Journal ArticleDOI
Fuzzy rough sets, fuzzy preorders and fuzzy topologies
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TLDR
This paper shows that observations made by different authors at different times regarding one-to-one correspondence between the family of fuzzy preorders on a nonempty set and thefamily of all fuzzy topologies on this set satisfying certain extra conditions are essentially equivalent.About:
This article is published in Fuzzy Sets and Systems.The article was published on 2013-01-01. It has received 94 citations till now. The article focuses on the topics: Fuzzy set operations & Fuzzy number.read more
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Intuitionistic fuzzy multigranulation rough sets
TL;DR: This study develops a new multigranulation rough set model, called an intuitionistic fuzzy multigraphic rough set (IFMGRS), that is generalizations ofThree types of IFMGRSs are proposed that are extensions of three existing intuitionism fuzzy rough sets.
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Fuzzy β-covering based (I,T)-fuzzy rough set models and applications to multi-attribute decision-making
TL;DR: This work proposes two novel methodologies to solve MADM problems with evaluation of fuzzy information, which rely on novel and flexible fuzzy rough set models and observes that the optimal selected alternative is the same, which means that these two decision-making methods are reasonable.
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Generalized fuzzy rough approximation operators determined by fuzzy implicators
TL;DR: It is proved that there exists a one-to-one correspondence between the set of all reflexive and T-transitive fuzzy approximation spaces and theset of all fuzzy Alexandrov spaces such that the lower and upper I-fuzzy rough approximation operators in a fuzzy approximation space are, respectively, the fuzzy interior and closure operators in an fuzzy topological space.
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The axiomatic characterizations on L-fuzzy covering-based approximation operators
TL;DR: Focusing on three pairs of widely used L-fuzzy covering-based approximation operators, an axiom set is established for each of them, and their independence is examined.
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An intuitionistic fuzzy graded covering rough set
TL;DR: This study develops a new rough set model, which is a generalization of the β-neighborhood fuzzy covering rough sets and IF rough sets, and examines the IF graded approximation space, uncertainty measures, IF rough set, and computation methods for its reducts.
References
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Journal ArticleDOI
Fuzzy topological spaces and fuzzy compactness
TL;DR: It will be shown in a following publication that contrary to the results obtained up to now, the Tychonoff-product theorem is safeguarded with fuzzy compactness.
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Two views of the theory of rough sets in finite universes
TL;DR: This paper presents and compares two views of the theory of rough sets: the operator-oriented and set-oriented views, which interprets rough set theory as an extension of set theory with two additional unary operators.
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On the generalization of fuzzy rough sets
TL;DR: In this paper, some definitions of upper and lower approximation operators of fuzzy sets by means of arbitrary fuzzy relations are proposed and a special lower approximation operator is applied to a fuzzy reasoning system, which coincides with the Mamdani algorithm.
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Fuzzy preorder and fuzzy topology
Hongliang Lai,Dexue Zhang +1 more
TL;DR: This paper presents, by means of Alexandrov topology for fuzzy preordered sets and specialization order for fuzzy topological spaces, a systematic investigation of the interrelationship between fuzzy pre ordered sets, topological Spaces, and fuzzy topology spaces.
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On the topological properties of fuzzy rough sets
Keyun Qin,Zheng Pei +1 more
TL;DR: It is proved that the set of all lower approximation sets based on a reflexive and transitive fuzzy relation consists of a fuzzy topology which satisfies (TC) axiom; and conversely, a fuzzyTopology which obey (TC).