Multigranulation with different grades rough set in ordered information system

Abstract

The the graded rough set and multi-granulation rough set are two significant extended rough set models, both constructed on the the indiscernibility relations. The purpose of this paper is to study the good points of graded rough set in the multi-granulation environment which in different granule have different grades in ordered information system. Three new types multi-granulation with different grades rough set models are proposed, which include optimistic multi-granulation with different grades, pessimistic multi-granulation with different grades and the mean multi-granulation with different grades rough set. Then, their principal structure are studied, and their basic properties are obtained as well. Finally, we study a case about students' achievement estimate the performance of the proposed properties. In the viewpoint of granular computing, our study extension the classical rough set theory.

Multi-Granulation Graded Rough Intuitionistic Fuzzy Sets Models Based on Dominance Relation

“…References [13][14][15][16][17] discussed GRS in a multi-granulation environment. Moreover, for GRS, it has been studied that the equivalence relation has been extended to the dominance relation [13,14], the limited tolerance relation [17] and so forth [10,11]. In general, all these aforementioned studies have naturally contributed to the development of GRS.…”

“…Inspired by the research reported in References [5,[13][14][15][16][17], intuitionistic fuzzy sets (IFS) are also a theory which describe uncertainty [18]. IFS consisting of a membership function and a non-membership function are commonly encountered in uncertainty, imprecision, and vagueness [18].…”