Invertible approximation operators of generalized rough sets and fuzzy rough sets

(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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Further Study of MultigranulationT-Fuzzy Rough Sets

The Scientific World JOURNAL ◽

10.1155/2014/927014 ◽

2014 ◽

Vol 2014 ◽

pp. 1-18 ◽

Cited By ~ 2

Author(s):

Wentao Li ◽

Xiaoyan Zhang ◽

Wenxin Sun

Keyword(s):

Rough Set ◽

Rough Sets ◽

Approximation Space ◽

Fuzzy Rough Sets ◽

Fuzzy Rough Set ◽

Upper Approximation ◽

Fuzzy Approximation ◽

Approximation Operators ◽

Special Instance

The optimistic multigranulationT-fuzzy rough set model was established based on multiple granulations underT-fuzzy approximation space by Xu et al., 2012. From the reference, a natural idea is to consider pessimistic multigranulation model inT-fuzzy approximation space. So, in this paper, the main objective is to make further studies according to Xu et al., 2012. The optimistic multigranulationT-fuzzy rough set model is improved deeply by investigating some further properties. And a complete multigranulationT-fuzzy rough set model is constituted by addressing the pessimistic multigranulationT-fuzzy rough set. The full important properties of multigranulationT-fuzzy lower and upper approximation operators are also presented. Moreover, relationships between multigranulation and classicalT-fuzzy rough sets have been studied carefully. From the relationships, we can find that theT-fuzzy rough set model is a special instance of the two new types of models. In order to interpret and illustrate optimistic and pessimistic multigranulationT-fuzzy rough set models, a case is considered, which is helpful for applying these theories to practical issues.

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On Fuzzy Rough Sets and Their Topological Structures

Mathematical Problems in Engineering ◽

10.1155/2014/546372 ◽

2014 ◽

Vol 2014 ◽

pp. 1-17 ◽

Cited By ~ 5

Author(s):

Weidong Tang ◽

Jinzhao Wu ◽

Dingwei Zheng

Keyword(s):

Set Theory ◽

Rough Set ◽

Rough Sets ◽

Rough Set Theory ◽

Fuzzy Relations ◽

Fuzzy Rough Sets ◽

Approximation Spaces ◽

Topological Structures ◽

Fuzzy Approximation ◽

Approximation Operators

The core concepts of rough set theory are information systems and approximation operators of approximation spaces. Approximation operators draw close links between rough set theory and topology. This paper is devoted to the discussion of fuzzy rough sets and their topological structures. Fuzzy rough approximations are further investigated. Fuzzy relations are researched by means of topology or lower and upper sets. Topological structures of fuzzy approximation spaces are given by means of pseudoconstant fuzzy relations. Fuzzy topology satisfying (CC) axiom is investigated. The fact that there exists a one-to-one correspondence between the set of all preorder fuzzy relations and the set of all fuzzy topologies satisfying (CC) axiom is proved, the concept of fuzzy approximating spaces is introduced, and decision conditions that a fuzzy topological space is a fuzzy approximating space are obtained, which illustrates that we can research fuzzy relations or fuzzy approximation spaces by means of topology and vice versa. Moreover, fuzzy pseudoclosure operators are examined.

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L-fuzzifying approximation operators in fuzzy rough sets

Information Sciences ◽

10.1016/j.ins.2018.12.021 ◽

2019 ◽

Vol 480 ◽

pp. 14-33 ◽

Cited By ~ 8

Author(s):

Bin Pang ◽

Ju-Sheng Mi ◽

Zhen-Yu Xiu

Keyword(s):

Rough Sets ◽

Fuzzy Rough Sets ◽

Approximation Operators

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An axiomatic approch of interval-valued intuitionistic fuzzy rough sets based on interval-valued intuitionistic fuzzy approximation operators

2012 2nd International Conference on Consumer Electronics, Communications and Networks (CECNet) ◽

10.1109/cecnet.2012.6201619 ◽

2012 ◽

Author(s):

Fei Xu ◽

Haidong Yin ◽

Qiufeng Wu

Keyword(s):

Rough Sets ◽

Fuzzy Rough Sets ◽

Intuitionistic Fuzzy ