Search Results (22)

Trapezoidal-valued intuitionistic fuzzy numbers (TrVIFNs) are the real generalizations of intuitionistic fuzzy numbers, interval-valued intuitionistic fuzzy numbers, and triangular intuitionistic fuzzy numbers, which effectively model real-life problems that consist of imprecise and incomplete data. This study incorporates the Aczel-Alsina aggregation operators (which consist of parameter-based flexibility) for solving any group of decision-making problems modeled in a trapezoidal-valued intuitionistic fuzzy (TrVIF) environment. In this study, we first define new operations on TrVIFNs based on the Aczel-Alsina operations. Secondly, we introduce new trapezoidal-valued intuitionistic fuzzy aggregation operators, such as the TrVIF Aczel-Alsina weighted averaging operator, the TrVIF Aczel-Alsina ordered weighted averaging operator, and the TrVIF Aczel-Alsina hybrid averaging operator, and we discuss their fundamental mathematical properties by examining various theorems. This study also includes a new algorithm named ‘three-stage multi-criteria group decision-making’, where we obtain the criteria weights using the newly proposed TrVIF-MEREC method. Additionally, we introduce a new modified algorithm called TrVIF-WASPAS to solve the multi-criteria decision-making (MCDM) problem in the trapezoidal-valued intuitionistic fuzzy environment. Then, we apply this proposed method to solve a model case study problem involving location selection for a wind power plant project. Then, we discuss the proposed algorithm’s sensitivity analysis by changing the criteria weights concerning different parameter values. Finally, we compare our proposed methods with various existing methods, like some subclasses of TrVIFNs such as IVIFWA, IVIFWG, IVIFEWA, and IVIFEWG, and also with some MCGDM methods of TrVIFNs, such as the Dombi aggregation operator-based method in TrVIFNs and the TrVIF-Topsis method-based MCGDM, to show the efficacy of our proposed algorithm. This study has many advantages, as it consists of a total ordering principle in ranking alternatives in the newly proposed TrVIF-MCGDM techniques and TrVIF-WASPAS MCDM techniques for the first time in the literature. Full article

Complex Intuitionistic Fuzzy Sets (CIFSs) are an advanced form of intuitionistic fuzzy sets that utilize complex numbers to effectively manage uncertainty and hesitation in multi-criteria decision making (MCDM). This paper introduces the Shapley Choquet integral (SCI), which is a powerful tool for integrating information from various sources while considering the importance and interactions among criteria. To address ambiguity and inconsistency, we apply the Aczel–Alsina (AA) t-norm and t-conorm, which offer greater flexibility than traditional norms. We propose two novel aggregation operators within the CIFS framework using the Aczel–Alsina Generalized Shapley Choquet Integral (AAGSCI): the Complex Intuitionistic Fuzzy Aczel–Alsina Weighted Average Generalized Shapley Choquet Integral (CIFAAWAGSCI) and the Complex Intuitionistic Fuzzy Aczel–Alsina Weighted Geometric Generalized Shapley Choquet Integral (CIFAAWGGSCI), along with their special cases. The properties of these operators, including idempotency, boundedness, and monotonicity, are thoroughly investigated. These operators are designed to evaluate complex and asymmetric information in real-life problems. A case study on selecting the optimal bridge design based on structural and aesthetic criteria demonstrates the applicability of the proposed method. Our results indicate that the proposed method yields more consistent and reliable outcomes compared to existing approaches. Full article

The paper presents an innovative method for tackling multi-attribute decision-making (MADM) problems within a hesitant fuzzy (HF) framework. Initially, the paper generalizes the Chi-square distance measure to the hesitant fuzzy context, defining the HF generalized Chi-square distance. Following this, the paper introduces the power average (P-A) operator and the power geometric (P-G) operator to refine the weights derived from Shannon entropy, taking into account the inter-attribute support. Leveraging the strengths of Aczel–Alsina operations and the power operation, the paper proposes the hesitant fuzzy Aczel–Alsina power weighted average (HFAAPWA) operator and the hesitant fuzzy Aczel–Alsina power weighted geometric (HFAAPWG) operator. Consequently, a hesitant fuzzy Aczel–Alsina power model is constructed. The applicability of this model is demonstrated through a case study examining the urban impacts of cyclonic storm Amphan, and the model’s superiority is highlighted through comparative analysis. Full article

