Decision Algorithm for Digital Media and Intangible-Heritage Digitalization Using Picture Fuzzy Combined Compromise for Ideal Solution in Uncertain Environments

Abstract

Modern digital media requires digitalization to protect cultural traditions, languages, and artistic expressions meant for future generations. Implementing the best digitalization strategy remains difficult because of unpredictable technological advances, changing digital preservation standards, and financial constraints. This study deals with these intricate challenges through the establishment of the picture fuzzy combined compromise for ideal solution (PF-COCOFISO) decision-making approach. The proposed framework employs picture fuzzy sets (PFSs) to develop symmetrical fuzzy assessment tools that better manage systems operating in uncertain technological settings. This practical research analyzes digital heritage archive optimization by assessing various digitalization approaches regarding important criteria, including technological adaptability and preservation standards, levels of accessibility, cultural maintenance, security systems, and sustainability initiatives. Multiple conflicting criteria can be optimally managed through the PF-COCOFISO selection process, which improves decision-making reliability. This research establishes an operational method which allows cultural organizations and digital archivists and policymakers to achieve intangible heritage digital accessibility symmetry while preserving heritage through structured methods during unstable times.

1. Introduction

Digital media is an essential tool in the modern era to protect and distribute intangible cultural heritage through folklore elements, languages, traditions, and performing arts [1]. The digitalization process adopts measures that give us easy access to heritage elements and preserve their cultural authenticity. Digitalization optimization encounters difficulties because of data quality, storage, security requirements, sustainability needs, accessibility barriers, and cost efficiency demands. Strategic choices for this domain prove difficult to implement, since new technologies create ambiguous situations alongside budget restrictions and ethical considerations, which need step-by-step assessment approaches.

Decision-making uncertainty can be solved through the fuzzy set (FS) theory introduced by Zadeh [2], which enables flexible reasoning by using membership degrees (MDs). The research by Atanassov [3] introduced intuitionistic fuzzy sets by combining MDs with non-membership degrees (NMDs). The research in this field progressed to the development of Pythagorean fuzzy sets [4] alongside q-rung orthopair fuzzy sets (q-ROFS) [5], which improved our ability to model uncertainty. Cuong [6] introduced a refined abstinence degree (AD) within PFSs, making these structures applicable for the optimization of digitalization strategies.

Multi-criteria decision-making (MCDM) methods allow for the evaluation of various factors through structured frameworks. A combined compromise solution (COCOSO) is a method that uses various aggregation functions to create optimal decisions [7]. The combined compromise for ideal solution (COCOFISO) method emerged after COCOSO because it overcame its limitations in complex criterion relationships through enhanced normalization techniques and flexible weighting systems to improve decision accuracy [8].

This study uses the picture fuzzy COCOFISO (PF-COCOFISO) methodology to optimize intangible cultural heritage digitalization strategies. An actual heritage preservation project shows how the methodology can use seven key factors to choose effective digitalization strategies that produce more sustainable results and improve their precision while preserving heritage assets.

1.1. Digital Media and Intangible-Heritage Digitalization

Existing academic research about digital media and intangible cultural heritage digitalization examines different aspects, including digitization preservation, information sharing, and technology innovation. Digital media enhances cultural heritage interaction, according to Houis et al. [9] and Jin and Liu [10], who investigate its role in media dissemination alongside visual representation transformation. Li [11] explores how digital communication affects the handcrafted-cultural-heritage domain. The protection of intangible heritage through digital technology depends on mobile programs, according to Liu [12]. Engagement with cultural heritage through virtual spaces, including the metaverse, was analyzed by Zhang et al. [13]. Leshkevich and Motozhanash [14] investigate how artificial intelligence supports the digitalization process of cultural heritage objects in Russia. Digital media should coexist better with heritage preservation efforts, according to Shuai and Li [15] and Terras et al. [16], who demonstrate how mass-digitized content delivers value in creative settings. Macri and Cristofaro [17] analyze the role of digitalization in supporting sustainable development through European program initiatives. This body of research confirms that digital media systems are essential for advancing the intangible cultural heritage space because they enable protection as well as accessibility, symmetry, and involvement.

1.2. COCOFISO MCDM Approach

Decision analysis requires MCDM methods due to the absence of successful criteria coordination structures. The MCDM techniques used for the evaluation process include the technique for order of preference by similarity to ideal solution (TOPSIS), the VIekriterijumsko KOmpromisno Rangiranje (VIKOR), the preference ranking organization method for enrichment evaluations (PROMETHEE), and multi-objective optimization on the basis of ratio analysis (MOORA), which lead to efficient decision-making under uncertain conditions. The standard evaluation tools encounter performance restrictions when working with hesitation and conflicting assessments, especially during digital heritage preservation operations. The COCOFISO method is preferred because it unites numerous compromise strategies which lead to decisions based on equilibrium. PF-COCOFISO addresses uncertainty issues and delivers enhanced decision precision by implementing a solution that handles expert disagreement and evaluation hesitancy. Multiple MCDM approaches have been utilized for decision-making, and they present a research opportunity to create a method specific to optimal intangible-heritage digitalization needs, which PF-COCOFISO addresses. This study introduces PF-COCOFISO to enhance the robustness of results because it effectively processes incomplete, vague, and hesitant evaluations that frequently occur during cultural heritage digitization. The PF-COCOFISO system simultaneously tracks multiple types of uncertainties, making it a fitting approach for preserving digital media content. The system integrates various compromise solutions, thus minimizing decision ranking fluctuations caused by expert uncertainty or contradictory opinions to create dependable results. Gabriel Rasoanaivo et al. [8] examined COCOFISO’s potential as an expert system application, and it overcame COCOSO’s limitations in handling expert problems. Sen and Toksoy [18] developed gray COCOFISO, which integrates gray numbers to enhance precise supplier selection and decision-making. Rasoanaivo and Tata [19] employed COCOFISO to rank universities in Madagascar, while Nirinarivelo and Rasoanaivo [20] used it to assess employment conditions throughout the nation’s regions. COCOSO can be integrated with industrial and safety evaluation to help improve underground mining sensor selection, according to Wang et al. [21]. Haseli et al. [22] established COCOSO as a core component of decision-making platforms for sustainable urban transportation through group interactions. Bihari et al. [23] developed supplier ranking applications using the generalized trapezoidal fuzzy-COCOSO model and generalized fuzzy-number methodology. COCOSO has been employed to inspecte liquefied natural gas storage tanks [24] while managing knowledge in supply chains [25]. Zheng et al. [26] developed a new decision-making model based on interval-valued q-ROFS for COCOSO applications. Maliha et al. [27] conducted a study to evaluate sodium alginate-based antibacterial and edible packaging by integrating entropy and the COCOSO methodology. The COCOFISO methodology shows flexibility, since researchers have proven its ability to help with decision-making in multiple engineering fields and economic and environmental applications. The assessment tools TOPSIS and VIKOR succeed at decision analysis but fail to handle uncertain conditions and contradictory evaluations during complex problem-solving. The COCOFISO approach implements numerous compromise methods to produce decisions through an equilibrium-based decision-making mechanism. This study brings forward PF-COCOFISO as an enhancement tool with better decision-making capabilities. The implementation of hesitation enables precise decision-making in uncertain situations, thus making it appropriate for digital media and intangible-heritage digitalization.

1.3. Research Gap and Motivations

Digital media technologies have revolutionized intangible-heritage preservation through artificial intelligence restoration, blockchain storage and virtual reality exhibitions, and cloud-based repositories. Digitalization demands complex handling since it involves multiple influencing factors such as technology development and financial constraints, cultural background, ethical considerations, and sustainability issues. Today’s research focuses on technical details, yet needs an organized approach to handle uncertainties, including data deterioration, standard changes, and user participation. Existing research fails to deliver an advanced MCDM methodology that unites uncertainty assessment with strategy prioritization in digitalization. The COCOSO methodology faces limitations when dealing with connected evaluation criteria, yet COCOFISO extends this framework by introducing adaptable weighting mechanisms for effective decision aggregation. The use of COCOFISO for intangible-heritage digitalization purposes has not been studied yet. The motivations of this study are summarized as follows:

• To address digitalization uncertainty, a structured decision-making approach should be used to evaluate technological risks, financial limitations, and cultural acceptance levels.
• The combination of PFSs with COCOFISO represents an enhanced MCDM approach to heritage preservation by enabling better management of ambiguous and dubious choices.
• Current research lacks an organized evaluation approach that accommodates multiple competing criteria related to heritage digitalization.
• A decision-support model should assist governments, cultural institutions, and digital archivists in developing the best digitalization approaches.

1.4. Objectives and Contributions

The main objective of this research involves creating an enhanced decision-support model to optimize the use of digital media applications for intangible-heritage digitalization. The COCOFISO method bridges various elements which help heritage practitioners find preservation strategies which fulfill the requirements of technological feasibility and financial sustainability, alongside cultural appropriateness with ethical soundness and viewer accessibility requirements. This research implements the PF-COCOFISO model by using it to assess different digitalization alternatives through seven evaluation criteria in a real-life application. Developing and modifying functionalities within the model needs thorough sensitivity and comparative analyses demonstrating its practical usage accuracy.

