et al. [40] viewed this evaluation as a multi-criteria decision-making (MCDM) problem, with results from text analytics populating the evaluation or decision matrix, and a case study of 300 Philippine higher education institutions demonstrating their proposed agenda.

Despite their work, three critical gaps have become direct consequences that require further attention, forming the main gaps in the domain literature. Firstly, such an attempt by Encenzo et al. [40] was exclusively implemented in higher education institutions, leaving more critical industries with a greater impact on sustainability out of the analysis. Industries such as petroleum, construction, and manufacturing drive increased material use, energy consumption, and waste generation, which have an adverse impact on the triple bottom line. Addressing how the strategic directions of these industries fit well with the SDGs is a much-needed effort in advancing sustainability. Secondly, the similarity indices proposed by Encenzo et al. [40] based on text analytics have limitations in their semantic capability that could be addressed well by utilizing more advanced tools, such as large language models (LLMs). Thirdly, the text analytics evaluations reported by Encenzo et al. [40] are expressed as real numbers, which fail to capture ambiguities given the imprecise nature of textual interpretation. Finally, despite the importance of evaluating mission statements, vision statements are equally essential strategic documents in organizations that communicate crucial insights into their strategic priorities and efforts toward sustainability. While Encenzo et al. [40] limit their analysis to mission statements, incorporating vision statements offers a more thorough understanding of how well an organization’s strategic direction aligns with the SDGs.

1.2. Research Question

Thus, this work offers an extension of the agenda first initiated by Encenzo et al. [40] by offering the following contributions: (1) expanding the case of other organizations outside the education sector (e.g., top Philippine companies) while incorporating vision and mission statements in the analysis, to offer a more holistic evaluation of fitness at a greater scope, (2) leveraging the capabilities of LLMs in text analytics, thereby improving the text semantic analysis espoused in the previous analysis, and in the process, demonstrating the integration of LLMs in MCDM problems, and (3) integrating fuzziness into the problem domain by using a novel fuzzy set extension of an MCDM method in order to augment the proposed multi-criteria evaluation of organizational vision and mission statements. Effectively, it answers the following research question:

How do we evaluate the semantic alignment of organizational direction statements with the UN SDGs using an LLM-based fuzzy MCDM platform?

1.3. Study Contributions

This work advances several contributions to the literature. Firstly, in our proposed method, we utilized LLM to generate intuitionistic fuzzy evaluations on the alignment between the vision and mission statements of organizations and the SDGs. Compared to the text analytics evaluation employed by Encenzo et al. [40], LLMs offer more nuanced semantic assessments of vision and mission alignment with the SDGs, and their advanced natural language understanding could enhance the robustness of these measurements [41]. Secondly, among the fuzzy set extensions available in the literature to handle ambiguity and imprecision in decision-making, both Işık [42] and Işık [43] highlighted the efficacy of intuitionistic fuzzy sets (IFSs) as a more natural way of evaluating imprecise objects. Proposed by Atanassov [44], IFS theory extends Zadeh’s fuzzy set theory [45] by introducing the non-membership function and the consequent hesitancy function, which assign degrees to a set of objects. The integration of IFSs in MCDM has increased significantly over the last two decades, as reported in literature reviews by Afful-Dadzie et al. [46] and Sharma et al. [47]. On the other hand, instead of the EDAS (Evaluation Based on Distance from Average Solution) method deployed in Encenzo et al. [40], this work explores the extension of an emerging PROBID (Preference Ranking On the Basis of Ideal-average Distance) method proposed by Wang et al. [48]. The PROBID method combines the strengths of the EDAS and the more popular TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) by bringing the notion of ideal and average solutions into a single methodological framework. Its use has been demonstrated primarily on engineering problems (e.g., [49,50,51,52]), with some extensions put forward [53,54,55]. Drawing on previous observations of the efficacy of IFS [42,43,56], we propose an extension of the PROBID method to handle imprecise information modeled as IFS. In doing so, we address the imprecision of LLM evaluations in the domain problem and contribute to the fuzzy MCDM literature. Finally, aside from these methodological contributions, this work offers a better perspective of how the strategic directions of organizations align with the SDGs. In the process, designing more effective directions will help inform more targeted initiatives to advance the sustainability agenda within their domain of control.

This paper is structured as follows. Section 2 reviews the literature on vision and mission statements and provides a brief and relevant background on LLMs. Section 3 outlines the preliminaries of IFS and the PROBID method in order to present readers with a working background. Section 4 demonstrates the adoption of the proposed IF-PROBID to an actual evaluation of top Philippine corporations. A robustness check of the study findings with those obtained from comparable IF extensions of MCDM methods is espoused in Section 5. An integrated visualization generated by IF-PROBID rankings on vision and mission statements is presented in Section 6. Insights into the findings are discussed in Section 7, while Section 8 enumerates some study limitations and avenues for future work. It ends with concluding remarks in Section 9.

2. Literature Review

2.1. Vision and Mission Statements

With the emergence of new technologies, the influx of information, and the impending crises within the industrial environment, adapting to change has become an inevitable condition for global competitiveness. Strategic management is crucial for organizations to navigate unpredictable conditions arising from globalization, technological advancements, mergers, and demographic shifts. It guides organizations in forming clear directions and measurable goals. One of its pillars is strategy formulation, which involves integrating organizational learning from previous experiences into goals and strategies, considering both the external and internal environments. In general, strategy formulation yields the vision, mission, and goal statements of an organization. Organizations establish these statements as the foundation of their strategic plan on how they behave and operate, often associated with organizational identity [57], as they are crucial for survival and reputation.

Forming a vision and mission is fundamental to strategic management, regardless of the plan to implement [58]. Vision is the future image of the organization, reflecting both current and future goals, and influencing overall success [59]. It should be a “strategic and applicable vision” that is compelling enough to shape organizational actions and fuel strategies [58]. Vision plays a crucial role in setting goals and objectives, providing a strategic planning framework for management, and motivating workers to rally around a common purpose. Kotter and Heskett [60] noted that having a consistent organizational vision consistently leads to increased revenues, job-creating capacities, share prices, and profit growth ratios. On the other hand, an organization’s mission is its identity, distinguishing it from its competitors and guiding its activities. It unites managers and personnel to provide motivation, guide responsibilities, and utilize resources to achieve goals. Consequently, lacking a clear goal and vision can lead to adverse outcomes with stakeholders, consumers, and shareholders [37].

With pressures primarily from stakeholders, organizations integrate the sustainability agenda into their strategic directions. Lee et al. [61] conducted an exploratory study to address sustainability in higher education at Australian universities. They found that most universities did not have well-developed visions and missions attributing to sustainability. They emphasized the importance of a clear vision and mission statement to guide sustainability policies and practices, unify higher education’s disparate missions at the university faculty level, and ensure consistent institutional communication and policies for sustainable development. Additionally, a bibliometric case study on fifteen public higher education institutions by Trevisan et al. [62] provides insights into the critical role of aligning vision statements with sustainability goals, as this fosters a sense of purpose and direction for further sustainability efforts and a collective understanding of sustainability. Meanwhile, Qin et al. [63] found, in a study of the world’s top five hospitals, that hospitals’ visions and missions reflect their social responsibility and sustainability. The vision guides management by promoting fairness for patients and employees, while also enhancing efficiency.

Mirvis et al. [64] claimed that long-established companies, such as Kodak and Corning Inc. in the United States, Matsushita Electric Industrial and Sumitomo Corporation in Asia, and Shell Oil and Nestle in Europe, serve as case studies demonstrating the importance of a clear vision, mission, and values in driving sustainability. These companies have a forward-looking perspective and enduring values, which contribute to their corporate longevity and a cohesive sense of identity and sustainability [64]. Insights from case studies suggest that companies need to consider their vision, mission, and values to ensure success in promoting the sustainability agenda. The vision would describe the future goals of a company, providing a framework for strategy and motivation. The mission defines the purpose of a company, such as Ben & Jerry’s, which Mirvis et al. [64] observed had a distinct focus on community values over commercial interests. On the other hand, Kanter [65] discovered that Vanguard companies surpass mere lists of values displayed on walls and websites by leveraging their codified values and principles as a robust strategic guidance system. In his work, Senge [66] integrated vision, mission, and values into a cohesive set of guiding principles for businesses, defining vision as the “What”, mission as the “Why”, and values as the “How”.

Mirvis et al. [64] viewed that, while over 75% of executives worldwide acknowledge the critical role of sustainability in their firms’ financial performance, only 30–40% are actively implementing substantial measures to integrate it into their organizational processes. They contend that this gap is caused by a lack of clear ideas on sustainability, a lack of alignment among firms on responsibility for environmental, social, and governance concerns, and a lack of strong commitment to sustainability. Industrial organizations often prioritize short-term profit over good intentions, leading to the neglect or marginalization of sustainability efforts. While credible CEO management and a robust operational framework can help bridge these gaps, it is equally critical to integrate sustainability and corporate social responsibility into a company’s vision, mission, and values [64]. In the current literature, studies evaluating how the sustainability agenda is integrated into vision and mission statements are unfortunately scarce, with only Encenzo et al. [40] promoting an intuitive multi-criteria evaluation framework based on the semantic alignment of these statements and those of the UN SDGs. However, the framework of Encenzo et al. [40] contains methodological gaps that could be further enhanced to become more responsive to intricacies, such as the inherent uncertainty of the evaluation process.

2.2. Large Language Models

Artificial Intelligence (AI) algorithms are crucial for machines to comprehend and communicate in human language, presenting a persistent research challenge in achieving human-like reading, writing, and communication abilities [67]. Initially developed for text-based tasks such as translation, LLMs are now applied in robotics for reasoning and generation, interpreting ambiguous human language and multimodal input, and generating desired output [68]. Significant progress in natural language processing (NLP) has led to the development of potent language models such as the Generative Pre-trained Transformer (GPT) series [69,70,71], which include LLMs like ChatGPT (GPT-3.5 and GPT-4) [72]. Through extensive pre-training on vast volumes of textual data, these models have demonstrated exceptional performance in various NLP tasks, including question answering, text summarization, and language translation. Specifically, the ChatGPT model has demonstrated promise in various domains, including thinking, healthcare, education, text generation, science, and human-machine interaction [73].