Selecting optimal design solutions is inherently complex due to multiple criteria encompassing users’ uncertain needs, experiences, and costs. This process must manage uncertainty and ambiguity, making developing a scientific, rational, and efficient guidance method imperative. Bipolar T-spherical fuzzy sets (BTSFS), a hybrid of bipolar fuzzy sets and T-spherical fuzzy sets, effectively handle the bipolarity inherent in all elements. In this work, we propose a Weighted Aggregated Sum Product Assessment (WASPAS) method based on BTSFS and the Aczel–Alsina T-norm (AATN) and T-conorm (AATCN) to address the problem of selecting conceptual design solutions. We first establish operational rules for BTSFS using AATN and AATCN and introduce weighted aggregation operators (BTSFAAWA) and geometric aggregation operators (BTSFAAWG) while examining fundamental properties, such as idempotency, boundedness, and monotonicity. Subsequently, we propose a two-stage BTSFS-based WASPAS method; criterion weights are calculated using the BTSFAAWA operator, and final rankings are obtained through comprehensive calculations using both the weighted sum method (WSM) based on BTSFAAWA and the weighted product method (WPM) based on BTSFAAWG. Finally, we validate the effectiveness of our method through a case study of the selection of cultural and creative products. Sensitivity and comparative analyses are conducted to demonstrate the advantages of our approach. Full article

Based on the approximation spaces, the interval-valued intuitionistic fuzzy rough set (IVIFRS) plays an essential role in coping with the uncertainty and ambiguity of the information obtained whenever human opinion is modeled. Moreover, a family of flexible t-norm (TNrM) and t-conorm (TCNrM) known as the Aczel–Alsina t-norm (AATNrM) and t-conorm (AATCNrM) plays a significant role in handling information, especially from the unit interval. This article introduces a novel clustering model based on IFRS using the AATNrM and AATCNrM. The developed clustering model is based on the aggregation operators (AOs) defined for the IFRS using AATNrM and AATCNrM. The developed model improves the level of accuracy by addressing the uncertain and ambiguous information. Furthermore, the developed model is applied to the segmentation problem, considering the information about the income and spending scores of the customers. Using the developed AOs, suitable customers are targeted for marketing based on the provided information. Consequently, the proposed model is the most appropriate technique for the segmentation problems. Furthermore, the results obtained at different values of the involved parameters are studied. Full article

In order to further investigate the level of online medical services in China and improve the medical experience of patients, this study aims to establish an online review-driven picture fuzzy multi-criteria group decision-making (MCGDM) approach for the online medical service evaluation of doctors. First, based on the Aczel–Alsina t-norm and t-conorm, the normal picture fuzzy Aczel–Alsina operations involving a variable parameter are defined to make the corresponding operations more flexible than other operations. Second, two picture fuzzy Aczel–Alsina aggregation operators are developed, and the corresponding properties are discussed as well. Third, combined with the online review information of China’s medical platform Haodaifu, the online review-driven evaluation attributes and their corresponding weights are obtained, which can make the evaluation model more objective. Fourth, an extended normal picture fuzzy complex proportional assessment (COPRAS) decision-making method for the service quality evaluation of online medical services is proposed. Finally, an empirical example is presented to verify the feasibility and validity of the proposed method. A sensitivity analysis and a comparison analysis are also conducted to demonstrate the effectiveness and flexibility of the proposed approach. Full article