This study presents multiple novel advancements which contribute to the research on digitalizing intangible heritage and MCDM methodologies. This research introduces PF-COCOFISO as an innovative decision-making framework which uses scientific approaches for optimizing digitalization approaches. Incorporating PFSs allows decision-makers to address uncertainty more effectively than conventional MCDM methods by processing uncertain, neutral, and hesitant inputs. Decisions about digitalization approaches become more accurate and rank selection more reliable through COCOFISO within decision-making processes. Previous intangible-heritage research centered on technical aspects, but this study emphasizes decision technologies for successful heritage preservation processes. This study delivers crucial information to cultural administrators as well as government entities and digital archive personnel to support their development of sustainable digitalization planning strategies.

1.5. Structure of the Study

This paper is organized as follows: Section 2 discusses the methodology, including preliminary knowledge related to PFSs, proposes the PF-COCOFISO technique and details the steps, and assesses digital media and intangible-heritage digitalization using the PF-COCOFISO technique. Section 3 discusses the results. Section 4 compares existing MCDM techniques, discusses this study’s theoretical and practical implications, performs sensitivity analysis by changing the parameter values to determine the validity of results, and discusses the study’s advantages and limitations. Finally, Section 5 summarizes the study’s key findings and the future direction of this research.

2. Method

2.1. Preliminary Knowledge

This section introduces essential concepts needed to develop the proposed approach. We then define PFSs and their operational laws. We describe the enhanced COCOFISO method that followed COCOSO with its precise formulation structure and decision aggregation process. These key concepts provide essential foundations for PF-COCOFISO’s implementation in digital media projects regarding intangible-heritage digitalization.

Definition 1

([6]). For a fixed universe T and its subset,${\rm M}=\{ \Gamma , \rho \left(\Gamma \right), \tau \left(\Gamma \right),\nu (\Gamma \left)\right| \Gamma ϵ{\rm T}\}$, known as PFSs, where$\rho \left(\Gamma \right)\in [0, 1]$ denotes the MD, $\tau \left(\Gamma \right)\in [0, 1]$ denotes the AD, and$\nu \left(\Gamma \right)\in [0, 1]$ denotes the NMD. These degrees satisfy the following condition:

$$0 \le \rho \left(\mathsf{\Gamma }\right)+\tau \left(\mathsf{\Gamma }\right)+\nu \left(\mathsf{\Gamma }\right)\le 1.$$

Moreover, the refusal degree (RD) for each PFS${\rm M}$ is defined as

$$\varphi =1-\rho \left(\mathsf{\Gamma }\right)-\tau \left(\mathsf{\Gamma }\right)-\nu \left(\mathsf{\Gamma }\right).$$

Definition 2

([6]). Let${{\rm M}}_i=\left( {\rho }_i\left(\Gamma \right), {\tau }_i\left(\Gamma \right),{\nu }_i\left(\Gamma \right)\right), {{\rm M}}_j=\left({\rho }_j\left(\Gamma \right), {\tau }_j\left(\Gamma \right),{\nu }_j\left(\Gamma \right)\right)$ be two picture fuzzy values (PFVs) and$\lambda >0, \lambda$ be any scalar number; then, it satisfies the following operations:

• ${\mathsf{{\rm M}}}_i\oplus {\mathsf{{\rm M}}}_j=\left(\begin{array}{c}{\rho }_i\left(\mathsf{\Gamma }\right)+{\rho }_j\left(\mathsf{\Gamma }\right)-{\rho }_i\left(\mathsf{\Gamma }\right).{\rho }_j\left(\mathsf{\Gamma }\right),\\ {\tau }_i\left(\mathsf{\Gamma }\right).{\tau }_j\left(\mathsf{\Gamma }\right),\\ {\nu }_i\left(\mathsf{\Gamma }\right).{\nu }_j\left(\mathsf{\Gamma }\right)\end{array}\right)$
• ${\mathsf{{\rm M}}}_i\otimes {\mathsf{{\rm M}}}_j=\left(\begin{array}{c}{\rho }_i\left(\mathsf{\Gamma }\right).{\rho }_j\left(\mathsf{\Gamma }\right),\\ {\tau }_i\left(\mathsf{\Gamma }\right).{\tau }_j\left(\mathsf{\Gamma }\right),\\ {\nu }_i\left(\mathsf{\Gamma }\right)+{\nu }_j\left(\mathsf{\Gamma }\right)-{\nu }_i\left(\mathsf{\Gamma }\right).{\nu }_j\left(\mathsf{\Gamma }\right)\end{array}\right)$
• $\lambda .{\mathsf{{\rm M}}}_i=\left(\begin{array}{c}1-{\left(1-{\rho }_i\left(\mathsf{\Gamma }\right)\right)}^{\lambda },\\ {\left({\tau }_i\left(\mathsf{\Gamma }\right)\right)}^{\lambda },\\ {\left({\nu }_i\left(\mathsf{\Gamma }\right)\right)}^{\lambda }\end{array}\right)$
• ${\mathsf{{\rm M}}}_i^{\lambda }=\left(\begin{array}{c}{\left({\rho }_i\left(\mathsf{\Gamma }\right)\right)}^{\lambda },\\ {\left({\tau }_i\left(\mathsf{\Gamma }\right)\right)}^{\lambda },\\ 1-{\left(1-{\nu }_i\left(\mathsf{\Gamma }\right)\right)}^{\lambda } \end{array}\right)$
• ${\mathsf{{\rm M}}}_i^c=\left({\rho }_i\left(\mathsf{\Gamma }\right),{\tau }_i\left(\mathsf{\Gamma }\right),{\nu }_i\left(\mathsf{\Gamma }\right)\right)$

Definition 3.

The score and accuracy function of a PFS is defined by

$$S=\left(\rho -\nu \right)-\left(\tau -\nu \right)$$

(1)

$$A=\rho +\tau +\nu$$

(2)

2.2. PF-COCOFISO Technique

This section provides a novel and efficient method for COCOFISO in an environment of PFVs. Figure 1 shows a detailed flowchart of the methodology.

2.3. COCOFISO Techniques Based on PFVs

The following describes the algorithm based on the proposed approach:

• Step 1: Using the linguistic concepts, each parameter’s collection of alternatives, parameters, and weight values are defined to create the decision matrix.

  $${\left(\widehat{M_{\mathcal{i}\mathcal{j}}}\right)}_{\mathcal{m}\times \mathcal{n}}=\begin{array}{c}{A}_1\\ A_2\\ ⋮\\ A_{\mathcal{i}}\end{array}\left[\begin{array}{cccc}{C}_1& C_2& \dots & C_{\mathcal{j}}\\ \left({\rho }_{11},{\tau }_{11},{\nu }_{11}\right)& \left({\rho }_{12},{\tau }_{12},{\nu }_{12}\right)& \dots & \left({\rho }_{1\mathcal{n}},{\tau }_{1\mathcal{n}},{\nu }_{1\mathcal{n}}\right)\\ \left({\rho }_{21},{\tau }_{21},{\nu }_{21}\right)& \left({\rho }_{22},{\tau }_{22},{\nu }_{23}\right)& \dots & \left({\rho }_{2\mathcal{n}},{\tau }_{2\mathcal{n}},{\nu }_{2\mathcal{n}}\right)\\ ⋮& ⋮& \ddots & ⋮\\ \left({\rho }_{\mathcal{m}1},{\tau }_{\mathcal{m}1},{\nu }_{\mathcal{m}1}\right)& \left({\rho }_{\mathcal{m}2},{\tau }_{\mathcal{m}2},{\nu }_{\mathcal{m}3}\right)& \dots & \left({\rho }_{\mathcal{m}\mathcal{n}},{\tau }_{\mathcal{m}\mathcal{n}},{\nu }_{\mathcal{m}\mathcal{n}}\right)\end{array}\right]$$
• Step 2: For the purpose of assessing the optimal solution, the following formula is used to normalize the alternative matrix according to either the cost or benefit type:

  $$F_{ij}=\left({\displaystyle \frac{{\rho }_{ij}}{\sqrt{\sum _{i=1}^m{\left({\rho }_{ij}\right)}^2}}},{\displaystyle \frac{{\tau }_{ij}}{\sqrt{\sum _{i=1}^m{\left({\tau }_{ij}\right)}^2}}},{\displaystyle \frac{{\nu }_{ij}}{\sqrt{\sum _{i=1}^m{\left({\nu }_{ij}\right)}^2}}}\right)$$

  (3)
• Step 3: This method identified two ways to aggregate the parameter’s weight values during the decision-making process: the sum of the normalized matrix’s power weights ${\mathcal{P}}_i$ and the sum of the normalized matrix’s product by weight values ${\mathcal{S}}_i$.

