Characterizations of coverings for upper approximation operators being closure operators

Bian, Xiaoxia; Wang, Pei; Bai, Xin; Chen, Bin

doi:10.1016/j.ins.2015.03.060

Cited by 11 publications

(3 citation statements)

References 40 publications

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“…e topological interior and closure operators are two basic definitions in the topological theory. e theory of topology has a close contact with the theory of rough set based on the connections between the topological interior and closure operators and the lower and upper approximation operators, and there exists much result on relationships between topology and covering rough sets [20,[33][34][35][36][37][38][39]. Moreover, topological reductions for three types of covering rough sets in covering information systems have been discussed [40].…”

Section: Introductionmentioning

confidence: 99%

Numerical Characterizations of Topological Reductions of Covering Information Systems in Evidence Theory

Zhang

2021

Mathematical Problems in Engineering

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The reductions of covering information systems in terms of covering approximation operators are one of the most important applications of covering rough set theory. Based on the connections between the theory of topology and the covering rough set theory, two kinds of topological reductions of covering information systems are discussed in this paper, which are characterized by the belief and plausibility functions from the evidence theory. The topological spaces by two pairs of covering approximation operators in covering information systems are pseudo-discrete, which deduce partitions. Then, using plausibility function values of the sets in the partitions, the definitions of significance and relative significance of coverings are presented. Hence, topological reduction algorithms based on the evidence theory are proposed in covering information systems, and an example is adopted to illustrate the validity of the algorithms.

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Section: Introductionmentioning

confidence: 99%

Numerical Characterizations of Topological Reductions of Covering Information Systems in Evidence Theory

Zhang

2021

Mathematical Problems in Engineering

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“…Chen and Li defined open sets, closed sets, rough inclusion, rough equality on covering rough sets and studied some of their properties [7][8][9]. Ge, Bai, Yun, Bian and Wang gave topological characterizations of the covering C for covering upper approximation operators to be closure operators [2,12]. Restrepo and Gómez investigated properties of covering approximation operators being closure and topological closure in a framework of sixteen pairs of dual approximation operators [28].…”

Section: Introductionmentioning

confidence: 99%

Topological structures of a type of granule based covering rough sets

Zhang¹,

Li²

2018

Filomat

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Rough set theory is one of important models of granular computing. Lower and upper approximation operators are two important basic concepts in rough set theory. The classical Pawlak approximation operators are based on partition and have been extended to covering approximation operators. Covering is one of the fundamental concepts in the topological theory, then topological methods are useful for studying the properties of covering approximation operators. This paper presents topological properties of a type of granular based covering approximation operators, which contains seven pairs of approximation operators. Then, topologies are induced naturally by the seven pairs of covering approximation operators, and the topologies are just the families of all definable subsets about the covering approximation operators. Binary relations are defined from the covering to present topological properties of the topological spaces, which are proved to be equivalence relations. Moreover, connectedness, countability, separation property and Lindelöf property of the topological spaces are discussed. The results are not only beneficial to obtain more properties of the pairs of covering approximation operators, but also have theoretical and actual significance to general topology.

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“…G. Liu also used axiomatic method to characterize covering-based rough sets [41][42][43]. X. Bian et al gave characterizations of covering-based approximation spaces being closure operators [31]. Ge et al proposed not only general, but also topological characterizations of coverings for these operators being closure operators [25,[29][30].…”

Section: Introductionmentioning

confidence: 99%

The characterizations of upper approximation operators based on special coverings

Wang

2017

Open Mathematics

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Abstract:In this paper, we discuss the approximation operators apr NS and apr S which are based on NS.U / and S. We not only obtain some properties of NS.U / and S, but also give examples to show some special properties. We also study sufficient and necessary conditions when they become closure operators. In addition, we give general and topological characterizations of the covering for two types of covering-based upper approximation operators being closure operators.

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Characterizations of coverings for upper approximation operators being closure operators

Cited by 11 publications

References 40 publications

Numerical Characterizations of Topological Reductions of Covering Information Systems in Evidence Theory

Numerical Characterizations of Topological Reductions of Covering Information Systems in Evidence Theory

Topological structures of a type of granule based covering rough sets

The characterizations of upper approximation operators based on special coverings

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