Abstract
In real life, human opinion cannot be limited to yes or no situations as shown in an ordinary fuzzy sets and intuitionistic fuzzy sets but it may be yes, abstain, no, and refusal as treated in Picture fuzzy sets or in Spherical fuzzy (SF) sets. In this article, we developed a comprehensive model to tackle decision-making problems, where strong points of view are in the favour; neutral; and against some projects, entities, or plans. Therefore, a new approach of covering-based spherical fuzzy rough set (CSFRS) models by means of spherical fuzzy β -neighborhoods (SF β -neighborhoods) is adopted to hybrid spherical fuzzy sets with notions of covering the rough set. Then, by using the principle of TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) to present the spherical fuzzy, the TOPSIS approach is presented through CSFRS models by means of SF β -neighborhoods. Via the SF-TOPSIS methodology, a multi-attribute decision-making problem is developed in an SF environment. This model has stronger capabilities than intuitionistic fuzzy sets and picture fuzzy sets to manage the vague and uncertainty. Finally, the proposed method is demonstrated through an example of how the proposed method helps us in decision-making problems.
Highlights
The dominant notion of q Fuzzy set by Zadeh [1] plays a vital role in the field of mathematics.This theory brought a revolution in the field mathematics and in science and technology.Different direct and indirect generalizationw of this theory have been made which are successfully applied to solve the problems of real situations
Cuong [6] originated the notion of Picture fuzzy set (PFS) which was consider as a successful extension of Intuitionistic fuzzy set (IFS) by put together the ideas of the membership grade (MG), neutral grade (NG), and nonmembership grade (NMG) of an object with the condition that the sum of these three grades belong to the unit closed interval [0, 1]; for details of the study, see References [7,8,9]
A new approach is adopted to hybrid spherical fuzzy sets with notions of covering rough set and TOPSIS, and their application is presented in multi-attribute decision making
Summary
The dominant notion of q Fuzzy set by Zadeh [1] plays a vital role in the field of mathematics. Yager enquired this scenario in References [3,4] and initiated the notion of a Pythagorean fuzzy set (PytFS) This concept became more favorable among the scholars and was considered a significant generalization of IFSs. The main difference between IFSs and PytFSs is that, in the case of PytFSs, the sum of MG and NMG is greater than 1, but their squares sum belong to the unit interval [0, 1]. Cuong [6] originated the notion of Picture fuzzy set (PFS) which was consider as a successful extension of IFSs by put together the ideas of the MG, NG, and NMG of an object with the condition that the sum of these three grades belong to the unit closed interval [0, 1]; for details of the study, see References [7,8,9].
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