Decision Support System For Energy Source Selection Based On Credibility Fuzzy Information.

This main objective of this work is to define some new operations of credibility fuzzy numbers using Hamacher t-norm and t-conorm. These operation are more generalized operation for credibility fuzzy numnbers, we apply these operations to aggregation operators for credibility fuzzy numbers. Furthermore, using the basic operational laws of Hamacher t-norm and t-conorm, we develop a series of credibility fuzzy Hamacher aggregation operators like credibility fuzzy Hamacher weighted averaging (CFHWA) and credibility fuzzy Hamacher geometric (CFHWG) aggregation operators. we also explained some of the proposed Hamacher aggregation operators properties like commutativity, idempotency and monotonicity. In order to validate the proposed Hamacher aggregation operators for credibility fuzzy numbers, we develop general algorithm for decision making technique under credibility fuzzy numbers and using these operators. The proposed algorithm is apply to electricity crises in Pakistan problems. Finally a comparison with other existing methods is done to check the accuracy and validation of the proposed methods. At rest the proposed method is verified by other well known methods.

Uncertainty evaluations through interval-valued Pythagorean hesitant fuzzy Archimedean aggregation operators in multicriteria decision making

In many cases, use of Pythagorean hesitant fuzzy sets may not be sufficient to characterize uncertain information associated with decision making problems. From that view point the concept of interval-valued Pythagorean hesitant fuzzy sets are introduced in this paper. Considering the flexibility with the general parameters, Archimedean t-conorms and t-norms are applied to develop several operational laws in interval-valued Pythagorean hesitant fuzzy environment. Some characteristics of the developed operators are presented. The newly developed operators are used to derive a methodology for solving multicriteria decision making problems with interval-valued Pythagorean hesitant fuzzy information. Finally, two illustrative examples are provided to establish the validity of the proposed approach and are compared with the existing technique to exhibit its flexibility and effectiveness.

The operational properties of linguistic interval valued q-Rung orthopair fuzzy information and its VIKOR model for multi-attribute group decision making

As a generalization of linguistic q-rung orthopair fuzzy set (Lq-ROFS), linguistic interval valued q-Rung orthopair fuzzy set (LIVq-ROFS) is a new concept to deal with complex and uncertain decision making problems which Lq-ROFS cannot handle. Due to the lack of information in decision making process, decision makers mostly prefer to give their preferences in interval form rather than a crisp number. In this situations, LIVq-ROFS appears up as a useful tool. In this work, we define operational laws of LIVq-ROFS and prove some properties. Furthermore, we propose the conception of the LIVq-ROF weighted averaging operator and give its formula by mathematical induction. To compare two or more linguistic interval valued q-Rung orthopair fuzzy numbers (LIVq-ROFNs), the improved form of score function is also given. Considering the powerfulness of LIVq-ROFSs handling ambiguity and complex uncertainty in practical problems, the key innovation of this paper is to develop the linguistic interval-valued q-rung orthopair fuzzy VIKOR model that is significantly different from the existing VIKOR methodology. The computing steps of this newly created model are briefly presented. Finally, the effectiveness of model is verified by an example and through comparative analysis, the superiority of VIKOR method is further illustrated.

Some New Logarithmic Aggregation Operators and their Application to Group Decision Making Problem Based on t-Norm and t-Conorm

In this paper, a logarithmic operational law for intuitionistic fuzzy numbers is defined, in which the based1 is a real number such that1 ∈(0,1) with condition1 ≠ 1. Some properties of logarithmic operational laws have been studied and based on these, several Einstein averaging and Einstein geometric operators namely, logarithmic intuitionistic fuzzy Einstein weighted averaging (LIFEWA) operator, logarithmic intuitionistic fuzzy Einstein ordered weighted averaging (LIFEOWA) operator, logarithmic intuitionistic fuzzy Einstein hybrid averaging (LIFEHA) operator, logarithmic intuitionistic fuzzy Einstein weighted geometric (LIFEWG) operator, logarithmic intuitionistic fuzzy Einstein ordered weighted geometric (LIFEOWG) operator, and logarithmic intuitionistic fuzzy Einstein hybrid geometric (LIFEHG) operator have been introduced, which can overcome the weaknesses of algebraic operators. Furthermore, based on the proposed operators a multi-attribute group decision-making problem is established under logarithmic operational laws. Finally, an illustrative example is used to illustrate the applicability and validity of the proposed approach and compare the results with the existing methods to show the effectiveness of it.

Heronian Mean Operators Based on Novel Complex Linear Diophantine Uncertain Linguistic Variables and Their Applications in Multi-Attribute Decision Making

In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to truth, falsity, reference parameters, and their uncertain linguistic terms to handle problematic and challenging data in factual life impasses. By using the elaborated CLDULSs, some operational laws are also settled. Furthermore, by using the power Einstein (PE) aggregation operators based on CLDULS: the complex linear Diophantine uncertain linguistic PE averaging (CLDULPEA), complex linear Diophantine uncertain linguistic PE weighted averaging (CLDULPEWA), complex linear Diophantine uncertain linguistic PE Geometric (CLDULPEG), and complex linear Diophantine uncertain linguistic PE weighted geometric (CLDULPEWG) operators, and their useful results are elaborated with the help of some remarkable cases. Additionally, by utilizing the expounded works dependent on CLDULS, I propose a multi-attribute decision-making (MADM) issue. To decide the quality of the expounded works, some mathematical models are outlined. Finally, the incomparability and relative examination of the expounded approaches with the assistance of graphical articulations are evolved.

A further investigation on q-rung orthopair fuzzy Einstein aggregation operators

Aggregation of q-rung orthopair fuzzy information serves as an important branch of the q-rung orthopair fuzzy set theory, where operations on q-rung orthopair fuzzy values (q-ROFVs) play a crucial role. Recently, aggregation operators on q-ROFVs were established by employing the Einstein operations rather than the algebraic operations. In this paper, we give a further investigation on operations and aggregation operators for q-ROFVs based on the Einstein operational laws. We present the operational principles of Einstein operations over q-ROFVs and compare them with those built on the algebraic operations. The properties of the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator and q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator are investigated in detail, such as idempotency, monotonicity, boundedness, shift-invariance and homogeneity. Then, the developed operators are applied to multiattribute decision making problems under the q-rung orthopair fuzzy environment. Finally, an example for selecting the design scheme for a blockchain-based agricultural product traceability system is presented to illustrate the feasibility and effectiveness of the proposed methods.

Correlation Measures for Cubic m-Polar Fuzzy Sets with Applications

A cubic m -polar fuzzy set (CmPFS) is a new hybrid extension of m -polar fuzzy set and cubic set. A CmPFS is a robust model to express multipolar information in terms of m fuzzy intervals representing membership grades and m fuzzy numbers representing nonmembership grades. In this article, we explore some new operational laws of CmPFSs, produce some related results, and discuss their consequences. We propose relative informational coefficients and relative noninformational coefficients for CmPFSs. These coefficients are analyzed to investigate further properties of CmPFSs. Based on these coefficients, we introduce new correlation measures and their weighted versions for CmPFSs. The value of proposed correlation measures is symmetrical and lies between −1 and 1. Moreover, the applications of the proposed correlation in pattern recognition and medical diagnosis are developed. The feasibility and efficiency of suggested correlation measures is determined by respective illustrative examples.

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.