ChatGPT, developed by OpenAI, revolutionizes text analytics by leveraging AI technology. This advanced language model, built upon the powerful GPT-3, has captivated the general public due to its exceptional capabilities in understanding and responding to various prompts. The model’s success can be traced to its robust underlying architecture [74]. The language model’s ability to understand natural language, adapt to different contexts, and generate human-like responses has made it a formidable tool for a wide range of applications [41,75,76]. ChatGPT excels in text analytics due to its enhanced accuracy and versatility [41,76]. Unlike traditional AI solutions, ChatGPT’s advanced NLP technology enables it to quickly and accurately understand customer queries and generate natural-sounding responses, thereby revolutionizing the customer service experience for businesses [76]. Furthermore, the model’s ability to grasp and react to a diverse range of prompts, from crafting poetry to generating computer code, has paved the way for its application in various fields. This adaptability is a manifestation of the model’s versatility and potential [41,74].

Current in-depth evaluations on the semantic understanding capability of ChatGPT and other LLMs offer diverse findings. For instance, Yang et al. [77] conducted experiments to assess the ambiguity resolution ability of ChatGPT and found that it achieves random-level performance in understanding human sentences, suggesting its limited capability. With tens of thousands of automated tasks, Kocoń et al. [78] examined the capabilities of ChatGPT in 25 NLP tasks. In comparison with state-of-the-art solutions, their findings revealed that ChatGPT has an average loss of quality of about 25%, with more difficult tasks reporting higher losses. Titus [79] provided an exposition of statistics-of-occurrence models, which include ChatGPT, and argued that a necessary condition for a system to possess semantic understanding is met. From these expositions, Titus [79] argued that these models do not plausibly satisfy such conditions and produce meaningful texts but merely “reflect the semantic information that exists in the aggregate given strong correlations between word placement and meaningful use”.

Other empirical findings suggest the opposite. Martínez-Cruz et al. [80] conducted experiments to evaluate the performance of ChatGPT in generating keyphrases from lengthy documents. They found that ChatGPT outperforms state-of-the-art models, generating high-quality keyphrases in diverse domains. Lihammer [81] compared the semantic similarity of political statements generated by Swedish political representatives and those generated by ChatGPT. Their findings showed that ChatGPT demonstrates higher accuracy (over 60%) in reflecting the political positions of Swedish political parties. To investigate the problem-solving capabilities of ChatGPT, Orrù et al. [82] administered 30 problems divided into two sets to ChatGPT. With known performance levels of human participants, they observed that ChatGPT’s performance is consistent with the mean success rate of human subjects, indicative of its problem-solving potential. In three NLP tasks related to sense disambiguation of acronyms and symbols, semantic similarity, and relatedness, Liu et al. [83] evaluated the performance of LLMs, including ChatGPT. They found that LLMs outperformed previous machine learning approaches, with an accuracy of 95% in acronym and symbol sense disambiguation and over 70% in similarity and relatedness tasks. This finding was somewhat supported by Oka et al. [84], who performed experiments to test whether LLMs can replicate human scoring tasks. Their results suggest that human-model scoring achieves an inter-rater reliability of 0.63, which closely resembles the reliability of human-human scoring, ranging from 0.67 to 0.70. Drawn from a series of investigations, Thelwall [85] communicated their observations by highlighting the capability of ChatGPT in understanding and performing complex text processing tasks, in which ChatGPT produces plausible responses. For ChatGPT to achieve better results in complex tasks, Thelwall [85] recommended the following: “repeating the prompts multiple times in different sessions and averaging the ChatGPT outputs”. This current study subscribes to this stream of the literature, capitalizing on the capabilities of ChatGPT in semantic similarity tasks. Galamiton et al. [86] reported such an attempt in a large-scale application that utilized ChatGPT to perform text analytics tasks by comparing two statements and producing evaluation scores as outputs. Also, Selle et al. [87] used ChatGPT in examining how a news article subscribes to a pre-defined set of criteria that characterizes support, with evaluations expressed as IFS. Thus, our study draws inspiration from such cases of adoption, with guidance from the literature, particularly Thelwall [85], which emphasizes the importance of prompt repetitions and generating averages in output scores.

2.3. Intuitionistic Fuzzy Multi-Criteria Decision-Making Methods

Due to the popularity of MCDM in countless applications, the field has been expanding exponentially over the last decade. Two methodological actions are usually elucidated in studies that address MCDM problems, expressed as a hierarchy of goals, criteria, and alternatives: (1) the assignment of priority weights of the criteria and (2) the evaluation of the alternatives given the criteria weights. The list of methods that handle such problems has been expanding, with Ocampo [88] offering a more comprehensive list of 47 methods. With the presence of imprecise and ill-defined components of MCDM problems, the notion of uncertainty within the decision-making process was almost instantly recognized in the literature. The volume of published works in this domain is overwhelming, with literature reviews reported by Mardani et al. [89], Kahraman et al. [90], and Pelissari et al. [91], apart from some documented sector-specific applications in civil engineering [92], construction management [93], energy planning [94], hospitality and tourism [95], and service operations [96]. As Pelissari et al. [91] described, the current literature primarily focuses on ambiguity as the dominant type of uncertainty, which is widely handled by fuzzy set theory and its extensions. Fuzzy set theory, proposed in the monumental work of Zadeh [45], introduces a function that assigns a grade of membership to each element in a reference set to a value within a closed interval $\left[0,1\right]$, instead of a binary membership function characterized in the classical set.

However, the realization of later studies on the limitations of Zadeh’s fuzzy set in modelling certain types of ambiguity has led to the introduction of fuzzy set extensions. These include, among others, the notion of the IFS [44], which introduces the concept of a non-membership function in addition to the membership function of Zadeh’s fuzzy set. Among other fuzzy set extensions, several realizations have been espoused in the literature in favor of the IFS. For instance, Lee et al. [97] suggested that IFSs become useful when uncertainties arise in assigning membership degrees. While comparing with Pythagorean fuzzy sets, Fermatean fuzzy sets, and $q$-rung orthopair fuzzy sets, Işık [42] argued that the IFS is more preferable than other fuzzy set extensions as it is computationally efficient and avoids the risk of violating validity conditions. Sevastjanov et al. [56] supported this argument, highlighting that other extensions hold limited practical significance despite their mathematical accuracy. These insights led to the IFS extensions of several MCDM methods, including the IF-AHP (Analytic Hierarchy Process) [98,99], IF-TOPSIS [100], IF-ELECTRE (ÉLimination Et Choix Traduisant la REalité) [101], IF-VIKOR (VlseKriterijuska Optimizacija I Komoromisno Resenje) [102], IF-TODIM (Tomada de Decisão Interativa Multicritério) [103], IF-PROMETHEE (Preference Ranking Organization METHod for Enrichment Evaluation) [104], IF-MOORA (Multi-Objective Optimization on the basis of Ratio Analysis) [105], IF-ANP (Analytic Network Process) [106], IF-WASPAS (Weighted Aggregated Sum Product Assessment) [107,108], IF-MULTIMOORA (MOORA plus Full Multiplicative Form) [109], IF-CODAS (Combinative Distance-Based Assessment) [110], IF-ARAS (Additive Ratio Assessment) [111], IF-COPRAS (COmplex PRoportional Assessment) [112], IF-EDAS (Evaluation based on Distance from Average Solution) [113], IF-SWARA (Step-wise Weight Assessment Ratio Analysis) [114], IF-MARCOS (Measurement of Alternatives and Ranking according to Compromise Solution) [115], IF-ORESTE (Organization, Rangement Et Synthese De Donnes Relationnels) [116], IF-MABAC (Multi-Attributive Border Approximation area Comparison) [117], IF-MAIRCA (Multi-Attributive Ideal-Real Comparative Analysis) [118], IF-CoCoSo (Combined Compromise Solution) [119], IF-FUCOM (Full Consistency Method) [120], IF-OPA (Ordinal Priority Approach) [121], IF-MACONT (Mixed Aggregation by Comprehensive Normalization Technique) [122], IF-BWM (Best-Worst Method) [123,124,125], IF-AROMAN (Alternative Ranking Order Method Accounting for Two-Step Normalization) [126], IF-CRADIS (Compromise Ranking of Alternatives from Distance to Ideal Solution) [127], IF-RAMS (Ranking Alternatives by Median Similarity) [128], IF-ITARA (Indifference Threshold-Based Attribute Ratio Analysis) [129], and IF-RATMI (Ranking Alternatives by Trace to Median Index) [128], and IF-COBRAC (COmparisons Between RAnked Criteria) [130], among others.

Table 1. IFS extensions of MCDM methods.

