h. garg

The conception of T-spherical fuzzy set (TSFS) is a recent phenomenon in the environment of fuzzy notions that describe opinion about some certain objects under uncertainties with the help of four types of degrees known as the degree of membership (DM), degree of abstinence (DA), degree of non-membership (DNM) and degree of refusal (DR). The focus of this manuscript, to examine the interrelationship among any numbers of T-spherical fuzzy numbers (TSFNs) by the use Maclaurin symmetric mean (MSM) operators. We investigate and develop T-spherical fuzzy (TSF) MSM (TSFMSM) operator, TSF weighted MSM (TSFWMSM) operator, TSF dual MSM (TSFDMSM) operator, TSF weighted dual MSM (TSFWDMSM) operator. By using these investigated operators, some special cases of the explored operators are also developed, and their properties are examined. In addition, an algorithm for handling multi attribute decision making (MADM) problems based MSM operators in TSF setting. An illustrative example to check the applicability of the MSM operators of TSFSs is presented where the evaluation of technology commercialization is observed. To show the superiority of the newly established MSM operators, a comprehensive comparative study is designed numerically. In view of the comparative analysis, some advantages of the new MSM operators of the TSFNs are stated.

As a generalization of the intuitionistic fuzzy sets (IFSs), complex IFSs (CIFSs) is a powerful and worthy tool to realize the imprecise information by using complex-valued membership degrees with an extra term, named as phase term. Divergence measure is a valuable tool to determine the degree of discrimination between the two sets. Driven by these fundamental characteristics, it is fascinating to manifest some divergence measures to the CIFSs. In this paper, we explain a method to solve the multi-criteria decision-making (MCDM) problem under CIFS environment. For it, firstly, the divergence measures are introduced between two CIFSs and examined their several properties and relations. Secondly, a novel algorithm is given based on the proposed measures to solve the problems in which weights corresponding to criteria are resolved using maximizing deviation method. Thirdly, a reasonable example is provided to verify the developed approach and to exhibit its practicality and utility with a comparative analysis to show its more manageable and adaptable nature.

Multi-criteria group decision-making is a process in which decision makers assess the performance of alternatives on the basis of conflicting criteria to opt the most worthy alternative as solution. TOPSIS and ELECTRE are effective and commonly used methods to solve multiple criteria decision-making problems. The aim of this study is to propose two new models, namely, complex Pythagorean fuzzy TOPSIS (CPF-TOPSIS) method and complex Pythagorean fuzzy ELECTRE I (CPF-ELECTRE I) method, to tackle multiple criteria group decision-making problems comprising complex Pythagorean fuzzy data. In these methods, we compare complex Pythagorean fuzzy numbers on the basis of their score functions. We use revised closeness index for the ranking of alternatives in CPF-TOPSIS method. {In complex Pythagorean fuzzy concordance and discordance sets, we compare the alternatives on being superior and inferior to other alternatives on the basis of score degree, accuracy degree and indeterminacy. In CPF-ELECTRE I method, we use outranking decision graph to obtain the best alternative.} We illustrate the structure of both methods with the help of flow charts. To verify the accuracy of {proposed methods}, we present an explanatory example for selection of best interior designer for a hotel renovation. {We authenticate the proposed techniques by providing a brief comparative analysis of these methods with existing methods}.