Distance measures on intuitionistic fuzzy sets based on intuitionistic fuzzy dissimilarity functions

Some distance measures for pythagorean cubic fuzzy sets: Application selection in optimal treatment for depression and anxiety

Pythagorean cubic fuzzy sets represent an advancement beyond conventional interval-valued Pythagorean sets, integrating the principles of Pythagorean fuzzy sets and interval-valued Pythagorean fuzzy sets. Given the critical significance of distance measures in real-world decision-making and pattern recognition tasks, it is noteworthy that there exists a notable gap in the literature regarding distance measures specifically tailored for Pythagorean cubic fuzzy sets. The objectives of this paper are:•To define novel generalized distance measures between Pythagorean cubic fuzzy sets (PCFSs) to tackle intricate decision-making challenges.•These novel distance measures are undergoing testing on a real-world scenario concerning the management of anxiety and depression to evaluate their effectiveness and practical application.•We have illustrated the boundedness and nonlinear characteristics inherent in these distance measures. In addition, we conduct comparative analyses with existing approaches to validate the proposed methodology, thereby providing insights into its advantages and potential applications.

Decision Support System Based on Complex Fractional Orthotriple Fuzzy 2-Tuple Linguistic Aggregation Operator

In this research, we provide tools to overcome the information loss limitation resulting from the requirement to estimate the results in the discrete initial expression domain. Through the use of 2-tuples, which are made up of a linguistic term and a numerical value calculated between [0.5,0.5), the linguistic information will be expressed. This model supports continuous representation of the linguistic data within its scope, permitting it to express any information counting received through an aggregation procedure. This study provides a novel approach to develop a linguistic multi-attribute group decision-making (MAGDM) approach with complex fractional orthotriple fuzzy 2-tuple linguistic (CFOF2TL) assessment details. Initially, the concept of a complex fractional orthotriple fuzzy 2-tuple linguistic set (CFO2TLS) is proposed to convey uncertain and fuzzy information. In the meantime, simple aggregation operators, such as CFOF2TL weighted average and geometric operators, are defined. In addition, the CFOF2TL Maclaurin’s symmetric mean (CFOF2TLMSM) operators and their weighted shapes are presented, and their attractive characteristics are also discussed. A new MAGDM approach is built using the developed aggregation operators to address managing economic crises under COVID-19 with the CFOF2TL information. As a result, the effectiveness and robustness of the developed method are accompanied by an empirical example, and a comparative study is carried out by contrasting it with previous approaches.

Incomplete intuitionistic fuzzy behavioral group decision-making based on multigranulation probabilistic rough sets and MULTIMOORA for water quality inspection

Water quality inspection (WQI) is one of the primary ways to ensure the safe utilization of water resources, and complicated data modeling, fusion and analysis play a significant role in seeking the resource with the best water quality. Nevertheless, the challenges of missing data, relatively large differences in decision results and bounded rationality owned by decision-makers (DMs) in terms of WQI still exist nowadays. Thus, from the aspect of stable and behavioral decision-making in multi-granularity incomplete intuitionistic fuzzy information systems (MG-IIFISs), the paper investigates a comprehensive multi-attribute group decision-making (MAGDM) approach for the application of WQI. First, the concept of MG-IIFISs is built by modeling MAGDM problems with intuitionistic fuzzy numbers (IFNs), then a new transformation scheme is constructed for transforming MG-IIFISs into multi-granularity intuitionistic fuzzy information systems (MG-IFISs) based on the similarity principle. Second, three types of multigranulation intuitionistic fuzzy probabilistic rough sets (MG IF PRSs) are developed by referring to the MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the full MULTIplicative form) method. Afterwards, attribute weights are objectively calculated based on the best-worst method (BWM), and a new stable and behavioral MAGDM approach is constructed by means of the TODIM (an acronym in Portuguese for interactive multi-criteria decision-making) method. At last, a case study in the setting of WQI is conducted with the support of a UCI data set, and sensitivity analysis, comparative analysis and experimental analysis are investigated to display the validity of the proposed approach. In general, the proposed approach improves the stability of decision results via MULTIMOORA and BWM, and also fully considers the bounded rationality of DMs’ psychological behaviors from the aspect of the TODIM method, which has certain advantages in the community of MAGDM studies.

Intuitionistic fuzzy-valued neutrosophic multi-sets and numerical applications to classification

A single-valued neutrosophic multi-set is characterized by a sequence of truth membership degrees, a sequence of indeterminacy membership degrees and a sequence of falsity membership degrees. Nature of a single-valued neutrosophic multi-set allows us to consider multiple information in the truth, indeterminacy and falsity memberships which is pretty useful in multi-criteria group decision making. In this paper, we consider sequences of intuitionistic fuzzy values instead of numbers to define the concept of intuitionistic fuzzy-valued neutrosophic multi-set. In this manner, such a set gives more powerful information. We also present some set theoretic operations and a partial order for intuitionistic fuzzy-valued neutrosophic sets and provide some algebraic operations between intuitionistic fuzzy-valued neutrosophic values. Then, we develop two types of weighted aggregation operators with the help of intuitionistic fuzzy t-norms and t-conorms. By considering some well-known additive generators of ordinary t-norms, we give the Algebraic weighted arithmetic and geometric aggregation operators and the Einstein weighted arithmetic and geometric aggregation operators that are the particular cases of the weighted aggregation operators defined via general t-norms and t-conorms. We also define a simplified neutrosophic valued similarity measure and we use a score function for simplified neutrosophic values to rank similarities of intuitionistic fuzzy-valued neutrosophic multi-values. Finally, we give an algorithm to solve classification problems using intuitionistic fuzzy-valued neutrosophic multi-values and proposed aggregation operators and we apply the theoretical part of the paper to a real classification problem.