IF-MCDM Extensions	Proponents
IF-AHP	Sadiq and Tesfamariam [98]; Xu and Liao [99]
IF-TOPSIS	Boran et al. [100]
IF-ELECTRE	Wu and Chen [101]
IF-VIKOR	Devi [102]
IF-TODIM	Krohling et al. [103]
IF-PROMETHEE	Liao and Xu [104]
IF-MOORA	Pérez-Domínguez et al. [105]
IF-ANP	Liao et al. [106]
IF-WASPAS	Stanujkić and Karabašević [107]; Mishra et al. [108]
IF-MULTIMOORA	Zhang et al. [109]
IF-CODAS	Karagoz et al. [110]
IF-ARAS	Mishra et al. [111]
IF-COPRAS	Kumari and Mishra [112]
IF-EDAS	Mishra et al. [113]
IF-SWARA	Mishra et al. [114]
IF-MARCOS	Ecer and Pamucar [115]
IF-ORESTE	Tao et al. [116]
IF-MABAC	Mishra et al. [117]
IF-MAIRCA	Ecer [118]
IF-CoCoSo	Tripathi et al. [119]
IF-FUCOM	Dey et al. [120]
IF-OPA	Majumder and Salomon [121]
IF-MACONT	Mishra et al. [122]
IF-BWM	Wan and Dong [123]; Liu et al. [124]; Cheng and Chen [125]
IF-AROMAN	Hu et al. [126]
IF-CRADIS	Işık and Adalar [127]
IF-RAMS	Chatterjee and Chakraborty [128]
IF-ITARA	Yildirim et al. [129]
IF-RATMI	Chatterjee and Chakraborty [128]
IF-COBRAC	Biswas et al. [130]
IF-PROBID	This work.

shows the list of IFS extensions of MCDM methods. Note that this list may not be exhaustive. Despite the leverage of IFS in handling ambiguity in the decision-making process and the strength of the PROBID method, the corresponding IF-PROBID extension is missing in the literature.

Some of the most recent applications of IF-MCDM extensions have been reported in the literature. For instance, Görçün et al. [131] handled the complex challenge of selecting crawler cranes in construction and project logistics by developing an IF consensus-based COPRAS model. Similarly, in the development of IF-ITARA, Yildirim et al. [129] demonstrated its application to the site selection problem for solar panel waste recycling plants. In higher education, Biswas et al. [130] proposed the IF-COBRAC under Dombi aggregation to identify key service quality attributes in higher education. Liu et al. [132] proposed a variant of IF-ELECTRE II for evaluating aluminum electrolysis cell conditions. While their approach balances subjective and objective insights, it suffers from high computational complexity and sensitivity to threshold settings in ELECTRE, which may distort rankings in real-world scenarios. Meanwhile, Mandal et al. [133] demonstrated the use of interval-valued IF-AHP for criteria weighting and interval-valued IF-TOPSIS for ranking Ph.D. supervisor options. Hendiani and Walther [134] proposed an interval-valued IF cumulative likelihood-based distance to ideal solution for sustainable supplier selection, using likelihood-based indicators to rank suppliers against adjustable ideal solutions. While offering greater precision than conventional approaches, their proposed method faces challenges in scalability and transparency when applied to large datasets.

In summary, MCDM methods, including the more recent PROBID, have shown IFS to improve the modeling of ambiguity during evaluation. Recent studies indicate that IF-MCDM methodologies enhance robustness in contexts marked by imprecise judgments, thereby facilitating a more effective assessment, particularly when evaluating the semantic alignment between strategic statements of organizations and the SDGs. Concurrently, LLMs have demonstrated considerable potential in the domain of semantic similarity assessments, although reservations regarding their consistency and interpretability persist. This potential encourages combining LLM outputs with IFS, viewing model responses as evidence with inherent uncertainty rather than absolute truths. Finally, to ensure reliability, complete rankings across methods are necessary to establish the efficacy of the proposed IF-PROBID.

3. Preliminaries

This section presents some preliminary concepts of IFS and PROBID to generate a self-contained article.

3.1. Intuitionistic Fuzzy Sets

As an extension of the fuzzy set theory proposed by Zadeh [45], IFSs introduce a non-membership function in addition to the membership function defined on the reference set. The formal definition and corresponding operations are provided as follows:

Definition 1 [44].

Suppose $\mathcal{U}$ is a finite, non-empty reference set. Then, an IFS  $A$ defined over $\mathcal{U}$ is

$$A=\left\{\langle x,{\mu }_A\left(x\right),{\nu }_A\left(x\right)\rangle :x\in \mathcal{U}\right\}$$

(1)

where ${\mu }_A:\mathcal{U}\to \left[0, 1\right]$ and ${\nu }_A:\mathcal{U}\to \left[0, 1\right]$ such that $0\le {\mu }_A\left(x\right)+{\nu }_A\left(x\right)\le 1,\forall x\in \mathcal{U}$. Here, ${\mu }_A\left(x\right)$ and ${\nu }_A\left(x\right)$ represent the membership and non-membership grades of $x$ in $A$, respectively. From these functions, the hesitancy degree ${\pi }_A\left(x\right)$, i.e., the degree of the lack of knowledge on $x$ in $A$, is defined as ${\pi }_A\left(x\right)=1-{\mu }_A\left(x\right)-{\nu }_A\left(x\right)$.

For convenience, Xu and Yager [135] called $A=\left({\mu }_A,{\nu }_A,{\pi }_A\right)$ an intuitionistic fuzzy number (IFN), where ${\mu }_A\in \left[0, 1\right]$, ${\nu }_A\in \left[0, 1\right]$, $0\le {\mu }_A+{\mu }_A\le 1$, and ${\pi }_A=1-{\mu }_A-{\nu }_A$.

The basic operations of these IFNs are defined by Atanassov [44] and De et al. [136]. Let $A=\left({\mu }_A,{\nu }_A\right)$, $A_1=\left({\mu }_{A_1},{\nu }_{A_1}\right)$, and $A_2=\left({\mu }_{A_2},{\nu }_{A_2}\right)$ be IFNs, and $\lambda >0$ is any positive real number. Then,

$$A_1\oplus A_2=\left({\mu }_{A_1}+{\mu }_{A_2}-{\mu }_{A_1}{\mu }_{A_2},{\nu }_{A_1}{\nu }_{A_2}\right)$$

(2)

$$A_1⨂A_2=\left({\mu }_{A_1}{\mu }_{A_2},{\nu }_{A_1}+{\nu }_{A_2}-{\nu }_{A_1}·{\nu }_{A_2}\right),$$

(3)

$$\lambda A=\left(1-{\left(1-{\mu }_A\right)}^{\lambda }, v_A^{\lambda }\right),$$

(4)

$$A^{\lambda }=\left({\mu }_A^{\lambda }, 1-{\left(1-{\nu }_A\right)}^{\lambda }\right).$$

(5)

Some distance functions were also introduced on IFS. The normalized Euclidean distance was put forward by Szmidt and Kacprzyk [137]. Suppose two sets of IFS $A_1\left(x_j\right)=\left({\mu }_{A_1}\left(x_j\right),{\nu }_{A_1}\left(x_j\right)\right)$ and $A_2\left(x_j\right)=\left({\mu }_{A_2}\left(x_j\right),{\nu }_{A_2}\left(x_j\right)\right)$, $j=1,\dots ,n$, are defined on $\mathcal{U}=\left\{x_1,\dots ,x_n\right\}$, then the normalized Euclidean distance, denoted by $d_E\left(A_1\left(x_j\right),A_2\left(x_j\right)\right)$, is shown as follows:

$$d_E\left(A_1\left(x_j\right),A_2\left(x_j\right)\right)=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{j=1}^n\left[{\left({\mu }_{A_1}\left(x_j\right)-{\mu }_{A_2}\left(x_j\right)\right)}^2+{\left({\nu }_{A_1}\left(x_j\right)-{\nu }_{A_2}\left(x_j\right)\right)}^2\right]}.$$

(6)

3.2. The PROBID Method

The notion of the PROBID method, introduced by Wang et al. [48], revolves around a thorough evaluation of all ideal solutions, including the average solution, to ascertain the performance score of each non-dominated solution or alternative. These ideal solutions span from the most positive to the most negative outcomes [48], making them reference points as in the TOPSIS and EDAS methods. The steps required in implementing the PROBID method are elaborated as follows [48]:

Step 1.

Formulate the normalized objective matrix. An objective matrix $F={\left(f_{ij}\right)}_{m\times n}$, where $f_{ij}$ signifies the $i$th $\left(i=1,\dots ,m\right)$ solution concerning the $j$th  $\left(j=1,\dots ,n\right)$ objective. In some notations, an objective matrix is also known as a decision matrix. Also, solutions and objectives are referred to as alternatives and criteria, respectively. $F$ is normalized into $\overline{F}={\left({\overline{f}}_{ij}\right)}_{m\times n}$ using the vector normalization described as follows:

$${\overline{f}}_{ij}={\displaystyle \frac{f_{ij}}{\sqrt{\sum _{i=1}^m{f}_{ij}^2}}},\hspace{1em}\hspace{1em}\hspace{1em}\forall i,j.$$

(7)

Step 2.

Establish the weighted normalized objective matrix, denoted as $\widehat{F}={\left({\widehat{f}}_{ij}\right)}_{m\times n}$, by applying the respective weights to each objective. The weight of each objective, represented as $w_j$, $j=1,\dots ,n$, can be obtained using various criterion weight generation tools for MCDM problems (e.g., entropy method, CRITIC (Criteria Importance through Intercriteria Correlation) method):

$${\widehat{f}}_{ij}={\overline{f}}_{ij}\times w_j,\hspace{1em}\hspace{1em}\hspace{1em}\forall i,j.$$

(8)

Step 3.

Define the set of Positive Ideal Solutions (PIS) where $A_{\left(1\right)}$ denotes the most PIS, $A_{\left(k\right)}$ represents the $k$th PIS, and $A_{\left(m\right)}$stands for the $m$th PIS (or the most Negative Ideal Solution). They are described as follows:

$$A_{\left(k\right)}=\left\{\left(Large\left({\widehat{f}}_j,k\right), \forall j\in J\right),\left(Small\left({\widehat{f}}_j,k\right) \forall j\in J^{\prime }\right)\right\}=\left\{{\widehat{f}}_{\left(k\right)1} \dots ,{\widehat{f}}_{\left(k\right)j},\dots ,{\widehat{f}}_{\left(k\right)n}\right\}, \forall k,$$

(9)

where $J$ and $J^{\prime }$ denote the sets of maximization and minimization objectives, respectively. $Large\left({\widehat{f}}_j,k\right)$indicates the $k$th largest value of the vector ${\widehat{f}}_j$, and $Small\left({\widehat{f}}_j,k\right)$ represents the $k$th smallest value of the vector ${\widehat{f}}_j$, ${\widehat{f}}_j=\left({\widehat{f}}_{1j},{\widehat{f}}_{2j},\dots ,{\widehat{f}}_{mj}\right)$. For instance, ${\widehat{f}}_{\left(1\right)2}$ denotes the best value (i.e., maximal value for $j\in J$ or minimal value for $j\in J^{\prime }$) in the second objective column, and ${\widehat{f}}_{\left(2\right)3}$ represents the second-best value in the third objective column, while ${\widehat{f}}_{\left(m\right)n}$is the $m$th best value in the $n$th objective column. Then, the average solution $\overline{A}=\left\{{\overline{f}}_1,\dots , {\overline{f}}_j,\dots ,{\overline{f}}_n\right\}$, where ${\overline{f}}_j$ is calculated as follows:

$${\overline{f}}_j={\displaystyle \frac{\sum _{k=1}^m{\widehat{f}}_{\left(k\right)j}}{m}},\hspace{1em}\hspace{1em}\hspace{1em}\forall j.$$

(10)

Step 4.

Compute the Euclidean distance of the $i$th solution (or alternative) to each of the $m$ ideal solutions, denoted as $S_{i\left(k\right)}$, as well as the average solution, represented as $S_{i\left(avg\right)}$, defined as follows:

$$S_{i\left(k\right)}=\sqrt{{\sum }_{j=1}^n{\left({\widehat{f}}_{ij}-{\widehat{f}}_{\left(k\right)j}\right)}^2},\hspace{1em}\hspace{1em}\hspace{1em}\forall i,k,$$

(11)

$$S_{i\left(avg\right)}=\sqrt{{\sum }_{j=1}^n{\left({\widehat{f}}_{ij}-{\overline{f}}_j\right)}^2},\hspace{1em}\hspace{1em}\hspace{1em}\forall i.$$

(12)

Step 5.

Determine the overall positive-ideal distance and overall negative-ideal distance, denoted as $S_{i\left(PIS\right)}$ and $S_{i\left(NIS\right)}$, respectively, as presented in the following:

$$S_{i\left(PIS\right)}=\left\{\begin{array}{c}{\displaystyle \sum _{k=1}^{\left(m+1\right)/2}}{\displaystyle \frac{S_{i\left(k\right)}}{k}}, \forall i, when m is an odd number\\ {\displaystyle \sum _{k=1}^{m/2}}{\displaystyle \frac{S_{i\left(k\right)}}{k}},\forall i, when m is an even number\end{array}\right.$$

(13)

$$S_{i\left(NIS\right)}=\left\{\begin{array}{c}{\displaystyle \sum _{k=\left(m+1\right)/2}^m}{\displaystyle \frac{S_{i\left(k\right)}}{k}}, \forall i, when m is an odd number\\ {\displaystyle \sum _{k={\displaystyle \frac{m}{2}}+1}^m}{\displaystyle \frac{S_{i\left(k\right)}}{k}}, \forall i, when m is an even number\end{array}\right.$$

(14)

Step 6.

Compute the Relative Closeness ($R_i$) and Performance Index ($P_i$), defined as follows:

$$R_i={\displaystyle \frac{S_{i\left(PIS\right)}}{S_{i\left(NIS\right)}}},\hspace{1em}\hspace{1em}\hspace{1em}\forall i,$$

(15)

$$P_i={\displaystyle \frac{1}{1+R_i^2}}+S_{i\left(avg\right)},\hspace{1em}\hspace{1em}\hspace{1em}\forall i.$$

(16)

where the most preferred solution is the one with the highest $P_i$ value.

4. Methodology

4.1. The Framework of the Study

The overall analytical framework of the study is summarized in Figure 1, wherein vision and mission statements from the Philippine Top 50 corporations are assessed for their alignment with the UN SDGs. From the framework, a semantic LLM tool in component (1) is employed to generate IFN scores of alignment for every vision statement of 50 corporations across 17 SDGs. The results are reflected in component (2) for the vision statements and component (3) for the mission statements. Evaluated using the proposed IF-PROBID method in component (4), two separate rankings are generated: (i) the ranking of corporations’ alignment to SDGs based on their vision statements, as shown in component (5), and (ii) a similar ranking but based on mission statements as reflected in component (6). Finally, an integrative visualization of the two rankings is presented in component (7) to highlight the relationship between the rankings of vision and mission statements, from which four distinct clusters of corporations can be derived.

4.2. The Generalized Intuitionistic Fuzzy PROBID

Figure 2 illustrates a schematic diagram of the proposed IF-PROBID.

The framework encapsulates two phases: (1) constructing the IF decision matrix and (2) ranking the alternatives using the proposed integrated IF-PROBID method:

Phase (1). Constructing the IF decision matrix.

Step 1.

Determine the list of decision criteria and alternatives for an MCDM problem.

Step 2.

Construct the IF decision matrix. The IF decision matrix is denoted as $\tilde{X}={\left({\tilde{x}}_{ij}\right)}_{m\times n}$ where ${\tilde{x}}_{ij}$ is the evaluation of the $i$th alternative under the $j$th criterion. In this case, ${\tilde{x}}_{ij}$ is an IFN, where ${\tilde{x}}_{ij}=\left({\mu }_{{\tilde{x}}_{ij}},{\nu }_{{\tilde{x}}_{ij}},{\pi }_{{\tilde{x}}_{ij}}\right)$ and ${\mu }_{{\tilde{x}}_{ij}}$, ${\nu }_{{\tilde{x}}_{ij}}$, and ${\pi }_{{\tilde{x}}_{ij}}$ represent the membership, non-membership, and the hesitancy degrees of ${\tilde{x}}_{ij}$ associated with the $j$th fuzzy criterion, respectively.

Phase (2). Proposed IF-PROBID method.

Step 3.

Form the weighted normalized IF decision matrix. Given the criteria weight vector $w=\left(w_1,\dots ,w_n\right)$, this step of the process conforms to the IF operation described in Equation (4), as shown in the following:

$${\tilde{f}}_{ij}=\left({\mu }_{{\tilde{f}}_{ij}},{\nu }_{{\tilde{f}}_{ij}},{\pi }_{{\tilde{f}}_{ij}}\right)=\left(1-{\left(1-{\mu }_{{\tilde{x}}_{ij}}\right)}^{w_j},{\left({\nu }_{{\tilde{x}}_{ij}}\right)}^{w_j},{\left(1-{\mu }_{{\tilde{x}}_{ij}}\right)}^{w_j}-{\left({\nu }_{{\tilde{x}}_{ij}}\right)}^{w_j}\right),$$

(17)

where ${\tilde{f}}_{ij}\in \tilde{F}$, $\tilde{F}$ is a weighted normalized IF decision matrix and $w_j\in w$, such that $\sum _{j=1}^n{w}_j=1$.

Step 4.

Define the set of IF-PIS, where ${\tilde{A}}_{\left(1\right)}$ represents the most PIS, ${\tilde{A}}_{\left(k\right)}$ denotes the $k$th PIS, and ${\tilde{A}}_{\left(m\right)}$ represents the $m$th PIS (or the NIS). Analogous to Equation (9),

$${\tilde{A}}_{\left(k\right)}=\left\{\left(Large\left({\tilde{f}}_j,k\right), \forall j\in J\right),\left(Small\left({\tilde{f}}_j,k\right), \forall j\in J^{\prime }\right)\right\}=\left\{{\tilde{f}}_{\left(k\right)1} \dots ,{\tilde{f}}_{\left(k\right)j},\dots ,{\tilde{f}}_{\left(k\right)n}, \forall k,\right\}$$

(18)

where $J$ and $J^{\prime }$ are the sets of maximization and minimization criteria (or objectives), respectively. $Large\left({\tilde{f}}_j,k\right)$ denotes the $k$th largest value of the vector ${\tilde{f}}_j$, and $Small\left({\tilde{f}}_j,k\right)$ denotes the $k$th smallest value of the vector ${\tilde{f}}_j$, ${\tilde{f}}_j=\left({\tilde{f}}_{1j},\dots ,{\tilde{f}}_{mj}\right)$. Consequently, $Large\left({\tilde{f}}_j,1\right)\ge Large\left({\tilde{f}}_j,2\right)\ge \dots \ge Large\left({\tilde{f}}_j,m\right)$ and $Small\left({\tilde{f}}_j,1\right)\le Small\left({\tilde{f}}_j,2\right)\le \dots \le Small\left({\tilde{f}}_j,m\right)$. Here, we can approximate that $Large\left({\tilde{f}}_j,1\right)\ge Large\left({\tilde{f}}_j,2\right)\ge \dots \ge Large\left({\tilde{f}}_j,m\right)\Rightarrow {\mu }_{{\tilde{f}}_{\left(1\right)j}}\ge {\mu }_{{\tilde{f}}_{\left(2\right)j}}\ge \dots \ge {\mu }_{{\tilde{f}}_{\left(m\right)j}}$ and $Small\left({\tilde{f}}_j,1\right)\le Small\left({\tilde{f}}_j,2\right)\le \dots \le Small\left({\tilde{f}}_j,m\right)\Rightarrow {\mu }_{{\tilde{f}}_{\left(1\right)j}}\le {\mu }_{{\tilde{f}}_{\left(2\right)j}}\le \dots \le {\mu }_{{\tilde{f}}_{\left(m\right)j}}$, although score functions for IFS may be alternatively deployed for this purpose. Note that ${\tilde{f}}_{\left(k\right)j}=\left({\mu }_{{\tilde{f}}_{\left(k\right)j}},{\nu }_{{\tilde{f}}_{\left(k\right)j}},{\pi }_{{\tilde{f}}_{\left(k\right)j}}\right)$, $\forall k,j$, remains an IFN.

