Journal ArticleDOI
A new rough set theory: rough soft hemirings
TLDR
The aim of this paper is to introduce the notion of a rough soft hemiring, which is an extended notion ofa rough hemiring and a soft hemires, and to study roughness in soft hemirings with respect to Pawlak approximation spaces.Abstract:
The aim of this paper is to introduce the notion of a rough soft hemiring, which is an extended notion of a rough hemiring and a soft hemiring. We study roughness in soft hemirings with respect to Pawlak approximation spaces. Some new rough soft operations are explored. In particular, lower and upper rough soft hemirings and k-idealistic, h-idealistic, strong h-idealistic idealistic soft hemirings are investigated. Finally, an important result on an upper strong h-idealistic rough soft hemiring via Bourne's congruence relations are obtained.read more
Citations
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Journal ArticleDOI
Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems
Journal ArticleDOI
On a novel uncertain soft set model
TL;DR: A kind of novel soft set model called a Z-soft fuzzy rough set is presented by means of three uncertain models: soft sets, rough sets and fuzzy sets, which is an important generalization of Z- soft rough fuzzy sets.
Journal ArticleDOI
A novel soft rough set
TL;DR: The concept of soft rough hemirings is introduced, which is an extended notion of a rough hemiring, which provides a new research idea for soft rough algebraic research.
Journal ArticleDOI
Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes
Bingzhen Sun,Weimin Ma,Xia Xiao +2 more
TL;DR: A new approach to multiple criteria group decision making problems, based on variable precision multigranulation fuzzy decision-theoretic rough set over two universes, and a cost-based method for sorting among all alternatives of group decision-making problems are established.
Journal ArticleDOI
Multigranulation fuzzy rough set over two universes and its application to decision making
TL;DR: The proposed models not only enrich the theory of multigranulation rough set but also make a tentative to provide a new perspective for multiple criteria group decision making with uncertainty.
References
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Book
Fuzzy sets
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Journal ArticleDOI
Soft set theory—First results
TL;DR: The main purpose of this paper is to introduce the basic notions of the theory of soft sets, to present the first results of the the theory, and to discuss some problems of the future.
Journal ArticleDOI
Soft set theory
TL;DR: The authors define equality of two soft sets, subset and super set of a soft set, complement of asoft set, null soft set and absolute soft set with examples and De Morgan's laws and a number of results are verified in soft set theory.
Journal ArticleDOI
Rudiments of rough sets
Zdziasław Pawlak,Andrzej Skowron +1 more
TL;DR: The basic concepts of rough set theory are presented and some rough set-based research directions and applications are pointed out, indicating that the rough set approach is fundamentally important in artificial intelligence and cognitive sciences.