  $${\mathcal{S}}_i=\left(\sum _{j=1}^n w_j{\rho }_{ij},\sum _{j=1}^n w_j{\tau }_{ij},\sum _{j=1}^n w_j{\nu }_{ij}\right) ; {\mathcal{P}}_i=\left(\sum _{j=1}^n {\left({\rho }_{ij}\right)}^{w_j}, \sum _{j=1}^n {\left({\tau }_{ij}\right)}^{w_j},\sum _{j=1}^n {\left({\nu }_{ij}\right)}^{w_j}\right)$$

  (4)

  The gray relational generation strategy is used to obtain the ${\mathcal{S}}_i$ value, while the weighted aggregated sum product assessment (WASPAS) multiplication approach is used to obtain the ${\mathcal{P}}_i$ value.
• Step 4: The $\mathcal{S}$ and $\mathcal{P}$ values are computed by weighing the relative importance of all alternatives according to the three evaluation score methodologies, which are described below:

  $$k_{\mathrm{ia} }={\displaystyle \frac{{\mathcal{P}}_i+{\mathcal{S}}_i}{\sum _{i=1}^m \left({\mathcal{P}}_i+{\mathcal{S}}_i\right)}}$$

  (5)

  $$k_{ib}={\displaystyle \frac{{\mathcal{P}}_i+{\mathcal{S}}_i}{1+ \frac{{\mathcal{P}}_i}{{1+\mathcal{P}}_i}+\frac{{\mathcal{S}}_i}{{1+\mathcal{S}}_i}}}$$

  (6)

  $$k_{ic}={\displaystyle \frac{\gamma \left({\mathcal{S}}_i\right)+\left(1-\gamma \right)\left({\mathcal{P}}_i\right)}{\left(\gamma \underset{i}{\mathrm{m}\mathrm{a}\mathrm{x}}{\mathcal{S}}_i +\left(1-\gamma \right)\underset{i}{\mathrm{m}\mathrm{a}\mathrm{x}} {\mathcal{P}}_i\right)}};0\le \gamma \le 1$$

  (7)

  Here,

• $k_{\mathrm{ia}}$ represents the weighted sum method (WSM) [28] and weighted product method (WPM) [29] scores’ arithmetic means;
• $k_{ib}$ represents the sum of the WSM’s and WPM’s relative scores;
• $k_{ic}$ represents the balanced compromise between the scores of the WSM and WPM models.

• Step 5: The scoring function (Equation (1)) then calculates the values of $k_i$, which are used to rank the alternatives [8].

  $$k_i=\left(\begin{array}{c}{\left(k_{ia}\ast k_{ib}\ast k_{ic}\right)}^{{\displaystyle \frac{1}{3}}}\\ +{\displaystyle \frac{1}{3}}\left(k_{ia}+k_{ib}+k_{ic}\right)\end{array}\right)$$

  (8)

2.4. Optimization of Digital Media and Intangible-Heritage Digitalization

Digital media defines any content format produced from digital sources that electronic devices process and distribute for digital storage and sharing. Digital media represents a fundamental modern-day communication tool, performing essential functions in education and the preservation of cultural heritage, together with entertainment. The components of intangible heritage include folklore, alongside traditions, languages, and performing arts, as non-physical cultural assets. The quick progression of technological systems requires the digitalization of intangible heritage because this method protects heritage while making it accessible to future generations. A representation of the cultural heritage digitization decision-making process is shown in more detail in Figure 2. This emphasizes important technological elements containing AI, together with cloud computing and cybersecurity and digital twins, because they optimize decision-making processes. Integrating these technologies creates a systematic approach for cultural heritage preservation management which follows the core principles of the decision algorithm for digitalization.

Intangible-heritage digitalization faces significant obstacles because new technologies create uncertainties in terms of resources and present cultural authenticity issues. Technical and organizational uncertainties emerge because digital storage is evolving, standard digitalization practices remain absent, and cultural elements risk distortion. Determining digital media strategies for heritage preservation demands considering the uncertainties surrounding them. A solid framework for decision-making should be adopted to select appropriate strategies that adapt to different conditions. Complexities associated with digital media optimization and heritage digitalization processes require the MCDM approach. Using PF-COCOFISO, users obtain an organized framework to process uncertain data inputs while running strategic choices through specified selection criteria. The PFS expands upon traditional FS by adding the MD, AD, and NMD, which enhances alternative evaluation methods.

• Example

This section showcases an optimized PF-COCOFISO method which evaluates digital heritage archival optimization in a real-life case. A national cultural protection program must evaluate digitalization strategies to determine the most effective approaches. Organizations select their digitalization strategies based on technological compatibility, financial limitations, cultural values, ethical standards, long-term viability, and accessibility needs. The selected strategy must be practical and align with long-term heritage preservation goals because these factors are essential. Digitalization strategies are articulated through twenty-seven alternatives assigned to seven decision criteria during the decision-making process.

• Evaluation criteria

The following is the criteria evaluation process:

• Technological Adaptability$C_1$: The implementation of digitalization strategies requires the capability to interface with new technologies. This criterion measures the approach’s potential for growth alongside its capability to merge with new technology and maintain protection against future changes.
• Data Preservation Quality$C_2$: Digital content must maintain symmetry in its original condition and integrity over the years. Preservation quality depends on resolution-quality descriptions, precise metadata entries, and the stable archival storage of digital artifacts.
• Cultural Sensitivity and Authenticity${ C}_3$: Cultural heritage, which has no tangible existence, needs protection. A proper evaluation examines how digitalization methods show traditions while preventing misinterpretation.
• Accessibility and Public Engagement$C_4$: The successful execution of digitalization programs depends on making heritage available to the public and possessing dynamic communications tools that function across diverse languages and offer educational resources.
• Cost-Effectiveness $C_5$: Financial limitations present a substantial challenge. This measuring criterion determines the success of digitalization alternatives by weighing the financial costs and potential for growth against operational expenses.
• Security and Intellectual Property Protection $C_6$: Protecting digitalized heritage is essential because it needs permanent cybersecurity and authorized access. This criterion analyzes the combination of encryption systems with the implementation of access controls and copyright protection methods.
• Sustainability and Environmental Impact $C_7$: Digital projects must achieve minimal environmental impact throughout their operations. This measuring standard evaluates digital infrastructure’s energy use, carbon emissions, and reuse potential.

• Alternatives

The following are the digitalization techniques investigated in this study:

• $A_1$: High-Resolution 3D Scanning;
• $A_2$: Augmented Reality-Based Interaction;
• $A_3$: Virtual Reality Archives;
• $A_4$: AI-Powered Language Translation;
• $A_5$: Cloud-Based Digital Archives;
• $A_6$: Open-Source Digital Libraries;
• $A_7$: Government-Sponsored Digital Initiatives;
• $A_8$: Blockchain for Heritage Authentication;
• $A_9$: Digital Storytelling Platforms;
• $A_{10}$: Gamification of Cultural Heritage;
• $A_{11}$: Automated Speech Recognition for Oral Traditions;
• $A_{12}$: AI-Based Content Restoration;
• $A_{13}$: Crowdsourced Heritage Documentation;
• $A_{14}$: Digital Exhibitions and Museums;
• $A_{15}$: Mobile Applications for Cultural Learning;
• $A_{16}$: Internet of Things for Heritage Monitoring;
• $A_{17}$: Digital Twin Technology for Historic Sites;
• $A_{18}$: Smart Contracts for Copyright Protection;
• $A_{19}$: Biometric Authentication for Exclusive Access;
• $A_{20}$: Sensor-Based Interactive Installations;
• $A_{21}$: AI-Driven Personalization of Heritage Content;
• $A_{22}$: High-Fidelity Digital Watermarking;
• $A_{23}$: Smart Glasses for Augmented Cultural Experience;
• $A_{24}$: Decentralized Peer-to-Peer Digital Archives;
• $A_{25}$: GIS Mapping for Historical Landmarks;
• $A_{26}$: Cloud-Based Metadata Management;
• $A_{27}$: AI-Assisted Content Verification;

The digitalization process for intangible cultural heritage needs an organized decision system to handle the uncertainty of using new technology while respecting traditions and working within budgetary limitations. Twenty-seven alternatives connected to seven decision criteria make up the digitalization strategies in the decision-making stage. The chosen criteria represent the fundamental heritage digitalization elements which ensure an evaluation process focusing on efficiency and cost-effectiveness alongside cultural appropriateness. The current case study demonstrates different alternative options being reviewed for selection purposes, proving PF-COCOFISO’s ability to handle heritage preservation difficulties effectively. Through the implementation of PFSs, the decision-making procedure becomes more precise and trustworthy, which supports cultural heritage management during the digital era.

A group of decision-makers who specialized in cultural heritage digitalization evaluated the weight values, which amounted to $\left(\mathrm{0.11,0.13,0.15,0.10,0.28,0.15,0.08}\right)$, from their practical domain knowledge of cultural heritage digitalization. Decision-makers hypothetically established these weights because they represent the importance rankings of evaluation criteria. The normalization condition $\sum _{i=1}^n{\mathrm{w}}_i=1$ maintains the proper balance in the distribution of criterion significance among the selected group. The assignment process establishes priority levels for digitalization strategies to make effective decisions.

