Abstract
Keeping in view the importance of new defined and well growing spherical fuzzy sets, in this study, we proposed a novel method to handle the spherical fuzzy multi-criteria group decision-making (MCGDM) problems. Firstly, we presented some novel logarithmic operations of spherical fuzzy sets (SFSs). Then, we proposed series of novel logarithmic operators, namely spherical fuzzy weighted average operators and spherical fuzzy weighted geometric operators. We proposed the spherical fuzzy entropy to find the unknown weights information of the criteria. We study some of its desirable properties such as idempotency, boundary and monotonicity in detail. Finally, the detailed steps for the spherical fuzzy decision-making problems were developed, and a practical case was given to check the created approach and to illustrate its validity and superiority. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our proposed method. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative.
Highlights
The complication of a system is growing every day in real life and getting the finest option from the set of possible ones is difficult for the decision makers
We develop a spherical fuzzy multi-criteria decision-making (MCDM) method based on the logarithmic aggregation operators, with the logarithmic operations of the spherical fuzzy sets (SFSs) handling spherical fuzzy MCDM within SFSs
We have revealed a novel logarithmic operation of SFSs with the real base number σ
Summary
The complication of a system is growing every day in real life and getting the finest option from the set of possible ones is difficult for the decision makers. There is little investigation on logarithmic operations on the IFSs and PyFSs. there is little investigation on logarithmic operations on the IFSs and PyFSs Motivated by these ideas, we develop a spherical fuzzy MCDM method based on the logarithmic aggregation operators, with the logarithmic operations of the spherical fuzzy sets (SFSs) handling spherical fuzzy MCDM within SFSs. the goal of this article is to propose the decision-making method for MCDM problems in which there exist the interrelationships among the criteria. In order to attain the research goal that has been stated above, the organization of this article is offered as: Section 2 concentrates on some basic notions and operations of existing extensions of fuzzy set theories and some discussion to propose the spherical fuzzy entropy.
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