Q-rung orthopair fuzzy sets have been proven to be highly effective at handling uncertain data and have gained importance in decision-making processes. Torra’s hesitant fuzzy model, on the other hand, offers a more generalized approach to fuzzy sets. Both of these frameworks have demonstrated their efficiency in decision algorithms, with numerous scholars contributing established theories to this research domain. In this paper, recognizing the significance of these frameworks, we amalgamated their principles to create a novel model known as Q-rung orthopair hesitant fuzzy sets. Additionally, we undertook an exploration of Aczel–Alsina aggregation operators within this innovative context. This exploration resulted in the development of a series of aggregation operators, including Q-rung orthopair hesitant fuzzy Aczel–Alsina weighted average, Q-rung orthopair hesitant fuzzy Aczel–Alsina ordered weighted average, and Q-rung orthopair hesitant fuzzy Aczel–Alsina hybrid weighted average operators. Our research also involved a detailed analysis of the effects of two crucial parameters: $\lambda$, associated with Aczel–Alsina aggregation operators, and N, related to Q-rung orthopair hesitant fuzzy sets. These parameter variations were shown to have a profound impact on the ranking of alternatives, as visually depicted in the paper. Furthermore, we delved into the realm of Wireless Sensor Networks (WSN), a prominent and emerging network technology. Our paper comprehensively explored how our proposed model could be applied in the context of WSNs, particularly in the context of selecting the optimal gateway node, which holds significant importance for companies operating in this domain. In conclusion, we wrapped up the paper with the authors’ suggestions and a comprehensive summary of our findings. Full article

Human activity recognition (HAR) is the process of interpreting human activities with the help of electronic devices such as computer and machine version technology. Humans can be explained or clarified as gestures, behavior, and activities that are recorded by sensors. In this manuscript, we concentrate on studying the problem of HAR; for this, we use the proposed theory of Aczel and Alsina, such as Aczel–Alsina (AA) norms, and the derived theory of Choquet, such as the Choquet integral in the presence of Atanassov interval-valued intuitionistic fuzzy (AIVIF) set theory for evaluating the novel concept of AIVIF Choquet integral AA averaging (AIVIFC-IAAA), AIVIF Choquet integral AA ordered averaging (AIVIFC-IAAOA), AIVIF Choquet integral AA hybrid averaging (AIVIFC-IAAHA), AIVIF Choquet integral AA geometric (AIVIFC-IAAG), AIVIF Choquet integral AA ordered geometric (AIVIFC-IAAOG), and AIVIF Choquet integral AA hybrid geometric (AIVIFC-IAAHG) operators. Many essential characteristics of the presented techniques are shown, and we also identify their properties with some results. Additionally, we take advantage of the above techniques to produce a technique to evaluate the HAR multiattribute decision-making complications. We derive a functional model for HAR problems to justify the evaluated approaches and to demonstrate their supremacy and practicality. Finally, we conduct a comparison between the proposed and prevailing techniques for the legitimacy of the invented methodologies. Full article

The intuitionistic hesitant fuzzy set is a significant extension of the intuitionistic fuzzy set, specifically designed to address uncertain information in decision-making challenges. Aggregation operators play a fundamental role in combining intuitionistic hesitant fuzzy numbers into a unified component. This study aims to introduce two novel approaches. Firstly, we propose a three-way model for investors in the business domain, which utilizes interval-valued equivalence classes under the framework of intuitionistic hesitant fuzzy information. Secondly, we present a multiple-attribute decision-making (MADM) method using various aggregation operators for intuitionistic hesitant fuzzy sets (IHFSs). These operators include the IHF Aczel–Alsina average $\left(IHF{\mathcal{A}}_{\mathcal{A}}\mathrm{A}\right)$ operator, the IHF Aczel–Alsina weighted average $\left(IHF{\mathcal{A}}_{\mathcal{A}}W{A}_{\mathsf{ϣ}}\right)$ operator, and the IHF Aczel–Alsina ordered weighted average $\left(IHF{\mathcal{A}}_{\mathcal{A}}OW{A}_{\mathsf{ϣ}}\right)$ operator and the IHF Aczel–Alsina hybrid average $\left(IHF{\mathcal{A}}_{\mathcal{A}}H{A}_{\mathsf{ϣ}}\right)$ operators. We demonstrate the properties of idempotency, boundedness, and monotonicity for these newly established aggregation operators. Additionally, we provide a detailed technique for three-way decision-making using intuitionistic hesitant fuzzy Aczel–Alsina aggregation operators. Furthermore, we present a numerical case analysis to illustrate the pertinency and authority of the esteblished model for investment in business. In conclusion, we highlight that the developed approach is highly suitable for investment selection policies, and we anticipate its extension to other fuzzy information domains. Full article