The steps of the COCOFISO model for the optimization of digital media and intangible-heritage digitalization are outlined below:

Step 1. The decision matrix is formed by defining the collection of alternatives utilizing the linguistic terms in

Table 1. Evaluation of alternatives by linguistic terms.

Linguistic Terms	PFVs
	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$
Extremely high (EH)	$1.00$	$0.00$	$0.00$
Very very high (VVH)	$0.85$	$0.10$	$0.05$
Very high (VH)	$0.80$	$0.10$	$0.10$
High (H)	$0.70$	$0.15$	$0.15$
Medium high (MH)	$0.60$	$0.20$	$0.20$
Medium (M)	$0.50$	$0.25$	$0.25$
Medium low (ML)	$0.40$	$0.30$	$0.30$
Low (L)	$0.25$	$0.35$	$0.40$
Very low (VL)	$0.10$	$0.25$	$0.65$
Very very low (VVL)	$0.05$	$0.20$	$0.75$

.

Step 2. Table 1 illustrates the linguistic terms that the decision-maker determined would be used for the PFVs. Alternatives are assessed against criteria through the picture fuzzy decision matrix according to the defined linguistic preferences shown in

Table 2. Picture fuzzy decision matrix.

	${\mathit{C}}_1$	${\mathit{C}}_2$	${\mathit{C}}_3$	${\mathit{C}}_4$	${\mathit{C}}_5$	${\mathit{C}}_6$	${\mathit{C}}_7$
${\mathit{A}}_{\mathbf{1}}$	$H$	$H$	$ML$	$L$	$MH$	$EH$	$MH$
${\mathit{A}}_{\mathbf{2}}$	$H$	$H$	$ML$	$L$	$MH$	$EH$	$MH$
${\mathit{A}}_{\mathbf{3}}$	$H$	$VVH$	$ML$	$L$	$MH$	$H$	$MH$
${\mathit{A}}_{\mathbf{4}}$	$M$	$EH$	$MH$	$L$	$MH$	$H$	$MH$
${\mathit{A}}_{\mathbf{5}}$	$M$	$VVL$	$MH$	$VVL$	$ML$	$L$	$ML$
${\mathit{A}}_{\mathbf{6}}$	$M$	$VVL$	$MH$	$VVL$	$ML$	$L$	$ML$
${\mathit{A}}_{\mathbf{7}}$	$L$	$VVH$	$MH$	$VVL$	$ML$	$L$	$ML$
${\mathit{A}}_{\mathbf{8}}$	$L$	$VVH$	$H$	$VVH$	$M$	$L$	$H$
${\mathit{A}}_{\mathbf{9}}$	$L$	$VVH$	$H$	$H$	$M$	$VVL$	$H$
${\mathit{A}}_{\mathbf{10}}$	$M$	$M$	$H$	$ML$	$H$	$M$	$H$
${\mathit{A}}_{\mathbf{11}}$	$H$	$EH$	$H$	$VVH$	$M$	$MH$	$H$
${\mathit{A}}_{\mathbf{12}}$	$H$	$EH$	$H$	$VVH$	$M$	$MH$	$H$
${\mathit{A}}_{\mathbf{13}}$	$VVH$	$H$	$H$	$VVH$	$M$	$MH$	$EH$
${\mathit{A}}_{\mathbf{14}}$	$EH$	$H$	$H$	$VVL$	$M$	$MH$	$ML$
${\mathit{A}}_{\mathbf{15}}$	$VVL$	$L$	$M$	$VL$	$H$	$ML$	$MH$
${\mathit{A}}_{\mathbf{16}}$	$VVL$	$L$	$M$	$VL$	$L$	$ML$	$MH$
${\mathit{A}}_{\mathbf{17}}$	$VVH$	$L$	$M$	$MH$	$L$	$ML$	$MH$
${\mathit{A}}_{\mathbf{18}}$	$VVH$	$L$	$L$	$MH$	$VL$	$H$	$M$
${\mathit{A}}_{\mathbf{19}}$	$VVH$	$VVL$	$L$	$MH$	$VVL$	$H$	$M$
${\mathit{A}}_{\mathbf{20}}$	$M$	$M$	$L$	$ML$	$VL$	$H$	$H$
${\mathit{A}}_{\mathbf{21}}$	$EH$	$H$	$H$	$VVL$	$M$	$MH$	$ML$
${\mathit{A}}_{\mathbf{22}}$	$M$	$EH$	$MH$	$L$	$MH$	$H$	$MH$
${\mathit{A}}_{\mathbf{23}}$	$VVH$	$VVL$	$L$	$MH$	$VVL$	$H$	$M$
${\mathit{A}}_{\mathbf{24}}$	$L$	$VVH$	$H$	$H$	$M$	$VVL$	$H$
${\mathit{A}}_{\mathbf{25}}$	$H$	$H$	$ML$	$L$	$MH$	$EH$	$MH$
${\mathit{A}}_{\mathbf{26}}$	$VVL$	$L$	$M$	$VL$	$L$	$ML$	$MH$
${\mathit{A}}_{\mathbf{27}}$	$MH$	$L$	$L$	$MH$	$VL$	$H$	$\mathrm{M}$

. The defined assessment methodology supports both reliable and consistent decision-making during the evaluation.

Step 3. The decision matrix is normalized using Equation (3) as shown in

Table 3. Normalization of decision matrix.

