Journal ArticleDOI
A novel soft rough set
Jianming Zhan,Qi Liu,Tutut Herawan +2 more
- Vol. 54, pp 393-402
TLDR
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.Abstract:
Graphical abstractDisplay Omitted In this paper, we investigate the relationships among rough sets, soft sets and hemirings. The concept of soft rough hemirings is introduced, which is an extended notion of a rough hemiring. It is pointed out that in this paper, we first apply soft rough sets to algebraic structure-hemirings. Further, we first put forward the concepts of C-soft sets and CC-soft sets, which provide a new research idea for soft rough algebraic research. Moreover, we study roughness in hemirings with respect to MSR-approximation spaces. Some new soft rough operations over hemirings are explored. In particular, lower and upper MSR-hemirings (k-ideal and h-ideal) are investigated. Finally, we put forth an approach for multicriteria group decision making problem based on modified soft rough sets and offer an actual example.read more
Citations
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Journal ArticleDOI
Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure.
Xindong Peng,Harish Garg +1 more
TL;DR: A new score function for interval-valued fuzzy number is proposed for tackling the comparison problem, the formulae of information measures are introduced and their transformation relations are pioneered, and the objective weights of various parameters are determined via new entropy method.
Journal ArticleDOI
A novel three-way decision model under multiple-criteria environment
TL;DR: This paper proposes a novel decision model based on the combination of three-way decisions and multi-criteria decision-making (MCDM), and proposes an aggregation method of loss functions to reflect the comprehensive losses of alternatives.
Journal ArticleDOI
A novel type of soft rough covering and its application to multicriteria group decision making
TL;DR: A novel type of soft rough covering is introduced by means of soft neighborhoods, and then it is used to improve decision making in a multicriteria group environment.
Journal ArticleDOI
N-soft sets and their decision making algorithms
TL;DR: This paperMotivated and introduced the concept of N-soft set as an extended soft set model, which is a cogent model for binary and non-binary evaluations in numerous kinds of decision making problems.
Journal ArticleDOI
A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making
Jianming Zhan,Kuanyun Zhu +1 more
TL;DR: The notion of Z-soft rough fuzzy sets of hemirings is introduced, which is an extended notion of soft rough sets andrough fuzzy sets that removes the limiting condition that full soft sets require in Feng-soft rougher sets and Meng-soft Rough fuzzy sets.
References
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Rough sets
TL;DR: This approach seems to be of fundamental importance to artificial intelligence (AI) and cognitive sciences, especially in the areas of machine learning, knowledge acquisition, decision analysis, knowledge discovery from databases, expert systems, decision support systems, inductive reasoning, and pattern recognition.
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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.