Step 5.

Compute the average solution. The average solution, denoted as $\tilde{V}=\left\{{\tilde{v}}_1,\dots , {\tilde{v}}_j,\dots ,{\tilde{v}}_n\right\}$, is calculated using an analogous formulation to Equation (10), defined as follows:

$${\tilde{v}}_j={\displaystyle \frac{\sum _{k=1}^m{\tilde{f}}_{\left(k\right)j}}{m}},$$

(19)

where ${\tilde{v}}_j=\left({\mu }_{{\tilde{v}}_j},{\nu }_{{\tilde{v}}_j},{\pi }_{{\tilde{v}}_j}\right)$ and ${\mu }_{{\tilde{v}}_j}={\displaystyle \frac{\sum _{k=1}^m{\mu }_{{\tilde{f}}_{ij}}}{m}}$, ${\nu }_{{\tilde{v}}_j}={\displaystyle \frac{\sum _{k=1}^m{\nu }_{{\tilde{f}}_{ij}}}{m}}$, and ${\pi }_{{\tilde{v}}_j}={\displaystyle \frac{\sum _{k=1}^m{\pi }_{{\tilde{f}}_{ij}}}{m}}$. Alternatively, the intuitionistic fuzzy weighted averaging operator may be used for obtaining ${\tilde{v}}_j$.

Step 6.

Calculate the Euclidean distance of the $i$th alternative to each of the $m$ ideal solutions, denoted as $S_{i\left(k\right)}$, as well as the average solution represented as $S_{i\left(avg\right)}$, defined as follows:

$$S_{i\left(k\right)}=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{j=1}^n\left[{\left({\mu }_{{\tilde{f}}_{ij}}-{\mu }_{{\tilde{f}}_{\left(k\right)j}}\right)}^2+{\left({\nu }_{{\tilde{f}}_{ij}}-{\nu }_{{\tilde{f}}_{\left(k\right)j}}\right)}^2\right]}, \forall i,$$

(20)

$$S_{i\left(avg\right)}=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{j=1}^n\left[{\left({\mu }_{{\tilde{f}}_{ij}}-{\mu }_{{\tilde{v}}_j}\right)}^2+{\left({\nu }_{{\tilde{f}}_{ij}}-{\nu }_{{\tilde{v}}_j}\right)}^2\right]}, \forall i.$$

(21)

Step 7.

Determine the overall positive-ideal distance and overall negative-ideal distance, denoted as $S_{i\left(PIS\right)}$ and $S_{i\left(NIS\right)}$, respectively, as presented in Equations (13) and (14).

Step 8.

Compute the Relative Closeness ($R_i$) and Performance Index ($P_i$) scores. This process implements Equations (15) and (16).

Step 9.

Determine the priority ranking of the alternatives. Alternatives are arranged according to the decreasing cardinality of $P_i$, $i=1,\dots ,m$, obtained from Equation (16).

4.3. Case Application: Evaluating the Alignment of Strategic Directions with the SDGs

The proposed IF-PROBID approach is implemented to assess the degree of alignment between the strategic statements of the top 50 Philippine corporations and the 17 SDGs outlined in the Appendix A. These corporations are presented in

Table 2. Top corporations of the Philippines for the year 2020 *.

Rank	CODE	Company Names	Sector
1	CORP 1	Manila Electric Co.	Manufacturing
2	CORP 2	BDO Unibank, Inc.	Private
3	CORP 3	Petron Corp.	Manufacturing
4	CORP 4	PMFTC, Inc.	Private
5	CORP 5	Mercury Drug Corp.	Manufacturing
6	CORP 6	Pilipinas Shell Petroleum Corp.	Manufacturing
7	CORP 7	Nestle Philippines, Inc.	Manufacturing
8	CORP 8	Globe Telecom, Inc.	Technology
9	CORP 9	Puregold Price Club, Inc.	Private
10	CORP 10	Toshiba Information Equipment (Philippines), Inc.	Technology
11	CORP 11	TI (Philippines), Inc.	Private
12	CORP 12	Philippine Associated Smelting and Refining Corp.	Manufacturing
13	CORP 13	Bank of the Philippine Islands	Private
14	CORP 14	Smart Communications, Inc.	Technology
15	CORP 15	San Miguel Brewery, Inc.	Manufacturing
16	CORP 16	Universal Robina Corp.	Manufacturing
17	CORP 17	Toyota Motor Philippines, Corp.	Manufacturing
18	CORP 18	PLDT, Inc.	Technology
19	CORP 19	JT International (Philippines), Inc.	Private
20	CORP 20	Robinson’s Supermarket Corp.	Manufacturing
21	CORP 21	Coca-Cola Beverages Philippines, Inc.	Manufacturing
22	CORP 22	Landbank of the Philippines	Private
23	CORP 23	Zuellig Pharma Corp.	Manufacturing
24	CORP 24	Accenture, Inc.	Technology
25	CORP 25	Epson Precision (Philippines), Inc.	Technology
26	CORP 26	Security Bank Corp.	Financial
27	CORP 27	Supervalue, Inc.	Private
28	CORP 28	Philippine Airlines, Inc	Service
29	CORP 29	Philippine National Bank	Private
30	CORP 30	STMicroelectronics, Inc.	Manufacturing
31	CORP 31	Procter & Gamble Philippines, Inc.	Consumer Staples
32	CORP 32	Chevron Philippines, Inc.	Manufacturing
33	CORP 33	China Banking Corp.	Financial
34	CORP 34	National Grid Corp. of the Philippines	Energy and Power
35	CORP 35	Zenith Foods Corp.	Consumer Staples
36	CORP 36	Rizal Commercial Banking Corp.	Financial
37	CORP 37	Unioil Petroleum Philippines, Inc.	Industrial
38	CORP 38	House Technology Industries Pte Ltd.	Retail Sector
39	CORP 39	Philippine Seven Corp.	Consumer Staples
40	CORP 40	SM Prime Holdings, Inc.	Real Estate
41	CORP 41	Union Bank of The Philippines	Finance
42	CORP 42	Sun Life of Canada (Philippines), Inc.	Finance
43	CORP 43	San Miguel Energy Corp.	Energy And Power
44	CORP 44	Samsung Electro-Mechanics Philippines Corp.	Industrial
45	CORP 45	PHOENIX Petroleum Philippines, Inc.	Industrial
46	CORP 46	HGST Philippines Corp.	Technology
47	CORP 47	Century Pacific Food, Inc.	Industrial

* based on highest gross revenue [138].

. In this case, strategic statements are proxied by vision and mission statements in the Supplementary Materials. These statements were obtained from the publicly accessible website of each corporation. Analogous to the approach that Encenzo et al. [40] utilized, semantic similarity evaluation is carried out using LLM, particularly ChatGPT (OpenAI’s GPT-3.5/4/5 architecture). Recent examples of utilizing ChatGPT as a text analytic tool to evaluate the similarity of two texts were also demonstrated by Galamiton et al. [86] and Selle et al. [87]. Two MCDM problems are considered in this case application. Each problem consists of supplying the vision or mission statement of corporation $i$ and SDG $j$; ChatGPT analyzes the semantic similarity of the two statements. The official definitions for each goal were obtained from the United Nations Department of Economic and Social Affairs (UN DESA) website to ensure consistency across different regions. Subsequently, the semantic similarity evaluation using ChatGPT produces three scores or IF parameters corresponding to the membership, non-membership, and hesitation degrees of the evaluation, indicating whether a statement fits a given SDG statement semantically. These scores populated the IF decision matrices (for both SDG-vision and SDG-mission statement alignments) in the generalized methodological structure in Figure 1. Only 47 corporations were considered out of the top 50 since three of them have combined mission and vision statements.

The following provides a detailed procedural flow for implementing the proposed IF-PROBID to illustrate its computational steps:

Phase 1. Obtaining the data.

Step 1.

Determine the list of decision criteria and alternatives. In this case, the SDGs comprise 17 goals, which are considered decision attributes or criteria. The vision and mission statements of the 47 corporations extracted from their websites were viewed as decision alternatives for the corresponding MCDM problems. With the steps and prompts outlined in Figure 3, the IF evaluation scores were obtained to populate the IF decision matrices.

Step 2.

Populate the decision matrices. The prompt in Figure 3 was made five times for each corporation’s statement across the SDGs. Then, the average of the five responses was considered, guided by the recommendation of Thelwall [85] in “repeating the prompts multiple times in different sessions and averaging the ChatGPT outputs”. Subsequently, the membership and non-membership scores corresponding to the IF evaluations generated from the average of the five ChatGPT responses were utilized to create the IF decision matrices. Two $47\times 17$ matrices were created to evaluate the semantic similarity of the two strategic direction statements: one for aligning the vision statements and another for aligning the mission statements with the SDGs. The IF decision matrices are available in the Supplementary Materials.

Phase 2. IF-PROBID application

Step 3.

Obtain the weighted normalized IF decision matrices. Utilizing Equation (17), with criteria weights set at $w_j={\displaystyle \frac{1}{n}}$, $\forall j$, the weighted normalized IF decision matrices were generated. Without further relevant theoretical or empirical studies, the equal-weight estimates for the criteria support the notion that the SDGs have equal priorities. For brevity, the weighted normalized IF decision matrix for the SDG-vision-statement semantic similarity is shown in the Supplementary Materials. Although its presentation is skipped, the semantic similarity of the counterpart SDG-mission statement can be obtained similarly.

Step 4.

Generate the vectors ${\tilde{A}}_{\left(k\right)}$, $k=1,\dots ,n$ using Equation (18). Highlighting again the SDG-vision-statement semantic similarity, the corresponding ${\tilde{A}}_{\left(k\right)}$ vectors are presented in the Supplementary Materials. The SDG-mission-statement semantic similarity counterpart can be likewise generated using a similar computational process.