In today’s fast-paced and dynamic business environment, investment decision making is becoming increasingly complex due to the inherent uncertainty and ambiguity of the financial data. Traditional decision-making models that rely on crisp and precise data are no longer sufficient to address these challenges. Fuzzy logic-based models that can handle uncertain and imprecise data have become popular in recent years. However, they still face limitations when dealing with complex, multi-criteria decision-making problems. To overcome these limitations, in this paper, we propose a novel three-way group decision model that incorporates decision-theoretic rough sets and intuitionistic hesitant fuzzy sets to provide a more robust and accurate decision-making approach for selecting an investment policy. The decision-theoretic rough set theory is used to reduce the information redundancy and inconsistency in the group decision-making process. The intuitionistic hesitant fuzzy sets allow the decision makers to express their degrees of hesitancy in making a decision, which is not possible in traditional fuzzy sets. To combine the group opinions, we introduce novel aggregation operators under intuitionistic hesitant fuzzy sets (IHFSs), including the IHF Aczel-Alsina average $\left(IHF{\mathcal{A}}_{\mathcal{A}}\mathrm{A}\right)$ operator, the IHF Aczel-Alsina weighted average $\left(IHF{\mathcal{A}}_{\mathcal{A}}W{A}_{\mathsf{ϣ}}\right)$ operator, the IHF Aczel-Alsina ordered weighted average $\left(IHF{\mathcal{A}}_{\mathcal{A}}OW{A}_{\mathsf{ϣ}}\right)$ operator, and the IHF Aczel-Alsina hybrid average $\left(IHF{\mathcal{A}}_{\mathcal{A}}H{A}_{\mathsf{ϣ}}\right)$ operator. These operators have desirable properties such as idempotency, boundedness, and monotonicity, which are essential for a reliable decision-making process. A mathematical model is presented as a case study to evaluate the effectiveness of the proposed model in selecting an investment policy. The results show that the proposed model is effective and provides more accurate investment policy recommendations compared to existing methods. This research can help investors and financial analysts in making better decisions and achieving their investment goals. Full article

Many aggregation operators are studied to deal with multi-criteria group decision-making problems. Whenever information has two aspects, intuitionistic fuzzy sets and Pythagorean fuzzy sets are employed to handle the information. However, q-rung orthopair fuzzy sets are more flexible and suitable because they cover information widely. The current paper primarily focuses on the multi-criteria group decision-making technique based on prioritization and two robust aggregation operators based on Aczel–Alsina t-norm and t-conorm. This paper suggests two new aggregation operators based on q-rung orthopair fuzzy information and Aczel–Alsina t-norm and t-conorm, respectively. Firstly, novel q-rung orthopair fuzzy prioritized Aczel–Alsina averaging and q-rung orthopair fuzzy prioritized Aczel–Alsina geometric operators are proposed, involving priority weights of the information. Several related results of the proposed aggregation operators are investigated to see their diversity. A multi-criteria group decision-making algorithm based on newly established aggregation operators is developed, and a comprehensive numerical example for the selection of the most suitable energy resource is carried out. The proposed aggregation operators are compared with other operators to see some advantages of the proposed work. The proposed aggregation operators have a wider range for handling information, with priority degrees, and are based on novel Aczel–Alsina t-norm and t-conorm. Full article

Artificial intelligence (AI) is a well-known and reliable technology that enables a machine to simulate human behavior. While the major theme of AI is to make a smart computer system that thinks like a human to solve awkward problems, machine learning allows a machine to automatically learn from past information without the need for explicit programming. In this analysis, we aim to derive the idea of Aczel–Alsina aggregation operators based on an intuitionistic fuzzy soft set. The initial stage was the discovery of the primary and critical Aczel–Alsina operational laws for intuitionistic fuzzy soft sets. Subsequently, we pioneer a range of applicable theories (set out below) and identify their essential characteristics and key results: intuitionistic fuzzy soft Aczel–Alsina weighted averaging; intuitionistic fuzzy soft Aczel–Alsina ordered weighted averaging; intuitionistic fuzzy soft Aczel–Alsina weighted geometric operators; and intuitionistic fuzzy soft Aczel–Alsina ordered weighted geometric operators. Additionally, by utilizing certain key information, including intuitionistic fuzzy soft Aczel–Alsina weighted averaging and intuitionistic fuzzy soft Aczel–Alsina weighted geometric operators, we also introduce the theory of the weighted aggregates sum product assessment method for intuitionistic fuzzy soft information. This paper also introduces a multi-attribute decision-making method, which is based on derived operators for intuitionistic fuzzy soft numbers and seeks to assess specific industrial problems using artificial intelligence or machine learning. Finally, to underline the value and reasonableness of the information described herein, we compare our obtained results with some pre-existing information in the field. This comparison is supported by a range of numerical examples to demonstrate the practicality of the invented theory. Full article

