The VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method provides a valuable means of evaluating options based on assessment criteria, intending to generate the finest compromise options through multiple-criteria optimization. However, decision-making often involves uncertainty, where decision-makers may lack complete information or struggle to predict outcomes accurately. Circular intuitionistic fuzzy (C-IF) sets offer a versatile way to represent uncertainty and indecision, adding circularity to intuitionistic fuzzy sets' membership and non-membership. C-IF sets bring sophistication by incorporating circular functions to address complicated ambiguity, alongside assigning membership and non-membership components. This research aims to create a C-IF VIKOR decision-support method to handle multiple-criteria compromise solutions with C-IF uncertainties. The study focuses on enhancing the augmented scoring function and Chebyshev distance metric in C-IF surroundings. The augmented scoring function exhibits unique characteristics, including a direct relationship between membership and function value, an inverse correlation with nonmembership, and reflection of information reliability. The enhanced C-IF Chebyshev distance measure combines radial and membership/nonmembership distances, considering their special features. The proposed C-IF VIKOR technique utilizes these concepts to identify superior and inferior options and determine the finest compromise solution using an identification mechanism and VIKOR indices. The method is demonstrated in the context of healthcare waste disposal and will undergo sensitivity analyses and comparative studies to showcase its advantages, adaptability, and robustness.

In an uncertain context of T-spherical fuzzy (T-SF) sets, the purpose of this study is to propound an efficacious multiple criteria choice model, named a T-SF REGIME method, predicated on a dominance analysis and a prioritization analysis. The REGIME methodology is a well-founded evaluation technique suitable for multiple criteria choice analysis owing to it has good applicability to the processing of qualitative information and to complex scenarios. Unlike the existing REGIME techniques, this paper takes advantage of a new Minkowski-type distance measure and an evolved Gaussian preference function to propound a ground-breaking T-SF REGIME model. This paper first concentrates on an evolution of the Minkowski-type distance measure and explores special cases with relevant properties for functional use. Next, this paper concerns an ascertainment of the evolved Gaussian preference function as a part of the proposed T-SF REGIME mechanism. This paper focuses on an advancement of the REGIME structure to T-SF uncertain contexts and unfolds an inventive T-SF REGIME methodology by virtue of superiority identifiers/indices, guide identifiers/indices, and joint generalized indices. The usefulness and strength points of the advanced methodology are scrutinized through a realistic application in the field of solar plant to prioritize the options of photovoltaic cells. The application results and comparisons corroborate the high efficiency and strengths of the evolved methodology.

The concept of Pythagorean fuzzy (PF) sets represents a superior tool to model complex uncertainties in an ambiguous and equivocal decision-making framework. In consideration of the significant capacity for exhibiting the uncertainty of subjective appraisals and estimations under the aegis of the PF theory, this paper presents a simple-to-operate decision-making approach that is grounded in some beneficial concepts of original likelihood functions and measurements of dominating and dominated characters. On the strength of beta distributions, this paper seeks to propound new notions of PF likelihood functions and likelihood-oriented dominating/dominated characters and to launch an exploitable multiple criteria evaluation method by means of a dominance ordering model for treating decision analysis within PF environments. This paper initiates an efficient beta distribution-based approach to the construction of novel PF likelihood functions that can quantify the possibility degrees of outranking and outranked relationships between Pythagorean membership grades. The applicable satisfaction and dissatisfaction estimations are established on the likelihood-oriented dominating and dominated characters, respectively. Furthermore, this paper formulates a straightforward dominance ordering model to obtain the ultimate dominance ranking orders of candidate alternatives and accomplish multiple criteria decision-making issues involving complicated uncertainty. A financing decision-making problem concerning working capital requirements is investigated to validate the application results using the advanced methodology. The real-world application is implemented to examine the reasonableness and efficacy of the established techniques. Moreover, comparative studies through the utility of a sensitivity analysis are performed to demonstrate the efficacy and merits of the dominance ordering model. The comparison results manifest that the initiated methodology is an advantageous and reliable decision-making technique that can enhance the methodological development regarding the multiple criteria evaluation model under PF uncertainty. Finally, recommendations for future research directions are also presented in the conclusions.