Step 5.

Compute the average solution. The average solution, denoted as ${\tilde{V}}_j$, was calculated using Equation (19).

Table 3. Computed ${\tilde{V}}_j$ vectors for the SDG-vision-statement semantic similarity evaluation.

Criteria	$\left({\mathit{\mu }}_{{\tilde{\mathit{V}}}_{\mathit{j}}},{\mathit{\nu }}_{{\tilde{\mathit{V}}}_{\mathit{j}}},{\mathit{\pi }}_{{\tilde{\mathit{V}}}_{\mathit{j}}}\right)$	Criteria	$\left({\mathit{\mu }}_{{\tilde{\mathit{V}}}_{\mathit{j}}},{\mathit{\nu }}_{{\tilde{\mathit{V}}}_{\mathit{j}}},{\mathit{\pi }}_{{\tilde{\mathit{V}}}_{\mathit{j}}}\right)$
C1	(0.036, 0.938, 0.025)	C10	(0.039, 0.936, 0.025)
C2	(0.035, 0.938, 0.027)	C11	(0.041, 0.932, 0.027)
C3	(0.035, 0.940, 0.025)	C12	(0.037, 0.936, 0.026)
C4	(0.035, 0.941, 0.024)	C13	(0.033, 0.941, 0.025)
C5	(0.037, 0.937, 0.026)	C14	(0.031, 0.947, 0.022)
C6	(0.033, 0.942, 0.025)	C15	(0.038, 0.937, 0.026)
C7	(0.040, 0.932, 0.028)	C16	(0.042, 0.932, 0.025)
C8	(0.042, 0.933, 0.026)	C17	(0.044, 0.929, 0.027)
C9	(0.042, 0.933, 0.025)

and

Table 4. Computed ${\tilde{V}}_j$ vectors for the SDG-mission-statement semantic similarity evaluation.

Criteria	$\left({\mathit{\mu }}_{{\tilde{\mathit{V}}}_{\mathit{j}}},{\mathit{\nu }}_{{\tilde{\mathit{V}}}_{\mathit{j}}},{\mathit{\pi }}_{{\tilde{\mathit{V}}}_{\mathit{j}}}\right)$	Criteria	$\left({\mathit{\mu }}_{{\tilde{\mathit{V}}}_{\mathit{j}}},{\mathit{\nu }}_{{\tilde{\mathit{V}}}_{\mathit{j}}},{\mathit{\pi }}_{{\tilde{\mathit{V}}}_{\mathit{j}}}\right)$
C1	(0.045, 0.936, 0.019)	C10	(0.038, 0.944, 0.018)
C2	(0.027, 0.960, 0.013)	C11	(0.039, 0.942, 0.019)
C3	(0.039, 0.943, 0.018)	C12	(0.043, 0.938, 0.019)
C4	(0.031, 0.953, 0.015)	C13	(0.034, 0.949, 0.017)
C5	(0.025, 0.962, 0.013)	C14	(0.024, 0.961, 0.014)
C6	(0.022, 0.966, 0.013)	C15	(0.029, 0.957, 0.014)
C7	(0.028, 0.958, 0.014)	C16	(0.037, 0.947, 0.016)
C8	(0.048, 0.931, 0.020)	C17	(0.040, 0.943, 0.017)
C9	(0.049, 0.930, 0.020)

present the ${\tilde{V}}_j$ vectors for the SDG-vision- and SDG-mission-statement semantic similarity evaluations, respectively.

Step 6.

Calculate the $S_{i\left(k\right)}$ ($\forall k$) and $S_{i\left(avg\right)}$ vectors. The application of Equations (20) and (21) produced these vectors. The corresponding $S_{i\left(k\right)}$ ($\forall k$) and $S_{i\left(avg\right)}$ vectors for the SDG-vision-statement semantic similarity evaluation are shown in the Supplementary Materials.

Step 7.

Determine the overall positive-ideal distance and overall negative-ideal distance, denoted as $S_{i\left(PIS\right)}$ and $S_{i\left(NIS\right)}$, respectively, as presented in Equations (13) and (14). The resulting matrix containing $S_{i\left(PIS\right)}$ and $S_{i\left(NIS\right)}$ for the SDG-vision statement evaluation can be found in the Supplementary Materials.

Step 8.

Obtain the $R_i$ and $P_i$ metrics as espoused in Equations (15) and (16), respectively. The data for the mission statement was treated using the same process. The resulting matrices, showing these vectors, are presented in the Supplementary Materials for evaluations of the vision and mission statements.

Step 9.

Rank the corporations in both evaluations. The ranking is based on a decreasing order of $P_i$ values. This process yields two separate rankings, one for each evaluation. The rankings for both evaluations are presented in the Supplementary Materials.

Table 5. Priority ranking of corporations based on the semantic similarity of their SDG-vision statements.

Rank	Corporation
1	PMFTC, Inc.
2	Puregold Price Club, Inc.
3	Century Pacific Food, Inc.
4	Zuellig Pharma Corp.
5	Accenture, Inc.
6	STMicroelectronics, Inc.
7	Samsung Electro-Mechanics Philippines Corp.
8	Toshiba Information Equipment (Philippines), Inc.
9	Petron Corp.
10	PHOENIX Petroleum Philippines, Inc.
11	TI (Philippines), Inc.
12	Pilipinas Shell Petroleum Corp.
13	Mercury Drug Corp.
14	BDO Unibank, Inc.
15	Epson Precision (Philippines), Inc.
16	Unioil Petroleum Philippines, Inc.
17	Philippine Associated Smelting and Refining Corp.
18	HGST Philippines Corp.
19	Bank of the Philippine Islands
20	SM Prime Holdings, Inc.
21	PLDT, Inc.
22	Procter & Gamble Philippines, Inc.
23	Zenith Foods Corp.
24	San Miguel Energy Corp.
25	Nestle Philippines, Inc
26	Union Bank of the Philippines
27	Sun Life of Canada (Philippines), Inc.
28	Philippine Seven Corp.
29	Chevron Philippines, Inc.
30	Globe Telecom, Inc.
31	Manila Electric Co.
32	Supervalue, Inc.
33	Security Bank Corp.
34	China Banking Corp.
35	Philippine National Bank
36	House Technology Industries Pte Ltd.
37	Universal Robina Corp.
38	National Grid Corp. of the Philippines
39	Smart Communications, Inc.
40	Coca-Cola Beverages Philippines, Inc.
41	JT International (Philippines), Inc.
42	San Miguel Brewery, Inc.
43	Robinson’s Supermarket Corp.
44	Philippine Airlines, Inc.
45	Rizal Commercial Banking Corp.
46	Landbank of the Philippines
47	Toyota Motor Philippines, Corp.

and

Table 6. Priority ranking of corporations based on the semantic similarity of their SDG-mission statements.

Rank	Corporation
1	PLDT, Inc.
2	Philippine Associated Smelting and Refining Corp.
3	San Miguel Brewery, Inc.
4	JT International (Philippines), Inc.
5	Petron Corp.
6	TI (Philippines), Inc.
7	San Miguel Energy Corp.
8	Puregold Price Club, Inc.
9	Century Pacific Food, Inc.
10	Epson Precision (Philippines), Inc.
11	HGST Philippines Corp.
12	Robinson’s Supermarket Corp.
13	PMFTC, Inc.
14	SM Prime Holdings, Inc.
15	Toyota Motor Philippines, Corp.
16	Chevron Philippines, Inc.
17	National Grid Corp. of the Philippines
18	Security Bank Corp.
19	PHOENIX Petroleum Philippines, Inc.
20	China Banking Corp.
21	Sun Life of Canada (Philippines), Inc.
22	Manila Electric Co.
23	Philippine Seven Corp.
24	Procter & Gamble Philippines, Inc.
25	Toshiba Information Equipment (Philippines), Inc.
26	Pilipinas Shell Petroleum Corp.
27	Philippine National Bank
28	Supervalue, Inc.
29	Globe Telecom, Inc.
30	Union Bank of the Philippines
31	House Technology Industries Pte Ltd.
32	Zuellig Pharma Corp.
33	Samsung Electro-Mechanics Philippines Corp.
34	Smart Communications, Inc.
35	Nestle Philippines, Inc.
36	STMicroelectronics, Inc.
37	Universal Robina Corp.
38	Accenture, Inc.
39	BDO Unibank, Inc.
40	Mercury Drug Corp.
41	Philippine Airlines, Inc.
42	Rizal Commercial Banking Corp.
43	Bank of the Philippine Islands
44	Unioil Petroleum Philippines, Inc.
45	Coca-Cola Beverages Philippines, Inc.
46	Zenith Foods Corp.
47	Landbank of the Philippines

show the resulting order of corporations based on SDG-vision- and SDG-mission-statement semantic similarity evaluations, respectively. Higher-ranked corporations in Table 5, such as PMFTC, Inc., exhibit a stronger semantic alignment of their vision statements with the SDGs. Conversely, lower-ranked corporations may have vision statements less explicitly tied to SDG targets or phrased in a way that is less semantically aligned with SDG-related language. On the other hand, the ranking in Table 6 illustrates the alignment between the mission statements of various corporations and the SDGs. It yields that PLDT, Inc. has the strongest alignment, while Landbank of the Philippines ranks last in the identified set of corporations.

5. Robustness Check

A robustness check was conducted to verify the results and compare the proposed IF-PROBID with other MCDM methods. In this section, the following four IF-integrated MCDM methods were compared: (1) IF-TOPSIS [139,140]; (2) IF-CODAS [110]; (3) IF-EDAS [113]; and (4) IF-VIKOR [102]. For brevity, the algorithmic steps for each method are not detailed here. To establish comparability, the same weight vector for the SDGs and the same IF decision matrices were used for the other IF-MCDM methods, ensuring that the resulting rankings differ only in the actions taken by the methods.

