Spherical fuzzy sets (SFSs) are a new extension of Cuong's picture fuzzy sets (PFSs). In SFSs, membership degrees satisfy the condition 0≤P2(x)+I2(x)+N2(x)≤1 instead of 0≤P(x)+I(x)+N(x)≤1 as is in PFSs. In the present work, we extend different strict archimedean triangular norm and conorm to aggregate spherical fuzzy information. Firstly, we define the SFS and discuss some operational rules. Generalized spherical aggregation operators for spherical fuzzy numbers utilizing these strict Archimedean t‐norm and t‐conorm are proposed. Finally, based on these operators, a decision‐making method has been established for ranking the alternatives by utilizing a spherical fuzzy environment. The suggested technique has been demonstrated with a descriptive example for viewing their effectiveness as well as reliability. A test checking the reliability and validity has also been conducted for viewing the supremacy of the suggested technique.

Spherical aggregation operators and their application in multiattribute group decision‐making

As the extension of fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, and picture fuzzy set, the spherical fuzzy set is characterized by three functions expressing the positive-membership degree, the neutral-membership degree and the negative-membership degree which the sum squares of them is equal or less than 1. In this work, we shall present some novel Dice similarity measures of spherical fuzzy sets and the generalized Dice similarity measures of spherical fuzzy sets and indicates that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based multiple attribute group decision making models with spherical fuzzy information. Then, we apply the generalized Dice similarity measures between spherical fuzzy sets to multiple attribute group decision making. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for selecting the desirable ERP system.

https://informatica.vu.lt/journal/INFORMATICA/article/875/file/pdf

The Generalized Dice Similarity Measures for Picture Fuzzy Sets and Their Applications

Reasonable and effective assessment of express service quality can help express company discover its own shortcomings and overcome them, which is crucial significant to enhance its service quality. When considering the decision assessment of express company, the key issue that emerge powerful ambiguity. Pythagorean fuzzy set as an efficient math tool can capture the indeterminacy successfully. The major focus of this manuscript is to explore various interactive Hamacher power aggregation operators for Pythagorean fuzzy numbers. Firstly, we defined novel interactive Hamacher operation, on this basis we presented some Pythagorean fuzzy interactive Hamacher power aggregation operators such as Pythagorean fuzzy interactive Hamacher power average, weighted average (PFIHPWA), ordered weighted average, Pythagorean fuzzy interactive Hamacher power geometric, weighted geometric (PFIHPWG) and ordered geometric operators,respectively. Meanwhile, we verified their general properties and specific cases as well. The salient feature of proposed operators is that they can not only reduce the impact of negative data and consider the interactions between membership and nonmembership degrees, but also provide more general results through a parameter. Secondly, we defined a Pythagorean fuzzy entropy measure, and then establish a method to determine the attribute weights. Further, based on the conceived PFIHPWA and PFIHPWG operators we explored a novel approach to manage multiple attribute decision making problems. At last, the proposed techniques are carried out in a real application concerning on the assessment of express service quality to display the applicability and effectiveness, as well as the influence of changed parameters on the results. In addition, its advantages are displayed by a systematic comparison with relevant approaches.

https://link.springer.com/content/pdf/10.1007/s00500-020-05193-z.pdf

Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight

Abstract Heronian mean (HM) operator has the advantages of considering the interrelationships between parameters, and linguistic intuitionistic fuzzy number (LIFN), in which the membership and non-membership are expressed by linguistic terms, can more easily describe the uncertain and the vague information existing in the real world. In this paper, we propose the partitioned Heronian mean (PHM) operator which assumes that all attributes are partitioned into several parts and members in the same part are interrelated while in different parts there are no interrelationships among members, and develop some new operational rules of LIFNs to consider the interactions between membership function and non-membership function, especially when the degree of non-membership is zero. Then we extend PHM operator to LIFNs based on new operational rules, and propose the linguistic intuitionistic fuzzy partitioned Heronian mean (LIFPHM) operator, the linguistic intuitionistic fuzzy weighted partitioned Heronian mean (LIFWPHM) operator, the linguistic intuitionistic fuzzy partitioned geometric Heronian mean (LIFPGHM) operator and linguistic intuitionistic fuzzy weighted partitioned geometric Heronian mean (LIFWPGHM) operator. Further, we develop two methods to solve multi-attribute group decision making (MAGDM) problems with the linguistic intuitionistic fuzzy information. Finally, we give some examples to verify the effectiveness of two proposed methods by comparing with the existing

Partitioned Heronian Means Based on Linguistic Intuitionistic Fuzzynumbers for Dealing with Multi-Attribute Group Decision Making

Inventive problem-solving map of innovative carbon emission strategies for solar energy-based transportation investment projects

Spherical fuzzy sets and their applications in multi-attribute decision making problems

The main objective of proposed work is to introduce a series of picture fuzzy weighted geometric aggregation operators by using t-norm and t-conorm. In this paper, we discussed generalized form of weighted geometric aggregation operator for picture fuzzy information. Further, the proposed geometric aggregation operators of picture fuzzy number are applied to multi-attribute group decision making problems. Also, we propose the TOPSIS method to aggregate the picture fuzzy information. To implement the proposed models, we provide some numerical applications of group decision making problems. Also compared with previous model, we conclude that the proposed technique is more effective and reliable.

Different Approaches to Multi-Criteria Group Decision Making Problems for Picture Fuzzy Environment

Spherical fuzzy sets (SFSs), recently proposed by Ashraf, is one of the most important concept to describe the fuzzy information in the process of decision making. In SFSs the sum of the squares of memberships grades lies in close unit interval and hence accommodate more uncertainties. Thus, this set outperforms over the existing structures of fuzzy sets. In real decision making problems, there is often a treat regarding a neutral character towards the membership and non-membership degrees expressed by the decision-makers. To get a fair decision during the process, in this paper, we define some new operational laws by Dombi t-norm and t-conorm. In the present study, we propose Spherical fuzzy Dombi weighted averaging (SFDWA), Spherical fuzzy Dombi ordered weighted averaging (SFDOWA), Spherical fuzzy Dombi hybrid weighted averaging (SFDHWA), Spherical fuzzy Dombi weighted geometric (SFDWG), Spherical fuzzy Dombi ordered weighted geometric (SFDOWG) and Spherical fuzzy Dombi hybrid weighted geometric (SFDHWG) aggregation operators and discuss several properties of these aggregation operators. These aforesaid operators are enormously used to help a successful solution of the decision problems. Then an algorithm by using spherical fuzzy set information in decision-making matrix is developed and applied the algorithm to decision-making problem to illustrate its applicability and effectiveness. Through this algorithm, we proved that our proposed approach is practical and provides decision makers a more mathematical insight before making decisions on their options. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our method. Results indicate that the proposed method is suitable and effective for decision process to evaluate their best alternative.

Shahzaib Ashraf

Papers

Spherical fuzzy sets and their applications in multi-attribute decision making problems

Spherical aggregation operators and their application in multiattribute group decision‐making

Different Approaches to Multi-Criteria Group Decision Making Problems for Picture Fuzzy Environment

Spherical fuzzy Dombi aggregation operators and their application in group decision making problems

Spherical fuzzy sets and its representation of spherical fuzzy t-norms and t-conorms