Complex picture fuzzy sets are the updated version of the complex intuitionistic fuzzy sets. A complex picture fuzzy set covers three major grades such as membership, abstinence, and falsity with a prominent characteristic in which the sum of the triplet will be contained in the unit interval. In this scenario, we derive the power aggregation operators based on the Aczel–Alsina operational laws for managing the complex picture of fuzzy values. These complex picture fuzzy power aggregation operators are complex picture fuzzy Aczel–Alsina power averaging, complex picture fuzzy Aczel–Alsina weighted power averaging, complex picture fuzzy Aczel–Alsina power geometric, and complex picture fuzzy Aczel–Alsina weighted power geometric operators. We also investigate their theoretical properties. To justify these complex picture fuzzy power aggregation operators, we illustrate a procedure of a decision-making technique in the presence of complex picture fuzzy values and derive an algorithm to evaluate some multi-attribute decision-making problems. Finally, a practical example is examined to illustrate the decision-making procedure under the consideration of derived operators, and their performance is compared with that of various operators to show the supremacy and validity of the proposed approaches. Full article

A T-spherical fuzzy set is a more powerful mathematical tool to handle uncertain and vague information than several fuzzy sets, such as fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, q-rung orthopair fuzzy set, and picture fuzzy set. The Aczel–Alsina t-norm and s-norm are significant mathematical operations with a high premium on affectability with parameter activity, which are extremely conducive to handling imprecise and undetermined data. On the other hand, the Hamy mean operator is able to catch the interconnection among multiple input data and achieve great results in the fusion process of evaluation information. Based on the above advantages, the purpose of this study is to propose some novel aggregation operators (AOs) integrated by the Hamy mean and Aczel–Alsina operations to settle T-spherical fuzzy multi-criteria decision-making (MCDM) issues. First, a series of T-spherical fuzzy Aczel–Alsina Hamy mean AOs are advanced, including the T-spherical fuzzy Aczel–Alsina Hamy mean (TSFAAHM) operator, T-spherical fuzzy Aczel–Alsina dual Hamy mean (TSFAADHM) operator, and their weighted forms, i.e., the T-spherical fuzzy Aczel–Alsina-weighted Hamy mean (TSFAAWHM) and T-spherical fuzzy Aczel–Alsina-weighted dual Hamy mean (TSFAAWDHM) operators. Moreover, some related properties are discussed. Then, a MCDM model based on the proposed AOs is built. Lastly, a numerical example is provided to show the applicability and feasibility of the developed AOs, and the effectiveness of this study is verified by the implementation of a parameters influence test and comparison with available methods. Full article

The complex t-spherical fuzzy set (Ct-SFS) is a potent tool for representing fuzziness and uncertainty compared to the picture fuzzy sets and spherical fuzzy sets. It plays a key role in modeling problems that require two-dimensional data. The present study purposes the aggregation technique of Ct-SFSs with the aid of Aczel–-Alsina (AA) operations. We first introduce certain novel AA operations of Ct-SFSs, such as the AA sum, AA product, AA scalar multiplication, and AA scalar power. Subsequently, we propound a series of complex t-spherical fuzzy averaging and geometric aggregation operators to efficiently aggregate complex t-spherical fuzzy data. In addition, we explore the different characteristics of these operators, discuss certain peculiar cases, and prove their fundamental results. Thereafter, we utilize these operators and propose entropy measures to frame a methodology for dealing with complex t-spherical fuzzy decision-making problems with unknown criteria weight data. Finally, we provide a case study about vehicle model selection to illustrate the presented method’s applicability followed by a parameter analysis and comparative study. Full article