Table 7. Ranking results across comparable methods in regard to SDG-vision-statement semantic similarity.

Corporations	SDG-Vision-Statement Semantic Similarity
	IF-PROBID	IF-TOPSIS	IF-CODAS	IF-EDAS	IF-VIKOR
CORP 1	30	32	30	33	33
CORP 2	14	14	10	14	18
CORP 3	8	10	13	10	10
CORP 4	1	1	1	1	1
CORP 5	13	13	12	13	7
CORP 6	11	8	6	6	8
CORP 7	25	21	18	26	28
CORP 8	30	32	30	33	33
CORP 9	1	1	1	1	1
CORP 10	6	7	8	7	9
CORP 11	8	10	13	10	10
CORP 12	17	17	17	20	21
CORP 13	19	22	28	19	14
CORP 14	37	39	39	35	26
CORP 15	42	43	43	41	35
CORP 16	38	40	44	40	38
CORP 17	47	47	47	47	43
CORP 18	20	25	26	18	15
CORP 19	39	35	38	36	31
CORP 20	43	44	41	42	36
CORP 21	41	41	45	39	29
CORP 22	46	46	46	46	32
CORP 23	5	6	9	8	4
CORP 24	7	9	15	12	6
CORP 25	14	14	10	14	18
CORP 26	33	31	33	30	27
CORP 27	32	30	29	31	39
CORP 28	44	42	40	44	47
CORP 29	35	36	36	38	30
CORP 30	4	4	5	4	13
CORP 31	22	24	25	21	22
CORP 32	28	29	32	27	16
CORP 33	34	34	35	32	24
CORP 34	40	37	34	43	45
CORP 35	23	20	23	22	46
CORP 36	45	45	42	45	44
CORP 37	16	16	16	16	17
CORP 38	36	38	37	37	41
CORP 39	29	28	24	29	42
CORP 40	21	19	19	23	25
CORP 41	26	26	27	24	20
CORP 42	27	27	22	28	40
CORP 43	24	23	20	25	23
CORP 44	10	5	4	5	12
CORP 45	12	12	7	9	5
CORP 46	18	18	21	17	37
CORP 47	3	3	3	3	3

and

Table 8. Ranking results across comparable methods in regard to SDG-mission-statement semantic similarity.

Corporations	SDG-Mission-Statement Semantic Similarity
	IF-PROBID	IF-TOPSIS	IF-CODAS	IF-EDAS	IF-VIKOR
CORP 1	22	26	29	18	14
CORP 2	39	42	39	44	47
CORP 3	8	7	7	9	22
CORP 4	13	15	14	26	45
CORP 5	40	41	42	41	35
CORP 6	28	29	22	1	46
CORP 7	33	35	30	36	27
CORP 8	27	32	33	28	19
CORP 9	6	25	28	22	15
CORP 10	25	23	25	21	16
CORP 11	5	6	6	8	11
CORP 12	2	2	2	3	2
CORP 13	43	43	43	42	30
CORP 14	34	31	32	32	43
CORP 15	3	3	4	5	3
CORP 16	37	33	37	27	10
CORP 17	20	18	12	29	34
CORP 18	1	1	1	2	1
CORP 19	4	4	3	6	6
CORP 20	12	9	9	13	23
CORP 21	44	45	45	46	42
CORP 22	47	46	47	45	39
CORP 23	31	27	26	33	25
CORP 24	38	38	38	38	44
CORP 25	10	10	11	12	13
CORP 26	14	17	20	15	9
CORP 27	29	24	27	19	7
CORP 28	41	39	40	39	24
CORP 29	26	37	35	35	26
CORP 30	36	34	36	30	21
CORP 31	24	22	23	24	31
CORP 32	17	14	17	17	12
CORP 33	16	16	19	16	18
CORP 34	18	20	13	4	32
CORP 35	46	47	46	47	40
CORP 36	42	40	41	40	28
CORP 37	45	44	44	43	41
CORP 38	32	30	34	25	17
CORP 39	23	21	18	31	38
CORP 40	15	12	16	14	29
CORP 41	30	28	24	34	33
CORP 42	19	13	21	11	5
CORP 43	7	5	8	7	4
CORP 44	35	36	31	37	36
CORP 45	21	19	15	23	20
CORP 46	11	11	5	20	37
CORP 47	9	8	10	10	8

present the ranking results for SDG-vision- and SDG-mission-statement semantic similarity across comparable methods, respectively. Detailed insights into the pairwise comparisons of MCDM methods, based on Spearman’s rank correlation coefficients ($\rho$), are shown in

Table 9. Spearman’s rank correlation coefficients ($\rho$) among comparable methods in regard to SDG-vision-statement semantic similarity.

	IF-PROBID	IF-TOPSIS	IF-CODAS	IF-EDAS	IF-VIKOR
IF-PROBID	1	0.9799	0.9807	0.9110	0.5959
IF-TOPSIS	0.9799	1	0.9738	0.9484	0.6588
IF-CODAS	0.9807	0.9738	1	0.8691	0.5358
IF-EDAS	0.9110	0.9484	0.8691	1	0.8145
IF-VIKOR	0.5959	0.6588	0.5358	0.8145	1

and

Table 10. Spearman’s rank correlation coefficients ($\rho$) among comparable methods in regard to SDG-mission-statement semantic similarity.

	IF-PROBID	IF-TOPSIS	IF-CODAS	IF-EDAS	IF-VIKOR
IF-PROBID	1	0.9889	0.9633	0.9896	0.8308
IF-TOPSIS	0.9889	1	0.9830	0.9860	0.8083
IF-CODAS	0.9633	0.9830	1	0.9603	0.7618
IF-EDAS	0.9896	0.9860	0.9603	1	0.8504
IF-VIKOR	0.8308	0.8083	0.7618	0.8504	1

.

Table 9 shows that the proposed IF-PROBID method demonstrates high comparability with IF-TOPSIS, IF-CODAS, and IF-EDAS with $\rho >0.9$, indicating that it produces comparable rankings. Meanwhile, the IF-VIKOR generates weak similarity with the proposed method at $\rho =0.5959$. Nevertheless, it compares highly with IF-PROBID for the SDG-mission-statement semantic similarity evaluation ($\rho =0.8308$). The results of Table 10 support the previous comparisons, indicating that IF-PROBID and other methods (i.e., IF-TOPSIS, IF-CODAS, and IF-EDAS) have very high comparability with $\rho >0.95$. In summary, the comparative analyses in this section reveal that IF-PROBID produces rankings consistent with those of other comparable IF variants of known MCDM methods, with some pairs demonstrating very strong correlations and others showing moderately strong correlations. These findings highlight the reliability and efficacy of the proposed IF-PROBID method in handling MCDM problems under information uncertainty.

6. Results Integration

In this section, we offer an integration of the two evaluations through a visualization that displays the trade-off between corporations aligning their vision and mission statements with the SDGs. To perform such a trade-off, a mapping is introduced that compromises a matrix of four distinct qualifications, where the horizontal axis represents the position of the corporation relative to others in SDG-vision semantic similarity. In contrast, the vertical axis corresponds to their SDG-mission semantic similarity ranks. Figure 4 illustrates the mapping of corporations in the SDG–vision–mission matrix. For the classification, the ${\displaystyle \frac{m}{2}}$ was considered, which, in this case, ${\displaystyle \frac{47}{2}}$ serves as the central line for both axes that separates the four classifications. Since the corporation that performs the best is the one closest to zero in rankings, the following depicts the four classifications: (Q1: highly aligned) the corporations in the bottom-left quadrant (blue) have high ranks in both vision and mission, (Q2: vision-aligned) corporations with high rankings on vision statements but low on mission statements are presented in the top-left quadrant (green), (Q3: mission-aligned) corporations in the orange bottom-right quadrant rank low on vision statements but high on mission statements, and (Q4: weakly aligned) in the top-right quadrant, corporations with a low rank on both statements are represented by red.

Figure 4 presents an aggregate pictorial representation of the alignment between the vision and mission statements of the corporations and the SDGs. Note that it merely reflects a relative representation, not an absolute position of the corporations. Hence, the matrix is dependent on the cohort of the corporations, which, in this case, represent the top 50 Philippine corporations. While this view may seem limited, it is worthwhile noting that corporations are best compared and benchmarked with the same cohort, rather than on heterogeneous classifications. The application of the proposed IF-PROBID yields 11 corporations belonging to Q1, where vision and mission statements are semantically highly aligned with the SDGs, while 12 of them are weakly aligned. Some corporations are merely vision- or mission-aligned, in which case greater emphasis becomes necessary to reevaluate the framing of their vision or mission statements.

7. Discussion and Insights

This study extends the literature by offering a computational framework for the semantic similarity evaluation of organizational strategic statements with the UN SDGs. In particular, it builds upon a previous study in the domain application by leveraging the capabilities of LLMs in symbol disambiguation, semantic similarity, and relatedness tasks, which have been empirically demonstrated in the emerging literature evaluating the efficacy of LLMs in various tasks. Viewed as a generalized MCDM problem, the strategic statements of organizations comprise the set of alternatives, while the UN 17 SDGs form the criteria set. To capture several concerns regarding LLMs, we posit the presence of imprecise data in the evaluation process and propose the utilization of IFS as an extension of the monumental fuzzy set theory in handling information ambiguity. In this regard, we developed an IF extension of the PROBID method, called IF-PROBID, which handles imprecise data while embracing the notion of ideal and average solutions as reference points for ranking. As a case demonstration, the proposed IF-PROBID method was applied to examine how well the vision and mission statements of the top 47 corporations in the Philippines semantically align with the 17 UN SDGs. ChatGPT generated the evaluations that populate the dataset, which provides membership, non-membership, and hesitancy scores after five repeated prompts, conforming to a recent study on the efficacy of multiple prompts and averaging them when LLMs perform relatedness tasks. In 7990 prompts, the IF-PROBID generates two separate rankings, one for the SDG-vision and another for SDG-mission alignment evaluations.

