Fixed points of covering upper and lower approximation operators

Estaji, Ali Akbar; Vatandoost, Mehdi; Pourkhandani, Rahimeh

doi:10.1007/s00500-019-04113-0

Cited by 4 publications

(1 citation statement)

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“…e attribute reduction of datasets in terms of the lower and upper approximation operators is one of most important applications of the rough set theory. e covering rough set is one of the most important extensions of the classical Pawlak rough sets, which has received increasing concern in recent years [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. By using the covering approximation operators, attribute reductions of covering information systems may be unraveled [22][23][24][25][26][27][28][29][30][31][32].…”

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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A fixed point theorem in rough semi-linear uniform spaces

Singh

Tiwari

2021

Theoretical Computer Science

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A study of fixed point sets based on Z-soft rough covering models

Khan

Park

Shoaib

et al. 2022

MATH

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<abstract><p>Z-soft rough covering models are important generalizations of classical rough set theory to deal with uncertain, inexact and more complex real world problems. So far, the existing study describes various forms of approximation operators and their properties by means of soft neighborhoods. In this paper, we propose the notion of $ Z $-soft rough covering fixed point set (briefly, $\mathcal{Z}$-$\mathcal{SRCFP}$-set) induced by covering soft set. We study the conditions that the family of $ \mathcal{Z} $-$ \mathcal{SRCFP} $-sets become lattice structure. For any covering soft set, the $ \mathcal{Z} $-$ \mathcal{SRCFP} $-set is a complete and distributive lattice, and at the same time, it is also a double p-algebra. Furthermore, when soft neighborhood forms a partition of the universe, then $ \mathcal{Z} $-$ \mathcal{SRCFP} $-set is both a boolean lattice and a double stone algebra. Some main theoretical results are obtained and investigated with the help of examples.</p></abstract>

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Fixed points of covering upper and lower approximation operators

Cited by 4 publications

References 48 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

A fixed point theorem in rough semi-linear uniform spaces

A study of fixed point sets based on Z-soft rough covering models

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