	${\mathit{C}}_1$			${\mathit{C}}_2$			${\mathit{C}}_3$			${\mathit{C}}_4$			${\mathit{C}}_5$			${\mathit{C}}_6$			${\mathit{C}}_7$
	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$
${\mathit{A}}_{\mathbf{1}}$	$0.21$	$0.14$	$0.09$	$0.21$	$0.14$	$0.08$	$0.14$	$0.24$	$0.22$	$0.10$	$0.28$	$0.17$	$0.25$	$0.15$	$0.10$	$0.32$	$0.00$	$0.00$	$0.19$	$0.18$	$0.18$
${\mathit{A}}_{\mathbf{2}}$	$0.21$	$0.14$	$0.09$	$0.21$	$0.14$	$0.08$	$0.14$	$0.24$	$0.22$	$0.10$	$0.28$	$0.17$	$0.25$	$0.15$	$0.10$	$0.32$	$0.00$	$0.00$	$0.19$	$0.18$	$0.18$
${\mathit{A}}_{\mathbf{3}}$	$0.21$	$0.14$	$0.09$	$0.25$	$0.09$	$0.03$	$0.14$	$0.24$	$0.22$	$0.10$	$0.28$	$0.17$	$0.25$	$0.15$	$0.10$	$0.22$	$0.13$	$0.09$	$0.19$	$0.18$	$0.18$
${\mathit{A}}_{\mathbf{4}}$	$0.15$	$0.23$	$0.15$	$0.30$	$0.00$	$0.00$	$0.21$	$0.16$	$0.15$	$0.10$	$0.28$	$0.17$	$0.25$	$0.15$	$0.10$	$0.22$	$0.13$	$0.09$	$0.19$	$0.18$	$0.18$
${\mathit{A}}_{\mathbf{5}}$	$0.15$	$0.23$	$0.15$	$0.01$	$0.18$	$0.40$	$0.21$	$0.16$	$0.15$	$0.02$	$0.16$	$0.32$	$0.17$	$0.23$	$0.15$	$0.08$	$0.30$	$0.25$	$0.13$	$0.27$	$0.27$
${\mathit{A}}_{\mathbf{6}}$	$0.15$	$0.23$	$0.15$	$0.01$	$0.18$	$0.40$	$0.21$	$0.16$	$0.15$	$0.02$	$0.16$	$0.32$	$0.17$	$0.23$	$0.15$	$0.08$	$0.30$	$0.25$	$0.13$	$0.27$	$0.27$
${\mathit{A}}_{\mathbf{7}}$	$0.08$	$0.32$	$0.24$	$0.25$	$0.09$	$0.03$	$0.21$	$0.16$	$0.15$	$0.02$	$0.16$	$0.32$	$0.17$	$0.23$	$0.15$	$0.08$	$0.30$	$0.25$	$0.13$	$0.27$	$0.27$
${\mathit{A}}_{\mathbf{8}}$	$0.08$	$0.32$	$0.24$	$0.25$	$0.09$	$0.03$	$0.25$	$0.12$	$0.11$	$0.34$	$0.08$	$0.02$	$0.21$	$0.19$	$0.13$	$0.08$	$0.30$	$0.25$	$0.22$	$0.13$	$0.13$
${\mathit{A}}_{\mathbf{9}}$	$0.08$	$0.32$	$0.24$	$0.25$	$0.09$	$0.03$	$0.25$	$0.12$	$0.11$	$0.28$	$0.12$	$0.06$	$0.21$	$0.19$	$0.13$	$0.02$	$0.17$	$0.47$	$0.22$	$0.13$	$0.13$
${\mathit{A}}_{\mathbf{10}}$	$0.15$	$0.23$	$0.15$	$0.15$	$0.23$	$0.13$	$0.25$	$0.12$	$0.11$	$0.16$	$0.24$	$0.13$	$0.29$	$0.12$	$0.08$	$0.16$	$0.21$	$0.16$	$0.22$	$0.13$	$0.13$
${\mathit{A}}_{\mathbf{11}}$	$0.21$	$0.14$	$0.09$	$0.30$	$0.00$	$0.00$	$0.25$	$0.12$	$0.11$	$0.34$	$0.08$	$0.02$	$0.21$	$0.19$	$0.13$	$0.19$	$0.17$	$0.12$	$0.22$	$0.13$	$0.13$
${\mathit{A}}_{\mathbf{12}}$	$0.21$	$0.14$	$0.09$	$0.30$	$0.00$	$0.00$	$0.25$	$0.12$	$0.11$	$0.34$	$0.08$	$0.02$	$0.21$	$0.19$	$0.13$	$0.19$	$0.17$	$0.12$	$0.22$	$0.13$	$0.13$
${\mathit{A}}_{\mathbf{13}}$	$0.26$	$0.09$	$0.03$	$0.21$	$0.14$	$0.08$	$0.25$	$0.12$	$0.11$	$0.34$	$0.08$	$0.02$	$0.21$	$0.19$	$0.13$	$0.19$	$0.17$	$0.12$	$0.32$	$0.00$	$0.00$
${\mathit{A}}_{\mathbf{14}}$	$0.31$	$0.00$	$0.00$	$0.21$	$0.14$	$0.08$	$0.25$	$0.12$	$0.11$	$0.02$	$0.16$	$0.32$	$0.21$	$0.19$	$0.13$	$0.19$	$0.17$	$0.12$	$0.13$	$0.27$	$0.27$
${\mathit{A}}_{\mathbf{15}}$	$0.02$	$0.18$	$0.44$	$0.07$	$0.32$	$0.21$	$0.18$	$0.20$	$0.19$	$0.04$	$0.20$	$0.28$	$0.29$	$0.12$	$0.08$	$0.13$	$0.26$	$0.19$	$0.19$	$0.18$	$0.18$
${\mathit{A}}_{\mathbf{16}}$	$0.02$	$0.18$	$0.44$	$0.07$	$0.32$	$0.21$	$0.18$	$0.20$	$0.19$	$0.04$	$0.20$	$0.28$	$0.10$	$0.27$	$0.20$	$0.13$	$0.26$	$0.19$	$0.19$	$0.18$	$0.18$
${\mathit{A}}_{\mathbf{17}}$	$0.26$	$0.09$	$0.03$	$0.07$	$0.32$	$0.21$	$0.18$	$0.20$	$0.19$	$0.24$	$0.16$	$0.09$	$0.10$	$0.27$	$0.20$	$0.13$	$0.26$	$0.19$	$0.19$	$0.18$	$0.18$
${\mathit{A}}_{\mathbf{18}}$	$0.26$	$0.09$	$0.03$	$0.07$	$0.32$	$0.21$	$0.09$	$0.27$	$0.30$	$0.24$	$0.16$	$0.09$	$0.04$	$0.19$	$0.33$	$0.22$	$0.13$	$0.09$	$0.16$	$0.22$	$0.22$
${\mathit{A}}_{\mathbf{19}}$	$0.26$	$0.09$	$0.03$	$0.01$	$0.18$	$0.40$	$0.09$	$0.27$	$0.30$	$0.24$	$0.16$	$0.09$	$0.02$	$0.15$	$0.38$	$0.22$	$0.13$	$0.09$	$0.16$	$0.22$	$0.22$
${\mathit{A}}_{\mathbf{20}}$	$0.15$	$0.23$	$0.15$	$0.15$	$0.23$	$0.13$	$0.09$	$0.27$	$0.30$	$0.16$	$0.24$	$0.13$	$0.04$	$0.19$	$0.33$	$0.22$	$0.13$	$0.09$	$0.22$	$0.13$	$0.13$
${\mathit{A}}_{\mathbf{21}}$	$0.31$	$0.00$	$0.00$	$0.21$	$0.14$	$0.08$	$0.25$	$0.12$	$0.11$	$0.02$	$0.16$	$0.32$	$0.21$	$0.19$	$0.13$	$0.19$	$0.17$	$0.12$	$0.13$	$0.27$	$0.27$
${\mathit{A}}_{\mathbf{22}}$	$0.15$	$0.23$	$0.15$	$0.30$	$0.00$	$0.00$	$0.21$	$0.16$	$0.15$	$0.10$	$0.28$	$0.17$	$0.25$	$0.15$	$0.10$	$0.22$	$0.13$	$0.09$	$0.19$	$0.18$	$0.18$
${\mathit{A}}_{\mathbf{23}}$	$0.26$	$0.09$	$0.03$	$0.01$	$0.18$	$0.40$	$0.09$	$0.27$	$0.30$	$0.24$	$0.16$	$0.09$	$0.02$	$0.15$	$0.38$	$0.22$	$0.13$	$0.09$	$0.16$	$0.22$	$0.22$
${\mathit{A}}_{\mathbf{24}}$	$0.08$	$0.32$	$0.24$	$0.25$	$0.09$	$0.03$	$0.25$	$0.12$	$0.11$	$0.28$	$0.12$	$0.06$	$0.21$	$0.19$	$0.13$	$0.02$	$0.17$	$0.47$	$0.22$	$0.13$	$0.13$
${\mathit{A}}_{\mathbf{25}}$	$0.21$	$0.14$	$0.09$	$0.21$	$0.14$	$0.08$	$0.14$	$0.24$	$0.22$	$0.10$	$0.28$	$0.17$	$0.25$	$0.15$	$0.10$	$0.32$	$0.00$	$0.00$	$0.19$	$0.18$	$0.18$
${\mathit{A}}_{\mathbf{26}}$	$0.02$	$0.18$	$0.44$	$0.07$	$0.32$	$0.21$	$0.18$	$0.20$	$0.19$	$0.04$	$0.20$	$0.28$	$0.10$	$0.27$	$0.20$	$0.13$	$0.26$	$0.19$	$0.19$	$0.18$	$0.18$
${\mathit{A}}_{\mathbf{27}}$	$0.18$	$0.18$	$0.12$	$0.07$	$0.32$	$0.21$	$0.09$	$0.27$	$0.30$	$0.24$	$0.16$	$0.09$	$0.04$	$0.19$	$0.33$	$0.22$	$0.13$	$0.09$	$0.16$	$0.22$	$0.22$

.

Step 4. The aggregation of the weight values of the parameter, including the sum of the product of the normalized matrix by the weight values${\mathcal{S}}_i$ and the sum of the power weights of the normalized matrix${\mathcal{P}}_i$, are evaluated by using Equation (4), as shown in

Table 4. Strategies to aggregate the weight values.

	${\mathcal{S}}_{\mathit{i}}$			${\mathcal{P}}_{\mathit{i}}$
	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$
${\mathit{A}}_{\mathbf{1}}$	$0.21$	$0.15$	$0.11$	$5.59$	$4.72$	$4.52$
${\mathit{A}}_{\mathbf{2}}$	$0.21$	$0.15$	$0.11$	$5.59$	$4.72$	$4.52$
${\mathit{A}}_{\mathbf{3}}$	$0.21$	$0.17$	$0.12$	$5.57$	$5.42$	$5.13$
${\mathit{A}}_{\mathbf{4}}$	$0.21$	$0.15$	$0.11$	$5.60$	$4.68$	$4.50$
${\mathit{A}}_{\mathbf{5}}$	$0.12$	$0.22$	$0.22$	$4.99$	$5.64$	$5.64$
${\mathit{A}}_{\mathbf{6}}$	$0.12$	$0.22$	$0.22$	$4.99$	$5.64$	$5.64$
${\mathit{A}}_{\mathbf{7}}$	$0.14$	$0.22$	$0.18$	$5.19$	$5.60$	$5.42$
${\mathit{A}}_{\mathbf{8}}$	$0.20$	$0.18$	$0.13$	$5.51$	$5.43$	$5.10$
${\mathit{A}}_{\mathbf{9}}$	$0.18$	$0.17$	$0.17$	$5.35$	$5.40$	$5.26$
${\mathit{A}}_{\mathbf{10}}$	$0.21$	$0.17$	$0.12$	$5.59$	$5.46$	$5.21$
${\mathit{A}}_{\mathbf{11}}$	$0.24$	$0.13$	$0.09$	$5.71$	$4.55$	$4.31$
${\mathit{A}}_{\mathbf{12}}$	$0.24$	$0.13$	$0.09$	$5.71$	$4.55$	$4.31$
${\mathit{A}}_{\mathbf{13}}$	$0.24$	$0.13$	$0.09$	$5.72$	$4.44$	$4.09$
${\mathit{A}}_{\mathbf{14}}$	$0.20$	$0.15$	$0.13$	$5.45$	$4.63$	$4.52$
${\mathit{A}}_{\mathbf{15}}$	$0.16$	$0.20$	$0.20$	$5.16$	$5.56$	$5.52$
${\mathit{A}}_{\mathbf{16}}$	$0.10$	$0.24$	$0.23$	$4.98$	$5.70$	$5.68$
${\mathit{A}}_{\mathbf{17}}$	$0.15$	$0.22$	$0.17$	$5.35$	$5.62$	$5.34$
${\mathit{A}}_{\mathbf{18}}$	$0.13$	$0.20$	$0.21$	$5.21$	$5.54$	$5.43$
${\mathit{A}}_{\mathbf{19}}$	$0.12$	$0.17$	$0.25$	$5.00$	$5.44$	$5.53$
${\mathit{A}}_{\mathbf{20}}$	$0.13$	$0.20$	$0.21$	$5.21$	$5.58$	$5.51$
${\mathit{A}}_{\mathbf{21}}$	$0.20$	$0.15$	$0.13$	$5.45$	$4.63$	$4.52$
${\mathit{A}}_{\mathbf{22}}$	$0.21$	$0.15$	$0.11$	$5.60$	$4.68$	$4.50$
${\mathit{A}}_{\mathbf{23}}$	$0.12$	$0.17$	$0.25$	$5.00$	$5.44$	$5.53$
${\mathit{A}}_{\mathbf{24}}$	$0.18$	$0.17$	$0.17$	$5.35$	$5.40$	$5.26$
${\mathit{A}}_{\mathbf{25}}$	$0.21$	$0.15$	$0.11$	$5.59$	$4.72$	$4.52$
${\mathit{A}}_{\mathbf{26}}$	$0.10$	$0.24$	$0.23$	$4.98$	$5.70$	$5.68$
${\mathit{A}}_{\mathbf{27}}$	$0.12$	$0.21$	$0.22$	$5.17$	$5.60$	$5.54$
max	$0.24$	$0.24$	$0.25$	$5.72$	$5.70$	$5.68$

