Soft rough fuzzy sets and soft fuzzy rough sets
TLDR
A new soft rough set model is proposed and its properties are derived and a more general model called soft fuzzy rough set is established.Abstract:
Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed.read more
Citations
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Journal ArticleDOI
Generalized picture distance measure and applications to picture fuzzy clustering
TL;DR: A generalized picture distance measure is proposed and integrated to a novel hierarchical picture fuzzy clustering method called Hierarchical Picture Clustering (HPC) and Experimental results show that the clustering quality of the proposed algorithm is better than those of the relevant ones.
Journal ArticleDOI
A survey of decision making methods based on certain hybrid soft set models
Xueling Ma,Qi Liu,Jianming Zhan +2 more
TL;DR: Some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets are reviewed, providing several novel algorithms in decision making problems by combining these kinds of hybrid models.
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 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.
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A survey of decision making methods based on two classes of hybrid soft set models
TL;DR: By compromising the above three uncertain theories, some reviews to DM methods based on two classes of hybrid soft models: SRF-sets and SFR-sets are elaborate and an overview of techniques based on the involved hybrid soft set models is expatiate.
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.
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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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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.
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Rough fuzzy sets and fuzzy rough sets
Didier Dubois,Henri Prade +1 more
TL;DR: It is argued that both notions of a rough set and a fuzzy set aim to different purposes, and it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems.