Abstract
Rough set approaches encounter uncertainty by means of boundary regions instead of membership values. In this paper, we develop the topological structure on soft rough set ( SR -set) by using pairwise SR -approximations. We define SR -open set, SR -closed sets, SR -closure, SR -interior, SR -neighborhood, SR -bases, product topology on SR -sets, continuous mapping, and compactness in soft rough topological space ( SRTS ). The developments of the theory on SR -set and SR -topology exhibit not only an important theoretical value but also represent significant applications of SR -sets. We applied an algorithm based on SR -set to multi-attribute group decision making (MAGDM) to deal with uncertainty.
Highlights
The problem of imperfect knowledge has been the center of attention for many years.In the field of mathematics, computer science, and artificial intelligence, researchers have used different methods to tackle the problem of uncertain and incomplete data, including probability theory, fuzzy set [1], and rough set [2,3] and soft set techniques [4,5,6]
We present some new results of SR-set theory and SR-topology
Soft rough set with the topology τSR is called a topological SR-set
Summary
The problem of imperfect knowledge has been the center of attention for many years. In the field of mathematics, computer science, and artificial intelligence, researchers have used different methods to tackle the problem of uncertain and incomplete data, including probability theory, fuzzy set [1], and rough set [2,3] and soft set techniques [4,5,6]. Soft set with decision making have studied by many researchers [7,8,9,10,11]. Introduced fuzzy parameterized fuzzy soft set (fpfs-set), fpfs-topology, and fpfs-compact spaces, with some important applications of fpfs-set to decision-making problems. They presented fns-mappings and fixed points of fns-mapping. Neutrosophic set and rough sets with decision making problems have studied by many researchers [34,35,36,37,38,39,40].
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