.

Step 5. This step involves the accumulation of S and P values by evaluating the relative weight values of each alternative under the defined approaches, which are called the three appraisal score approaches, by using Equations (5)–(7), given below in

Table 5. Appraisal score approaches.

	${\mathit{k}}_{\mathbf{ia} }$			${\mathit{k}}_{\mathit{i}\mathit{b}}$			${\mathit{k}}_{\mathit{i}\mathit{c}}$
	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$	$\mathit{\rho }$	$\mathit{\tau }$	$\mathit{\nu }$
${\mathit{A}}_{\mathbf{1}}$	$0.04$	$0.03$	$0.03$	$2.87$	$2.49$	$2.41$	$0.98$	$0.82$	$0.79$
${\mathit{A}}_{\mathbf{2}}$	$0.04$	$0.03$	$0.03$	$2.87$	$2.49$	$2.41$	$0.98$	$0.82$	$0.79$
${\mathit{A}}_{\mathbf{3}}$	$0.04$	$0.04$	$0.04$	$2.86$	$2.81$	$2.70$	$0.97$	$0.94$	$0.89$
${\mathit{A}}_{\mathbf{4}}$	$0.04$	$0.03$	$0.03$	$2.87$	$2.47$	$2.40$	$0.98$	$0.82$	$0.78$
${\mathit{A}}_{\mathbf{5}}$	$0.03$	$0.04$	$0.04$	$2.64$	$2.89$	$2.89$	$0.86$	$0.99$	$0.99$
${\mathit{A}}_{\mathbf{6}}$	$0.03$	$0.04$	$0.04$	$2.64$	$2.89$	$2.89$	$0.86$	$0.99$	$0.99$
${\mathit{A}}_{\mathbf{7}}$	$0.04$	$0.04$	$0.04$	$2.72$	$2.87$	$2.80$	$0.90$	$0.98$	$0.95$
${\mathit{A}}_{\mathbf{8}}$	$0.04$	$0.04$	$0.04$	$2.84$	$2.81$	$2.68$	$0.96$	$0.95$	$0.89$
${\mathit{A}}_{\mathbf{9}}$	$0.04$	$0.04$	$0.04$	$2.77$	$2.80$	$2.74$	$0.93$	$0.94$	$0.92$
${\mathit{A}}_{\mathbf{10}}$	$0.04$	$0.04$	$0.04$	$2.87$	$2.83$	$2.74$	$0.97$	$0.95$	$0.91$
${\mathit{A}}_{\mathbf{11}}$	$0.04$	$0.03$	$0.03$	$2.91$	$2.42$	$2.32$	$1.00$	$0.79$	$0.75$
${\mathit{A}}_{\mathbf{12}}$	$0.04$	$0.03$	$0.03$	$2.91$	$2.42$	$2.32$	$1.00$	$0.79$	$0.75$
${\mathit{A}}_{\mathbf{13}}$	$0.04$	$0.03$	$0.03$	$2.92$	$2.36$	$2.22$	$1.00$	$0.77$	$0.71$
${\mathit{A}}_{\mathbf{14}}$	$0.04$	$0.03$	$0.03$	$2.81$	$2.45$	$2.40$	$0.95$	$0.81$	$0.79$
${\mathit{A}}_{\mathbf{15}}$	$0.04$	$0.04$	$0.04$	$2.69$	$2.86$	$2.84$	$0.89$	$0.97$	$0.97$
${\mathit{A}}_{\mathbf{16}}$	$0.03$	$0.04$	$0.04$	$2.64$	$2.91$	$2.90$	$0.86$	$1.00$	$1.00$
${\mathit{A}}_{\mathbf{17}}$	$0.04$	$0.04$	$0.04$	$2.79$	$2.88$	$2.78$	$0.93$	$0.98$	$0.93$
${\mathit{A}}_{\mathbf{18}}$	$0.04$	$0.04$	$0.04$	$2.73$	$2.85$	$2.80$	$0.90$	$0.97$	$0.95$
${\mathit{A}}_{\mathbf{19}}$	$0.03$	$0.04$	$0.04$	$2.64$	$2.82$	$2.83$	$0.86$	$0.95$	$0.98$
${\mathit{A}}_{\mathbf{20}}$	$0.04$	$0.04$	$0.04$	$2.74$	$2.87$	$2.83$	$0.90$	$0.98$	$0.97$
${\mathit{A}}_{\mathbf{21}}$	$0.04$	$0.03$	$0.03$	$2.81$	$2.45$	$2.40$	$0.95$	$0.81$	$0.79$
${\mathit{A}}_{\mathbf{22}}$	$0.04$	$0.03$	$0.03$	$2.87$	$2.47$	$2.40$	$0.98$	$0.82$	$0.78$
${\mathit{A}}_{\mathbf{23}}$	$0.03$	$0.04$	$0.04$	$2.64$	$2.82$	$2.83$	$0.86$	$0.95$	$0.98$
${\mathit{A}}_{\mathbf{24}}$	$0.04$	$0.04$	$0.04$	$2.77$	$2.80$	$2.74$	$0.93$	$0.94$	$0.92$
${\mathit{A}}_{\mathbf{25}}$	$0.04$	$0.03$	$0.03$	$2.87$	$2.49$	$2.41$	$0.98$	$0.82$	$0.79$
${\mathit{A}}_{\mathbf{26}}$	$0.03$	$0.04$	$0.04$	$2.64$	$2.91$	$2.90$	$0.86$	$1.00$	$1.00$
${\mathit{A}}_{\mathbf{27}}$	$0.04$	$0.04$	$0.04$	$2.72$	$2.87$	$2.84$	$0.89$	$0.98$	$0.97$

.

Step 6. The alternatives are ranked based on the accumulated values of$k_i$ by using Equation (8), which are displayed in

Table 6. Ranking of the alternatives.