The aim of this article is to develop a novel multiple criteria decision analysis (MCDA) method using a Pearson-like correlation-based Pythagorean fuzzy (PF) compromise approach under complex uncertainty based on PF sets and interval-valued Pythagorean fuzzy (IVPF) sets. Because of the complexity and ambiguity involved in real-life decision-making situations, this article utilizes the theory of Pythagorean fuzziness, which is characterized by flexible degrees of membership, nonmembership, and indeterminacy to describe uncertain information more comprehensively. PF and IVPF sets possess exceptional abilities to accurately reflect the uncertainty, fuzziness, and vagueness inherent in the decision information. However, manipulating PF and IVPF information is a complicated and difficult task for most decision makers. In this regard, this article extends the well-known and widely used concept of correlation coefficients to develop simple and effective compromise models for solving MCDA problems in PF and IVPF contexts. This article conducts an extended analysis of Pearson-like correlation coefficients for PF and IVPF sets separately and introduces new concepts of PF and IVPF correlation coefficients to furnish a solid basis for the proposed methodology. Furthermore, this article develops useful concepts of PF and IVPF correlation-based closeness coefficients to simultaneously measure the relative closeness to the positive-ideal PF/IVPF solutions and the relative remoteness from the negative-ideal PF/IVPF solutions. On the basis of the developed concepts, this article proposes a novel Pearson-like correlation-based PF/IVPF compromise approach to address uncertain MCDA problems involving PF/IVPF information and determine the ultimate priority orders among competing alternatives. Finally, this article provides an illustrative application about a financing decision of working capital management to verify the developed approach and demonstrate its feasibility and practicality.

The concept of interval-valued Pythagorean fuzzy (IVPF) sets is capable of handling imprecise and ambiguous information and managing complex uncertainty in real-world applications. This paper focuses on multiple criteria decision analysis involving IVPF information and proposes a new outranking decision-making method that uses a closeness-based assignment model. In contrast to the existing assignment-based methodology, the uniqueness of this paper is the consideration of uncertain information represented by IVPF values, the determination of criterion-wise precedence rankings based on a closeness-based approach, and the development of a new measure for scalar representation. First, to underlie anchored judgments in subjective decision-making processes, this paper presents a compromising concept of the closeness index with the positive-ideal and negative-ideal IVPF values to identify criterion-wise precedence ranks among alternatives. Next, this paper defines the concept of matrices of precedence frequency and contribution to provide a basis for the proposed assignment model. To overcome the difficulty of lacking nontrivial scalar representations, a useful measure is also developed to appropriately describe IVPF values. Based on a closeness-based assignment approach, a novel outranking decision-making method is proposed to transform the extended criterion-wise ranks into the ultimate priority orders of the alternatives. The proposed method is first implemented in a practical problem of selecting a bridge construction method to demonstrate its feasibility and applicability. Moreover, its practicality and effectiveness are verified through a comparative analysis with relevant assignment-based approaches. Further comparative analyses with newly developed IVPF decision-making methods are conducted for both a risk evaluation problem and an investment problem to examine the advantages of the proposed method and extend the current technique by considering distinct preference information for adapting to the particularities in practice.

In the multiple attribute decision making (MADM) problem, it is crucial to properly assess the weights of attribute because the changes in the attribute weights would affect the ranking of alternatives. In addition, although the intuitionistic fuzzy (IF) set is widely extended to MADM problems, it turns out that the data and decision matrix get more complex and uncertain. Therefore, it is important to pay much attention to the credibility of data itself. However, there is little investigation on MADM with the credibility of data being explicitly taken into account. In this research, we propose a new objective weighting method by using IF entropy measures for MADM under the intuitionistic fuzzy environment. In terms of the nature of IF entropy, the attribute weights are assessed by the credibility of data. Moreover, several IF entropy measures are used and examined to figure out the difference between them with a series of simulation experiments. Four indices are employed to compare the ranking results by objective weights, including the contradiction rate, the inversion rate, the consistency rate and Spearman correlation coefficients. The experimental results indicate that different IF entropy measures would cause a totally different ranking result for attributes. In addition, when the numbers of alternative and attributes become large, the difference between rankings of attributes expands gradually.

