A rough set model based on fuzzifying neighborhood systems

Li, Lingqiang; Jin, Qiu; Bing-xue, Yao; Wu, Jiamin

doi:10.1007/s00500-020-04744-8

Cited by 19 publications

(6 citation statements)

References 55 publications

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“…Classical rough set theory is based on equivalence relations. However, the equivalence relation is too restrictive for most applications, thus fuzzification becomes another important method to get extensions of the classical rough set models Prade, 1990, 1992;Li et al, 2020). In the framework of relation-based fuzzy rough set theory, various fuzzy generalizations of approximation operators have been proposed and investigated.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy rough sets based on modular hememetrics

Zhang

Yao

2022

Preprint

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In this paper, we introduce a notion of modular hemimetrics, an extension of hemimetrics and modular metrics, as the basic structure to define and study fuzzy rough sets by using the usual addition and subtraction of real numbers. We define a pair of fuzzy upper and lower approximation operators and investigate their properties and interrelations. It is shown that upper definable sets and lower definable sets are equivalent. Definable sets form an Alexandrov fuzzy topology such that the upper and lower approximation operators are the closure and the interior operators respectively. At the end, an application of the modular hemimetrics based fuzzy rough set to the acquisition of color gradient images is proposed.

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Section: Introductionmentioning

confidence: 99%

Fuzzy rough sets based on modular hememetrics

Zhang

Yao

2022

Preprint

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“…Therefore, the classical rough set model has been proved to be useful in discovering the decision rules of the complete information systems. It is well known that the requirements of equivalence relation are too strict, so the equivalence relation is extended to any binary relation [7,31], covering [22,50], neighborhood(systems) [4,14,16,39,[42][43][44].…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, combined with fuzzy sets, rough sets are also extended to fuzzy environments [15,23,24,27,38]. For instance, the (fuzzy) relation-based fuzzy rough sets [5,7,31,38], the fuzzy covering-based fuzzy rough sets [18,22] and the fuzzy neighborhood (systems)-based fuzzy rough sets [6,11,16,40,55].…”

Section: Introductionmentioning

confidence: 99%

L-fuzzy generalized neighborhood systems-based pessimistic L-fuzzy rough sets and its applications

Gao

Bing-xue

2022

Preprint

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In this paper, a notion of L-fuzzy generalized neighborhood system is introduced and then a novel L-fuzzy rough sets based on it are defined and discussed. It is verified that model is an extension of Pang’s generalized neighborhood system-based pessimistic rough sets, and so called L-fuzzy generalized neighborhood system-based pessimistic L-fuzzy rough sets. Firstly, the basic properties of the pessimistic L-fuzzy rough sets is studied. Later, to regain some Pawlak’s prop- erties those are lost in pessimistic L-fuzzy rough sets, the serial, reflexive, transitive and symmetric conditions for L-fuzzy general neighborhood systems are defined. Secondly, the axiomatic researches of the pessimistic L- fuzzy rough sets (include the serial, reflexive and sym- metric cases) are given. Thirdly, a reduction theory based on preserving L-fuzzy approximation operators is established. Finally, one applied in information system, i.e., a three-way decision model based on pessimistic L- fuzzy rough sets, is builded. A simple practical example to show the effectiveness of our model is also presented.

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“…(Fuzzy) rough sets are closely related to (fuzzy) topology [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42]. e well-known result may be that there is a one-toone correspondence between reflexive and transitive (fuzzy) approximation spaces and quasidiscrete (fuzzy) topological spaces [26,37,38].…”

Section: Introductionmentioning

confidence: 99%

A New Single-Valued Neutrosophic Rough Sets and Related Topology

Jin

et al. 2021

Journal of Mathematics

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(Fuzzy) rough sets are closely related to (fuzzy) topologies. Neutrosophic rough sets and neutrosophic topologies are extensions of (fuzzy) rough sets and (fuzzy) topologies, respectively. In this paper, a new type of neutrosophic rough sets is presented, and the basic properties and the relationships to neutrosophic topology are discussed. The main results include the following: (1) For a single-valued neutrosophic approximation space U , R , a pair of approximation operators called the upper and lower ordinary single-valued neutrosophic approximation operators are defined and their properties are discussed. Then the further properties of the proposed approximation operators corresponding to reflexive (transitive) single-valued neutrosophic approximation space are explored. (2) It is verified that the single-valued neutrosophic approximation spaces and the ordinary single-valued neutrosophic topological spaces can be interrelated to each other through our defined lower approximation operator. Particularly, there is a one-to-one correspondence between reflexive, transitive single-valued neutrosophic approximation spaces and quasidiscrete ordinary single-valued neutrosophic topological spaces.

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A rough set model based on fuzzifying neighborhood systems

Cited by 19 publications

References 55 publications

Fuzzy rough sets based on modular hememetrics

Fuzzy rough sets based on modular hememetrics

L-fuzzy generalized neighborhood systems-based pessimistic L-fuzzy rough sets and its applications

A New Single-Valued Neutrosophic Rough Sets and Related Topology

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