	${\mathit{k}}_{\mathit{i}}$			Score Value	Ranking
${\mathit{A}}_{\mathbf{1}}$	$1.77$	$1.53$	$1.47$	$0.25$	$6$
${\mathit{A}}_{\mathbf{2}}$	$1.77$	$1.53$	$1.47$	$0.25$	$7$
${\mathit{A}}_{\mathbf{3}}$	$1.77$	$1.73$	$1.66$	$0.03$	$11$
${\mathit{A}}_{\mathbf{4}}$	$1.77$	$1.51$	$1.47$	$0.26$	$4$
${\mathit{A}}_{\mathbf{5}}$	$1.60$	$1.79$	$1.80$	$-0.19$	$24$
${\mathit{A}}_{\mathbf{6}}$	$1.60$	$1.79$	$1.80$	$-0.19$	$25$
${\mathit{A}}_{\mathbf{7}}$	$1.66$	$1.78$	$1.74$	$-0.12$	$19$
${\mathit{A}}_{\mathbf{8}}$	$1.75$	$1.73$	$1.65$	$0.02$	$13$
${\mathit{A}}_{\mathbf{9}}$	$1.70$	$1.72$	$1.69$	$-0.02$	$14$
${\mathit{A}}_{\mathbf{10}}$	$1.77$	$1.74$	$1.68$	$0.03$	$12$
${\mathit{A}}_{\mathbf{11}}$	$1.81$	$1.48$	$1.41$	$0.33$	$3$
${\mathit{A}}_{\mathbf{12}}$	$1.81$	$1.48$	$1.41$	$0.33$	$2$
${\mathit{A}}_{\mathbf{13}}$	$1.81$	$1.44$	$1.35$	$0.36$	$1$
${\mathit{A}}_{\mathbf{14}}$	$1.73$	$1.50$	$1.47$	$0.23$	$10$
${\mathit{A}}_{\mathbf{15}}$	$1.65$	$1.77$	$1.77$	$-0.12$	$20$
${\mathit{A}}_{\mathbf{16}}$	$1.60$	$1.81$	$1.81$	$-0.21$	$26$
${\mathit{A}}_{\mathbf{17}}$	$1.71$	$1.79$	$1.72$	$-0.08$	$16$
${\mathit{A}}_{\mathbf{18}}$	$1.67$	$1.76$	$1.74$	$-0.10$	$17$
${\mathit{A}}_{\mathbf{19}}$	$1.61$	$1.74$	$1.76$	$-0.13$	$23$
${\mathit{A}}_{\mathbf{20}}$	$1.67$	$1.78$	$1.76$	$-0.11$	$18$
${\mathit{A}}_{\mathbf{21}}$	$1.73$	$1.50$	$1.47$	$0.23$	$9$
${\mathit{A}}_{\mathbf{22}}$	$1.77$	$1.51$	$1.47$	$0.26$	$5$
${\mathit{A}}_{\mathbf{23}}$	$1.61$	$1.74$	$1.76$	$-0.13$	$22$
${\mathit{A}}_{\mathbf{24}}$	$1.70$	$1.72$	$1.69$	$-0.02$	$15$
${\mathit{A}}_{\mathbf{25}}$	$1.77$	$1.53$	$1.47$	$0.25$	$8$
${\mathit{A}}_{\mathbf{26}}$	$1.60$	$1.81$	$1.81$	$-0.21$	$27$
${\mathit{A}}_{\mathbf{27}}$	$1.66$	$1.78$	$1.77$	$-0.12$	$21$

.

3. Results

The PF-COCOFISO approach enabled decision-making in digital media and intangible-heritage digitalization by generating valuable rankings of alternatives across various conflicting choice factors. The evaluation criteria demonstrated the highest alignment with $A_{13}$, followed by $A_{12}$ and $A_{11}$, since these alternatives performed best, as shown in Figure 3. The decision parameters evaluations placed both $A_{26}$ and $A_{16}$ at the bottom of the ranking due to their deficiencies in meeting the necessary conditions. $A_5$, $A_6$, and $A_{19}$ obtained lower ranks as indicators, potentially pointing to financial restrictions, physical limitations, or moral challenges affecting their execution. Decision-makers found the middle-ranked options, $A_8$, $A_9$, and $A_{10}$, to represent a balanced but sub-optimal choice because they performed moderately well according to the evaluation criteria. PF-COCOFISO demonstrated its value through its complete decision-making approach, effectively emphasizing decision-making uncertainty while selecting appropriate digitalization methods for sustainable practices.

Computational Efficiency

The efficiency evaluation of PF-COCOFISO served to determine its potential use for handling complex digital media and intangible-heritage digitalization decisions. Applying PFSs alongside PF-COCOFISO is associated with decision-making targets in unpredictable situations during alternative selection and criterion evaluation. PF-COCOFISO achieves superior computational stability compared to traditional MCDM due to its weighted adaptive approach with modern fusion methods, which generates precise alternative prioritization results. The method produced precise answers with reasonable computational costs, making it a functional option for extensive decision-making applications. The model processes data efficiently throughout its execution due to its effective data convergence properties when working with substantial datasets and minimal computational challenges. PF-COCOFISO achieves practical success in decision-making applications because it uses an efficient framework that handles digitalization choices made under situations of uncertainty.

4. Discussion

4.1. Comparison Analysis

A comparative examination was performed to determine PF-COCOFISO’s performance against VIKOR [30], TOPSIS [31], MEREC [32], EDAS [33], and PROMETHEE [34], and the results are shown in

Table 7. Comparative study.

Features	PF-COCOFISO	VIKOR	TOPSIS	MEREC	EDAS	PROMETHEE
Handling uncertainty	$\mathrm{✓}$	$\mathrm{✗}$	$\mathrm{✗}$	$\mathrm{✗}$	$\mathrm{✗}$	$\mathrm{✗}$
Advanced aggregation	$\mathrm{✓}$	$\mathrm{✗}$	$\mathrm{✗}$	$\mathrm{✗}$	$\mathrm{✓}$	$\mathrm{✓}$
Dynamic weighting	$\mathrm{✓}$	$\mathrm{✓}$	$\mathrm{✗}$	$\mathrm{✓}$	$\mathrm{✓}$	$\mathrm{✓}$
Compromise-based solution	$\mathrm{✓}$	$\mathrm{✓}$	$\mathrm{✗}$	$\mathrm{✗}$	$\mathrm{✓}$	$\mathrm{✓}$
Ranking stability	$\mathrm{✓}$	$\mathrm{✓}$	$\mathrm{✓}$	$\mathrm{✓}$	$\mathrm{✗}$	$\mathrm{✓}$
Computational efficiency	$\mathrm{✓}$	$\mathrm{✗}$	$\mathrm{✓}$	$\mathrm{✗}$	$\mathrm{✓}$	$\mathrm{✗}$
Applicability in digital media	$\mathrm{✓}$	$\mathrm{✗}$	$\mathrm{✗}$	$\mathrm{✗}$	$\mathrm{✗}$	$\mathrm{✗}$

. The assessment relies on significant methodological characteristics that apply to digital media decision phases and intangible-heritage digitalization activities. In complex decision environments, PF-COCOFISO demonstrates better uncertainty management capabilities that make it a more appropriate tool for effectively handling inconsistent and ambiguous data. The decision strategies of VIKOR and PROMETHEE incorporating compromise-based methods fall short compared to that of PF-COCOFISO because this method adds advanced aggregation techniques and dynamic weighting mechanisms to improve decision robustness. The method presents better ranking stabilization and enhanced sensitivity evaluation, which protects outcomes from changes in decision criteria variables, thereby improving dependability. The method surpasses VIKOR as well as PROMETHEE and MEREC in terms of performance efficiency and, thus, functions optimally when processing extensive datasets for real-world decision-making needs. PF-COCOFISO presents adaptive capabilities which grant it precise context-sensitive digital media decision solutions, making it better than traditional methods in terms of operational performance and accuracy standards. The theoretical evaluation method applied in Table 7 analyzed the previous literature, and involved a side-by-side study and a theory-based analysis for a fair method capability evaluation.

PF-COCOFISO delivers superior performance in digital heritage digitization because it effectively handles uncertain situations, surpassing alternative MCDM methods, as shown in

Table 8. Comparison analysis with existing MCDM methods.

Authors	Methodology	Limitations	Remarks
Chang et al. [35]	Neutrosophic DEMATEL-TOPSIS	Lacks a strong hesitation-handling mechanism, limited conflict resolution	PF-COCOFISO incorporates hesitation degrees for more precise decision-making
Milošević et al. [36]	Fuzzy AHP and Interval AHP	High subjectivity in expert weight assignment, limited adaptability	PF-COCOFISO refines expert weight processing and improves adaptability
Pavlovskis et al. [37]	BIM and MCDM	Focuses on structured ranking but lacks uncertainty-handling	PF-COCOFISO manages uncertainty effectively and enhances ranking stability
She et al. [38]	Interval-Valued Neutrosophic Approach	Strong in VR evaluation but lacks comprehensive MCDM framework	PF-COCOFISO extends beyond VR, ensuring balanced decision-making for various heritage scenarios

. The existing methods of neutrosophic DEMATEL-TOPSIS and Interval AHP face problems due to subjective weight assignments, restricted adaptability, and insufficient conflict management systems. The BIM and MCDM approaches use rankings as their main approach, but they do not provide effective solutions for managing hesitation or uncertainty. The dynamic weighting systems and advanced hesitation-handling mechanism embedded in PF-COCOFISO represent features which elevate its strength in assessing complex digital heritage digitization strategies. This decision-making approach is highly suitable for research because it achieves superior objective management and enhanced reliability during decision-making processes.

4.2. Significance of the Study

Despite globalization and technological disruption, digitizing intangible cultural heritage enables the preservation of traditional knowledge, rituals, languages, and performing arts. Digitalization initiatives battle for success when there is no structured decision-making process, since funding deficits accompany wrong technology choices and cultural resistance. This research fills the gap between modern digital media innovation and cultural protection requirements through its scientifically proven decision-making approach for selecting ideal digitalization solutions. Society will gains substantial value from this examination because it enhances decision-making processes for heritage digitalization. This research presents an enhanced digitalization support system for heritage through PFS integration with the COCOFISO method, establishing clear and consistent decision-making processes. These evaluation measures serve as key standards to optimize digitalization techniques through cost-effective processes, technological sustainability, and cultural diversity. By employing the PF-COCOFISO model in different fields, researchers can expand MCDM applications specifically for cultural heritage, as well as digital media management and knowledge preservation strategies. This research implements an organized science-based approach to digitalization strategies for intangible heritage, ensuring sustainable operations and long-term accessibility.

