(α, β)−Pythagorean Fuzzy Numbers Descriptor Systems

By using pythagorean fuzzy sets and T-S fuzzy descriptor systems, the new (α, β)-pythagorean fuzzy descriptor systems are proposed in this paper. Their definition is given firstly, and the stability of this kind of systems is studied, the relation of (α, β)-pythagorean fuzzy descriptor systems and T-S fuzzy descriptor systems is discussed. The (α, β)-pythagorean fuzzy controller and the stability of (α, β)-pythagorean fuzzy descriptor systems are deeply researched. The (α, β)-pythagorean fuzzy descriptor systems can be better used to solve the problems of actual nonlinear control. The (α, β)-pythagorean fuzzy descriptor systems will be a new research direction, and will become a universal method to solve practical problems. Finally, an example is given to illustrate effectiveness of the proposed method.

Fermatean Hesitant Fuzzy Sets with Medical Decision Making Application

Fermatean fuzzy set idea obtained by combining fermatean fuzzy sets and hesitant fuzzy sets can be used in practice to simplify the solution of complicated multi-criteria decision-making (MCDM) problems. Initially, the notion of fermatean hesitant fuzzy set is given and the operations related to this concept are presented. Aggregation operators according to fermatean hesitant fuzzy sets are given and basic properties of these operators are studied. To choose the best alternative in practice, a novel MCDM method that is obtained with operators has been created. Finally, an example of infectious diseases was examined to indicate the effectiveness of the suggested techniques.

Harmonic Aggregation Operator with Trapezoidal Picture Fuzzy Numbers and Its Application in a Multiple-Attribute Decision-Making Problem

Picture fuzzy sets (PFSs) can be used to handle real-life problems with uncertainty and vagueness more effectively than intuitionistic fuzzy sets (IFSs). In the process of information aggregation, many aggregation operators under PFSs are used by different authors in different fields. In this article, a multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information. Three harmonic mean operators are developed namely trapezoidal picture fuzzy weighted harmonic mean (TrPFWHM) operator, trapezoidal picture fuzzy order weighted harmonic mean (TrPFOWHM) operator and trapezoidal picture fuzzy hybrid harmonic mean (TrPFHHM) operator. The related properties about these operators are also studied. At last, an MADM problem is considered to interrelate among these operators. Furthermore, a numerical instance is considered to explain the productivity of the proposed operators.

A New Approach for Spherical Fuzzy TOPSIS and Spherical Fuzzy VIKOR Applied to the Evaluation of Hydrogen Storage Systems

This study proposes a new perspective of the TOPSIS and VIKOR methods using the recently introduced spherical fuzzy sets (SFSs) to handle the vagueness in subjective data and the uncertainties in objective data simultaneously. When implementing these techniques using SFSs, two main problems might arise that can lead to incorrect results. Firstly, the reference points might change with the utilized score function. Secondly, the distance between reference points might not be the largest, as known, among the available ratings. To overcome these deficiencies and increase the robustness of these two methods, they are implemented without utilizing any reference points to minimize the effect of defuzzification and without measuring the distance to eliminate the effect of distance formulas. In the proposed methods, when using an SFS to express the performance of an alternative for a criterion, this SFS per se can be viewed as a measure of proximity to the aspired level. On the other hand, the conjugate of the SFS can be viewed as a measure of proximity to the ineffectual level. Two practical applications are presented to demonstrate the proposed techniques. The first example handles a warehouse location selection problem. The second example evaluates hydrogen storage systems for automobiles with different types of data (crisp, linguistic variables, type 1 fuzzy sets). These data are transformed to SFSs to provide a more comprehensive analysis. A comparative study is conducted with earlier versions of TOPSIS and VIKOR to explicate the adequacy of the proposed methods and the consistency of the results.