Abstract
The objective of this article is to explore and generalize the notions of soft set and rough set along with spherical fuzzy set and to introduce the novel concept called spherical fuzzy soft rough set that is free from all those complications faced by many modern concepts like intuitionistic fuzzy soft rough set, Pythagorean fuzzy soft rough set, and q-rung orthopair fuzzy soft rough set. Since aggregation operators are the fundamental tools to translate the complete information into a distinct number, so some spherical fuzzy soft rough new average aggregation operators are introduced, such as spherical fuzzy soft rough weighted average, spherical fuzzy soft rough ordered weighted average, and spherical fuzzy soft rough hybrid average aggregation operators. Also, the basic characteristics of these introduced operators have been elaborated in detail. Furthermore, a multi-criteria decision-making (MCDM) technique has been developed and a descriptive example is given to support newly presented work. At the end of this article, a comparative study of the introduced technique has been established that shows how our work is more superior and efficient compared to the picture fuzzy soft set.
Highlights
Fuzzy set theory is the extension of the crisp set theory introduced by Zadeh [1] and the idea of the fuzzy set was presented that considers only positive grade
intuitionistic fuzzy set (IFS) has attained more importance since its appearance and it has been widely used in decision-making problems, such as some intuitionistic fuzzy frank power aggregation operators are conceived by Zhang et al [3]
Yager [6] presented the design of Pythagorean fuzzy set (PyFS) as a generalization of IFS in which we use the necessary condition given as 0 ≤ ƒ2 + h2 ≤ 1
Summary
Fuzzy set theory is the extension of the crisp set theory introduced by Zadeh [1] and the idea of the fuzzy set was presented that considers only positive grade. Atanassov [2] introduced the notion of an intuitionistic fuzzy set (IFS) as an extension of fuzzy set in which we consider the positive grade as well as negative grade with the condition that the sum (positive grade, negative grade) is less than or equal to 1. Seikh and Mandal [4] introduced some intuitionistic fuzzy Dombi aggregation operators and applied them to MCDM problems. Note that in IFS, the restriction sum (ƒ, h) ∈ [0, 1] limits the possibility of positive grade "ƒ" and negative grade "h". To avoid this condition, Yager [6] presented the design of Pythagorean fuzzy set (PyFS) as a generalization of IFS in which we use the necessary condition given as 0 ≤ ƒ2 + h2 ≤ 1
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