4.3. Theoretical Implications

Digital media and intangible-heritage digitalization greatly benefit from PF-COCOFISO, since this approach provides organized decision-making structures that effectively manage unpredictable inputs, conflicting criteria, and hesitation in decision-making processes. The evaluation processes of TOPSIS, VIKOR, and PROMETHEE depend on fixed methodologies. Yet, PF-COCOFISO combines PFSs for treating the MD, NMD, and AD to create better digitalization strategies while maintaining symmetry. The enhancement of the COCOSO method within this research provides dynamic weighting capabilities and refined aggregation methods that boost its functionality in complex digital heritage preservation decision-making. Organizations can minimize data destruction risks through this systematic evaluation method while ensuring standards remain stable and people accept digitalization processes. The research method established here allows for analyses of digitalization approaches within various cultural areas, which include language conservation, performing arts history preservation, and indigenous wisdom documentation. The proposed extensions of this case study will confirm this research method’s wider practical application. Digital intangible-heritage research benefits from the PF-COCOFISO application because it enables gap resolution within existing decision frameworks.

4.4. Practical Implications

These research results will deliver essential real-world benefits to organizations operating in digital media along with intangible-heritage digitalization.

• When decision-makers use the PF-COCOFISO methodology, they can establish a structured way to rank and manage digital preservation plans, which protects important cultural heritage materials and historical documents.
• Digital heritage institutions and policymakers gain the ability to use data-based systems for choosing appropriate digitalization methods while managing resources, optimizing technology, and maintaining accuracy of preservation.
• The proposed approach enables heritage institutions to improve digital accessibility, which enables them to attract more users through interactive and immersive technologies.
• These research findings offer guidance to media organizations to enable them to make the best decisions about how to manage their content archives, digital broadcasting systems, and multimedia assets.
• This research demonstrates how community involvement protects cultural authenticity by leading decision-making processes.
• This research demonstrates how proper ethical guidelines need to exist for digital ownership management, cultural protocol handling, and heritage accessibility regulations.
• This research demonstrates how digital initiatives transform cultural identity as well as social learning methods while safeguarding heritage legacies.
• Although this study explores a nationwide project, its adaptable framework maintains flexibility for different heritage areas and locations.

4.5. Sensitivity Analysis

The PF-COCOFISO method’s effectiveness for digital media and intangible-heritage digitalization was measured by testing numerous weight modification scenarios. Figure 4 illustrates the weight sensitivity analysis, where the criteria weights are modified five times to evaluate the stability of rankings for twenty-seven alternatives. Each color in the bars represents the impact of different criteria under these weight variations. The results demonstrate that the method retains stable ranking orders, which especially applies to the high-positioned alternatives $A_{13}, A_{12},$ and $A_{11}$. Reliable decision-making results were obtained due to the method’s stability, which minimizes ranking variations due to slight expert weight modifications. The model shows high credibility because weight adjustments have no effect on the consistently low rankings of ${ A}_5$, $A_6$, $A_{16}$, and $A_{26}$. The ranking adjustments of the mid-ranked alternatives $A_8, A_9, A_{24}$, and $A_{10}$ mainly correspond to specific criterion variations rather than instability factors. The model benefits heritage digitalization projects because the PF-COCOFISO method avoids artificial ranking changes through its sensitivity control mechanism.

The PF-COCOFISO methodology proves its capability as a robust decision tool during digital media and intangible-heritage digitalization through sensitivity parameter analysis that tests various values of $\gamma$ from $0.1$ to $0.9$, as shown in Figure 5. The rankings of the $A_{13}, A_{12}$, and $A_{11}$ alternatives stay optimal as they consistently hold leadership positions in every parameter variation. The least successful alternatives among the analyzed alternatives demonstrate negative values in all weight variation scenarios. The specifications in the criteria adjustments lead to moderate ranking changes for the alternatives $A_8, A_9, A_{10}, A_{24}$, and $A_9$. The PF-COCOFISO method demonstrates reliable and stable ranking results through different parameter scenarios, thus establishing itself as a solid choice for strategic decision-making processes related to intangible-heritage preservation using digital approaches.

4.6. Validation of Results

The results of the sensitivity analysis confirmed that criterion weight variations have a minimal impact on alternative rankings, proving the dependency of method performance on practical applications. The evaluation established PF-COCOFISO as superior to the VIKOR, TOPSIS, MEREC, EDAS, and PROMETHEE approaches since it assists with full assessment and uncertainty management to create reliable decision outputs. Dependence ranking stability exists, especially with those highly ranked options $A_{13}, A_{12}, and A_{11}$, which confirms the model’s reliability when applied to real-world situations. PF-COCOFISO is validated as a suitable tool for optimizing digitalization strategies, leading to effective decision-making processes in intangible-heritage preservation.

4.7. Advantages of the Study

The advantages of this study are summarized as follows:

• The PF-COCOFISO model offers a systematic method to pick suitable digitalization methods for heritage preservation in a symmetric way that achieves technical excellence, budgetary efficiency, and cultural approval.
• COCOFISO operates through advanced aggregation approaches, together with dynamic weighting, to boost traditional MCDM methods while dealing with uncertain situations. The enhanced effectiveness of PF-COCOFISO enables decision-making when dealing with numerous types of uncertain conditions encountered during digital media assessments.
• PF-COCOFISO is chosen since it employs PFSs to manage uncertain expert assessments. Through this framework, a proper representation of hesitation and imprecision becomes vital in digitalization strategy assessments for heritage preservation.
• PF-COCOFISO offers an organized decision process which selects digitalization alternatives through optimal weight determination between technical feasibility, economic boundaries, and cultural resource significance to develop sustainable preservation approaches.
• Through optimized resource allocation, the model supports institutions, museums, and cultural organizations in efficiently distributing their funds and resources by highlighting cost-effective digitalization strategies.
• The proposed approach creates better ethical and cultural alignment through decision-maker preference integration, which establishes AI restoration methods and virtual reality development with blockchain-based archives compliant with ethical standards.
• The new model shows superiority against VIKOR, TOPSIS, MEREC, EDAS, and PROMETHEE through its more accurate assessment methods and dynamic weight adjustments, which work well for complicated criteria relationships.
• The PF-COCOFISO approach extends its application capacities to handling the digital archiving of heritage materials, the AI restoration of media content, and securing knowledge storage facilities.

4.8. Limitations of the Study

The PF-COCOFISO approach uses expert evaluations, and these assessments maintain cultural and ethical integrity and technological convergence. The computational complexity that enables adaptability requires substantial resources to operate effectively. The assessment method currently works with set strategies, so it needs additional alternatives to improve its usefulness. The method by which criteria are selected and weighted affects ranking outcomes, thus requiring consensus techniques to enhance objectivity. The large number of experts prevents ethical diversity, and extensive data collection remains challenging when studying intangible heritage. The model is a strong decision-support system that delivers reliable heritage digitalization support. To overcome the abovementioned limitations, future research will use spherical fuzzy sets [39] combined with interval-valued picture fuzzy models [40], which would enhance uncertainty management, thus providing superior decision-making results. Exploring bipolar-valued hesitant fuzzy sets introduced by Ullah et al. [41] and neutrosophic metric spaces introduced by Ahmad et al. [42] could provide strategies to handle conflicting inputs from decision-makers and a mathematical foundation for managing indeterminate heritage data. The optimization of MCDM in evolving digitalization strategies can be achieved by incorporating interval-valued spherical fuzzy Dombi aggregation [43] and interval-valued T-spherical fuzzy approaches [44]. Enhancing cultural heritage preservation requires research on integrating these methodologies with AI analytics to improve automation and scalability.

5. Conclusions

Digitalizing intangible heritage using advanced digital media technologies brings numerous possibilities while creating complex decision-related problems because of uncertainties about cultural appropriateness, technological change, and funding limitations. The PF-COCOFISO method was found to be a strong MCDM approach to solving complicated decision-making issues. The model efficiently resolves uncertain circumstances, hesitant assessments, and conflicting evaluation points by implementing PFSs to produce better-informed and balanced outcomes. The digital media and intangible-heritage digitalization process benefited from PF-COCOFISO, which proved its ability to select suitable digital preservation strategies through the systematic assessment of sustainability, accessibility, and ethical criteria. The modeling framework provided enhanced decision-making support with context-based precision, surpassing traditional MCDM procedures when applied to such problems. The assessment revealed that PF-COCOFISO delivers superior performance compared to traditional MCDM approaches, including VIKOR, TOPSIS, and PROMETHEE, due to its precise decision-making abilities during conditions of uncertainty and because it maintains symmetry in the evaluation process. This study demonstrates the necessity for creating decision systems that adapt to technological and cultural marketplace changes. This study establishes principles that allow the PF-COCOFISO model to expand its applications to digital healthcare systems and smart city planning facilities. This model could perform better within complex decision frameworks by integrating with other MCDM systems.