Rough Substructures Based on Overlaps of Successor in Quantales Under Serial Fuzzy Relations

Abstract

In this research article, a new connection between serial fuzzy relations and an extended version of rough sets in an algebraic structure quantale is established. The extended notion of rough sets consists of successor class and an overlap of the successor class of an element of a quantale. Thus a new approximation space based on serial fuzzy relations via the overlaps of successor in quantales, are introduced. The main purpose of this study is to provide basic algebraic structures based on serial fuzzy-relations. In this way, the new approximation space acquires certain appealing algebraic properties. Compatible fuzzy relations in quantale are being applied to introduce the notions of rough multiplicative set, rough m-system and further rough substructures of quantales. Following that, various quantale substructures are described in terms of successor overlaps under serial fuzzy relations, leading to the development of some key theorems. Moreover, several results including quantale homomorphism between rough substructures and their homomorphic images are provided. It is concluded that this new study is significantly easy and superior to various types of approximations in various types of algebraic structures. Furthermore, different examples are given to show the effectiveness of the developed approach and a comparative study of the investigated approach with some existing methods are expressed broadly which show that the investigated approach are more effective and easy than the existing approaches.

Keywords

• Quantale
• rough ideal
• SFrelations
• TCFR
• rough multiplicative set
• rough m-system