The purpose of this study is to extend the TOPSIS method for solving multiple attribute decision analysis problems with intuitionistic fuzzy data. Iintuitionistic fuzzy sets are capable of coping with imprecise information due to the fact that exact data may be difficult to be precisely determined since human judgments are often vague under many conditions. In this paper, a proposed intuitionistic fuzzy version of the TOPSIS method is presented and further deals with a comparative analysis of separation measures. For the sake of the comparison of intuitionistic fuzzy TOPSIS rankings yielded by different separation measures, a simulation experiment of different sizes was generated and examined. The consistency rate, the contradiction rate of the best alternative, and average Spearman correlation coefficients are utilized to conduct a pairwise comparison for all separation measures. The results which are inclusive of one hundred combinations of ten different categories of number for each alternatives and attributes indicate that the preference orders are hardly identical using different separation measures in the intuitionistic fuzzy TOPSIS method. The experimental analysis showed that the different definitions of IFS separations indeed significantly affect the final results by means of the intuitionistic fuzzy TOPSIS method. The comparative results presented in our experimental analysis indicate differentiations in a number of important aspects with some comparative indices.

Over the last decades, intuitionistic fuzzy sets have been applied to many different fields, such as logic programming, medical diagnosis, decision making, etc. The purpose of this paper is to develop a new methodology for solving multi-attribute decision-making problems with intuitionistic fuzzy information by using the concept of ELECTRE method. ELECTRE uses the concept of an outranking relationship. We also use TOPSIS method to rank all of the alternatives and to determine the best alternative. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Product involvement has been developed for a long period of time, and has been mature gradually. Intuitionistic fuzzy sets contain the concept of interval that could be used to solve the uncertain problems when respondents have uncertainty in answering questions. The intuitionistic fuzzy automata are mathematical machine for a finite state with a dynamic system operating in discrete time. The operation of the intuitionistic fuzzy automata is similar to the operation of individuals’ product involvement. Both of them do have the internal state to transform output state. This research tried to utilize the intuitionistic fuzzy automata to develop an integrated model of product involvement, and search for which one is the most suitable product involvement scale when we discuss product involvement in the intuitionistic fuzzy automata.

As far as marketing researchers are concerned, advertising involvement is an important segmentation variable; the advertisers view advertising involvement as a vital factor resulting in advertising effects. Advertising involvement has been discussed in several decades while little literature proposed a complete integrated model. Hence, we collect the antecedents and consequences for advertising involvement. Because the model that we attempt to develop includes too many variables, it is difficult to judge the functional relations among these variables and not appropriate to use a traditional statistical method. We take advantage of the automata to develop an integrated model of advertising involvement. In the social science, a great number of questions are abstract and hard to possess a certain answer. The intuitionistic fuzzy sets, which are generated from the fuzzy sets, more completely express the degree of uncertainty for people. We use the automata in the intuitionistic fuzzy sets, which are named intuitionistic fuzzy automata, to develop an integrated model of advertising involvement. The model is successfully generated. In the future, as long as obtaining consumerspsila degree of antecedents, we can predict their degree of advertising involvement and consequences in terms of this model.

Involvement has become an important variable in consumer behavior and marketing research for a long time. The purpose of this study is to develop a model that can explain the complicated relationship between antecedents, consequences, and different types of involvement at the same time to understand the internal state of consumers better. Specifically, this model has to be capable of handling the vague interactions between different types of involvement. We develop this integrated model by the using of the intuitionistic fuzzy automata. We choose the cell phone as the stimulus product in this research. There are 19 antecedents, 5 types of involvement, and 10 consequences in the integrated involvement model. According to the results, we find that the intuitionistic fuzzy automata can deal with the interactions between different types of involvement. Second, the intuitionistic fuzzy automata can observe the relations between antecedents, consequences, and 5 types of involvement at the same time. Besides, we can observe the internal state inside consumers through the intuitionistic fuzzy automata, especially the degree of hesitation when they make decisions.

This study develops an identification procedure for general fuzzy measures using genetic algorithms. In view of the difficulty in data collection in practice, the amount of input data is simplified through a sampling procedure concerning attribute subsets, and the corresponding detail design is adapted to the partial information acquired by the procedure. A specially designed genetic algorithm is proposed for better identification, including the development of the initialization procedure, fitness function, and three genetic operations. To show the applicability of the proposed method, this study simulates a set of experimental data that are representative of several typical classes. The experimental analysis indicates that using genetic algorithms to determine general fuzzy measures can obtain satisfactory results under the framework of partial information.