Complex intuitionistic fuzzy Maclaurin symmetric mean operators and its application to emergency program selection

Due to the indeterminacy and uncertainty of the decision-makers (DM) in the complex decision making problems of daily life, evaluation and aggregation of the information usually becomes a complicated task. In literature many theories and fuzzy sets (FS) are presented for the evaluation of these decision tasks, but most of these theories and fuzzy sets have failed to explain the uncertainty and vagueness in the decision making issues. Therefore, we use complex intuitionistic fuzzy set (CIFS) instead of fuzzy set and intuitionistic fuzzy set (IFS). A new type of aggregation operation is also developed by the use of complex intuitionistic fuzzy numbers (CIFNs), their accuracy and the score functions are also discussed in detail. Moreover, we utilized the Maclaurin symmetric mean (MSM) operator, which have the ability to capture the relationship among multi-input arguments, as a result, CIF Maclarurin symmetric mean (CIFMSM) operator and CIF dual Maclaurin symmetric mean (CIFDMSM) operator are presented and their characteristics are discussed in detail. On the basis of these operators, a MAGDM method is presented for the solution of group decision making problems. Finally, the validation of the propounded approach is proved by evaluating a numerical example, and by the comparison with the previously researched results.

Multi-criteria healthcare waste disposal location selection based on Fermatean fuzzy WASPAS method

Medical services inevitably generate healthcare waste (HCW) that may become hazardous to healthcare staffs, patients, the population, and the atmosphere. In most of the developing countries, HCW disposal management has become one of the fastest-growing challenges for urban municipalities and healthcare providers. Determining the location for HCW disposal centers is a relatively complex process due to the involvement of various alternatives, criteria, and strict government guidelines about the disposal of HCW. The objective of the paper is to introduce the WASPAS (weighted aggregated sum product assessment) method with Fermatean fuzzy sets (FFSs) for the HCW disposal location selection problem. This method combines the score function, entropy measure, and classical WASPAS approach within FFSs context. Next, a combined procedure using entropy and score function is proposed to estimate the criteria weights. To do this, a novel score function with its desirable properties and some entropy measures are introduced under the FFSs context. Further, an illustrative case study of the HCW disposal location selection problem on FFSs is established, which evidences the practicality and efficacy of the developed approach. Comparative discussion and sensitivity analysis are made to monitor the permanence of the introduced framework. The final results approve that the proposed methodology can effectively handle the ambiguity and inaccuracy in the decision-making procedure of HCW disposal location selection.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

Uncertainty-Aware Dissimilarity Measures for Interval-Valued Fuzzy Sets

Dissimilarities are a very usual way to compare two fuzzy sets and also two interval-valued fuzzy sets. In both cases, the dissimilarity between two sets is a number. In this work, we introduce a generalization of the notion of dissimilarity for interval-valued fuzzy sets such that it assumes values on the set of subintervals instead of the set of numbers. This seems to be more realistic taking into account the available information. We also investigate its relationship with the classical notions of dissimilarity between fuzzy sets and we obtain that the new class is richer than the existing one.

Diagnosing and routing electronic service quality improvement of academic libraries with the FMEA approach in an intuitionistic fuzzy environment

Purpose

In this way, the aim of this study is to expand and evelop the application of this technique in FMEA to rank failure modes of ESQ of academic libraries in an intuitionistic fuzzy environment. Assessment of electronic service quality (ESQ) of libraries is significantly important according to their major roles. It should be noted that the ESQ has a significant impact on customer satisfaction, which improves organizational performance. Accordingly, low ESQ means waste of organizational resources and poor user satisfaction. So, there is a dire need to reflect reasons inducing failure modes in academic library ESQ. Thus, investigation of failure modes affecting academic library ESQ is highly important. One solution in this area is utilization of the intuitionistic fuzzy (IF) failure mode and effects analysis (FMEA) as one of the widely used methods for prediction and identification of failure modes.

Design/methodology/approach

The present study in terms of objective is applied and in terms of the type of method is descriptive-analytical. The research sample included four experts of Yazd academic Libraries (Iran). To collect data, three types of questionnaires were distributed among experts. The purpose of the first questionnaire was to identify and reach an agreement on e-library failure modes. Type II questionnaire was used to determine the importance of identified risk factors and Type III questionnaire was used to prioritize the factors.

Findings

Results indicate that the difficulty of using websites, lack of provided information feedback to users and lack of links on the website to users' are the main priorities for improving ESQ in the studied academic libraries.

Originality/value

In this approach, the Intuitionistic fuzzy Elimination Et Choix Traduisant la REalité and technique for order of preference by similarity to ideal solution method were used to rank failure modes in academic library ESQ within the FMEA framework.]