The findings provide a ranking of corporations based on their vision statements, with the highest ranking representing the most aligned vision statement with the SDGs and the lowest ranking representing the least aligned statement. The top-ranked corporation was PMFTC, Inc. (Philip Morris Philippines Manufacturing Inc.), followed by Puregold Price Club, Inc. and Century Pacific Food, Inc., with Toyota Motor Philippines, Corp., at the bottom. On the other hand, the semantic alignment evaluation of the mission statements revealed that PLDT Inc. exhibits the strongest alignment with its mission, followed closely by Philippine Associated Smelting and Refining Corp. and San Miguel Brewery, Inc. Conversely, the Landbank of the Philippines demonstrates the weakest alignment, ranking last in the list. To integrate these two rankings and provide a clearer view, a cohort-dependent SDG–vision–mission matrix is proposed, mapping corporations along the vision-mission alignment trade-off. The proposed matrix equips decision-makers and stakeholders with an integrative visualization of the positions of corporations relative to one another within the same cohort. Four classifications were put forward on the nature of alignment of vision and mission statements: highly aligned, vision-aligned, mission-aligned, and weakly aligned.

The results of the mapping suggest that most corporations in the “highly-aligned” class belong to the private sector and the technology sector, with few from the industrial and real estate sectors. They exhibit high alignment in both statements. Corporations that are either “vision-aligned” or “mission-aligned” primarily came from the manufacturing sector, with a few also from the financial and consumer staples sectors. Finally, “weakly-aligned” corporations are associated with the manufacturing and private sectors, followed by the technology sector. These corporations may open up improvement opportunities for evaluating the framing of their strategic statements. To ensure the reliability of the findings obtained from the proposed IF-PROBID, a robustness check via comparative analysis with other established IF-MCDM extensions, such as the IF-TOPSIS, IF-CODAS, IF-EDAS, and IF-VIKOR, yields comparable rankings. This insight suggests that the proposed IF-PROBID can effectively handle MCDM problems with evaluations expressed as IFS. Despite the comparable results, the IF-PROBID combines the strengths of TOPSIS and EDAS, as demonstrated by Wang et al. [48], who show the efficacy of PROBID in avoiding rank reversals. In addition, the integration of IFS in the canonical PROBID provides a better representation of ambiguity following the inclusion of the hesitancy degree in the evaluation process without adding unnecessary computational complexity.

The results have several practical implications. Using vision and mission statements as indicators of corporate strategy helps managers evaluate how effectively their sustainability initiatives are reflected in formal strategic documents. Organizations with poor alignment may revise their mission and vision statements to better reflect their commitment to the SDGs, thereby enhancing legitimacy and building stakeholder trust. Industry-specific comparisons enable decision-makers to benchmark against direct competitors, leading to more relevant performance evaluations. Regulators, investors, and policymakers can use this model as a screening tool to assess how well firms’ stated strategies align with national or global sustainability objectives. The proposed IF-PROBID model can also be adapted to evaluate performance across different uncertain fields beyond corporate applications. For example, it may be used in education to assess how well university policies align with SDG 4 concerning quality education; in healthcare, to analyze the correspondence between hospital mission statements and health-related SDGs; in the public sector, to verify that development plans meet environmental or social objectives; or in technology adoption, to evaluate AI governance policies in relation to ethical standards. The proposed IF-PROBID is suitable for industries that require uncertainty-aware benchmarking, as it effectively handles ambiguous linguistic assessments.

8. Limitations and Future Work

Although valuable insights were presented, this work has some limitations. Firstly, relying solely on vision and mission statements may not fully capture an organization’s actual practices or its sustainability outcomes. Companies might show symbolic alignment in their statements without genuine implementation, which limits conclusions to declared strategies rather than real behaviors. For future work, the IF-PROBID method can be utilized to analyze corporate social responsibility reports instead of vision and mission statements, providing a more comprehensive view of corporate alignment with the 17 UN SDGs. CSR reports often include measurable actions, policies, and outcomes that better reflect an organization’s sustainability practices. Future studies could also explore the integration of financial performance data, ESG (Environmental, Social, and Governance) metrics, or industry-specific benchmarks to evaluate alignment. Secondly, giving equal importance to all SDGs simplifies evaluation but ignores the different significance each goal holds across various industries. Due to the diversity of the industry, corporations cannot fully address all 17 SDGs within their business models and operations. Thus, establishing the appropriate priority weight for sector-specific SDGs, which applies to most corporations in a given sector, could help produce better rankings and offer guidance on which SDGs to prioritize to maximize the balance between profitability and sustainability.

Thirdly, since each sector articulates its vision and mission differently, comparing industries directly can sometimes lead to biased or misleading conclusions. For instance, manufacturing companies generally emphasize efficiency, resource management, and environmental sustainability, whereas service organizations tend to concentrate on innovation, human capital development, and customer value. To ensure that assessments are equitable and meaningful, future work could compare corporations within the same industry and benchmark them against similar peers facing comparable operational challenges. Fourthly, the study’s focus on Philippine corporations limits the applicability of its findings to other countries or regions, necessitating consideration of cultural, linguistic, and policy differences. The generalizability of the method to different contexts or sectors beyond the tested sample of Philippine corporations remains to be fully validated, which could demonstrate its broader applicability. Fifthly, while LLMs have improved semantic analysis, they still face limitations related to the design of prompts, stability of semantic assessments, model versions, and repetition methods. The reliance on ChatGPT-generated data introduces possible biases or inconsistencies in the evaluation scores. While IFS mitigate uncertainty, LLM outputs are context-sensitive and cannot entirely substitute for expert validation. Lastly, the proposed IF-PROBID offers flexibility in other MCDM applications. Although effective, it may have potential weaknesses such as computational complexity when handling large datasets. Evaluating its rigor in handling large-scale problems with both objective and subjective datasets is an interesting area for future work.

9. Concluding Remarks

The SDGs represent a guiding framework for development, and considerable efforts have been made to integrate them into various facets of the economy and society. Countries translate these goals to fit best their level of involvement, such as incorporating them into national policy agendas and localizing them into strategies. The achievement of the SDGs requires not only the efforts of the government but also the collaboration of various sectors, including the private and business sectors, which have a significant impact on people, resources, and the environment. In a corporation operating within a sector, operations are directed by its strategic direction, reflected in its guiding vision, which is the organization’s goal, and its mission, which defines the purpose driving its daily activities to fulfill that vision. The alignment of these strategic statements with the SDGs became an agenda in a previous study. In this work, we view alignment evaluation as an MCDM problem and advance several limitations that form its major contributions. First, we leveraged the capabilities of LLMs in semantic similarity tasks while acknowledging their limitations by incorporating ambiguity into the evaluation process. Second, we developed an IF extension of the PROBID method, driven by the ambiguity representation of LLM evaluations and the uncertainty inherent in generalized MCDM problems.

The newly developed IF-PROBID was deployed to evaluate the semantic similarity alignment of the vision and mission statements of 47 top Philippine corporations with the SDGs. It seeks to better understand how deeply corporations value sustainability in their foundational operation strategy, effectively balancing profitability (i.e., corporations’ bottom line) and sustainability. Through 7990 prompts, ChatGPT provided alignment scores expressed as IFS. Results demonstrate the ability of ChatGPT to generate semantic similarity alignment scores that measure the fuzzy alignment of corporate visions and missions with the SDGs. The proposed IF-PROBID method indicates that the vision statements of Philip Morris Philippines Manufacturing Inc., Puregold Price Club, Inc., and Century Pacific Food, Inc. emerged as the top performers in aligning their vision statements with the SDGs. For mission statements, PLDT Inc., the Philippine Associated Smelting and Refining Corp., and San Miguel Brewery, Inc. showed the strongest alignment. At the same time, Toyota Corporation and Landbank of the Philippines showed the weakest sustainability alignment in their vision and mission statements, respectively.

The two rankings obtained by the IF-PROBID are integrated into a cohort-dependent matrix containing four distinct classifications representing the nature of the alignment of their mission and mission statements: highly aligned, vision-aligned, mission-aligned, and weakly aligned. Findings suggest that “highly-aligned” corporations belong to the private and technology sectors, with few corporations belonging to the industrial and real estate sectors. Meanwhile, “weakly-aligned” corporations come from the manufacturing and private sectors. These results highlight the industry-specific differences in their focus on sustainability. These findings contain idiosyncrasies and are not intended to be universal. Nevertheless, they can serve as starting points for discussion in the development of approaches to better understand the semantic alignment of organizational strategic statements. This study underlines that, although many firms demonstrate a commitment to sustainability, notable disparities still exist, particularly in industries with significant environmental impacts and high resource consumption. The framework allows for a more thorough assessment of strategic statements and provides practical tools for organizations aiming to improve their sustainability efforts, starting with the framing of their vision and mission statements. A robustness assessment verified the reliability of the proposed IF-PROBID, as its results closely aligned with those from other IF-MCDM methods, such as IF-TOPSIS, IF-CODAS, IF-EDAS, and IF-VIKOR. By combining the advantages of ideal- and average-based rankings with the ability of the IFS to handle ambiguity, IF-PROBID delivered consistent and straightforward results. The framework presented in this study collectively augments current methods, which are often limited to specific sectors, rely on basic textual analysis, and do not consider the inherent uncertainty in interpretation. The integration of LLMs with IFS effectively captures semantic depth and models ambiguity in the evaluation process. The proposed IF-PROBID provides dependable rankings, which could facilitate organizations in integrating their sustainability agenda more effectively.