Pythagorean Fuzzy Soft Einstein Ordered Weighted Average Operator in Sustainable Supplier Selection Problem

Pythagorean fuzzy soft set (PFSS) is the most influential and operative extension of the Pythagorean fuzzy set (PFS), which contracts with the parametrized standards of the substitutes. It is also a generalized form of the intuitionistic fuzzy soft set (IFSS) and delivers a well and accurate estimation in the decision-making (DM) procedure. The primary purpose is to prolong and propose ideas related to Einstein’s ordered weighted aggregation operator from fuzzy to PFSS, comforting the condition that the sum of the degrees of membership function and nonmembership function is less than one and the sum of the squares of the degree of membership function and nonmembership function is less than one. We present a novel Pythagorean fuzzy soft Einstein ordered weighted averaging (PFSEOWA) operator based on operational laws for Pythagorean fuzzy soft numbers. Furthermore, some essential properties such as idempotency, boundedness, and homogeneity for the proposed operator have been presented in detail. The choice of a sustainable supplier is also examined as an essential part of sustainable supply chain management (SSCM) and is considered a crucial multiattribute group decision-making (MAGDM) issue. In some MAGDM problems, the relationship between alternatives and uncertain environments will be the main reason for deficient consequences. We have presented a novel aggregation operator for PFSS information to choose sustainable suppliers to cope with those complex issues. The Pythagorean fuzzy soft number (PFSN) helps to represent the obscure information in such real-world perspectives. The priority relationship of PFSS details is beneficial in coping with SSCM. The proposed method’s effectiveness is proved by comparing advantages, effectiveness, and flexibility among the existing studies.

A Novel Approach to Decision Making Based on Interval-Valued Fuzzy Soft Set

Interval-valued fuzzy soft set theory is a powerful tool that can provide the uncertain data processing capacity in an imprecise environment. The two existing methods for decision making based on this model were proposed. However, when there are some extreme values or outliers on the datasets based on interval-valued fuzzy soft set for making decisions, the existing methods are not reasonable and efficient, which may ignore some excellent candidates. In order to solve this problem, we give a novel approach to decision making based on interval-valued fuzzy soft set by means of the contrast table. Here, the contrast table has symmetry between the objects. Our proposed algorithm makes decisions based on the number of superior parameter values rather than score values, which is a new perspective to make decisions. The comparison results of three methods on two real-life cases show that, the proposed algorithm has superiority to the existing algorithms for the feasibility and efficiency when we face up to the extreme values of the uncertain datasets. Our proposed algorithm can also examine some extreme or unbalanced values for decision making if we regard this method as supplement of the existing algorithms.

Fuzzy Soft Topology Based on Generalized Intersection and Generalized Union of Fuzzy Soft Sets

In this study, the generalized intersection and union operations of fuzzy soft set (FSS) are established on the basis of traditional FSS operations, which overcome the shortcomings of traditional FSS operations that do not meet De Morgan’s law, and a series of properties of generalized intersection and union operations of FSS are obtained. The fuzzy soft topology under generalized intersection and generalized union operation of FSSs is established. Finally, the topological construction of weak FSS and strong FSS is discussed, and the relationship between them and the topological construction of traditional FSS is obtained.

A Decision-Making Approach Based on Score Matrix for Pythagorean Fuzzy Soft Set

Pythagorean fuzzy soft set (PFSS) is the most powerful and effective extension of Pythagorean fuzzy sets (PFS) which deals with the parametrized values of the alternatives. It is also a generalization of intuitionistic fuzzy soft set (IFSS) which provides us better and precise information in the decision-making process comparative to IFSS. The core objective of this work is to construct some algebraic operations for PFSS such as OR-operation, AND-operation, and necessity and possibility operations. Furthermore, some fundamental properties have been established for PFSS utilizing the developed operations. Moreover, a decision-making technique has been offered for PFSS based on a score matrix. To demonstrate the validity of the proposed approach, a numerical example has been presented. Finally, to ensure the practicality of the established approach, a comprehensive comparative analysis has been presented. The obtained results show that our developed approach is most effective and delivers better information comparative to prevailing techniques.

On Soft Quantum B-Algebras and Fuzzy Soft Quantum B-Algebras

This paper aims to make a combination between the quantum B-algebras (briefly, X - A s) and two interesting theories (e.g., soft set theory and fuzzy soft set theory). Firstly, we propose the novel notions of soft quantum B-algebras (briefly, S ℚ B - A s), a soft deductive system of ℚ B - A s, and deducible soft quantum B-algebras (briefly, DS ℚ B - A s). Then, we discuss the relationship between S ℚ B - A s and DS ℚ B - A s. Furthermore, we investigate the union and intersection operations of DS ℚ B - A s. Secondly, we introduce the notions of a fuzzy soft quantum B-algebras (briefly, FS ℚ B - A s), a fuzzy soft deductive system of ℚ B - A s, and present some characterizations of FS ℚ B - A s, along with several examples. Finally, we explain the basic properties of homomorphism image of FS ℚ B - A s.

Multicriteria Decision-Making Approach for Aggregation Operators of Pythagorean Fuzzy Hypersoft Sets

The Pythagorean fuzzy hypersoft set (PFHSS) is the most advanced extension of the intuitionistic fuzzy hypersoft set (IFHSS) and a suitable extension of the Pythagorean fuzzy soft set. In it, we discuss the parameterized family that contracts with the multi-subattributes of the parameters. The PFHSS is used to correctly assess insufficiencies, anxiety, and hesitancy in decision-making (DM). It is the most substantial notion for relating fuzzy data in the DM procedure, which can accommodate more uncertainty compared to available techniques considering membership and nonmembership values of each subattribute of given parameters. In this paper, we will present the operational laws for Pythagorean fuzzy hypersoft numbers (PFHSNs) and also some fundamental properties such as idempotency, boundedness, shift-invariance, and homogeneity for Pythagorean fuzzy hypersoft weighted average (PFHSWA) and Pythagorean fuzzy hypersoft weighted geometric (PFHSWG) operators. Furthermore, a novel multicriteria decision-making (MCDM) approach has been established utilizing presented aggregation operators (AOs) to resolve decision-making complications. To validate the useability and pragmatism of the settled technique, a brief comparative analysis has been conducted with some existing approaches.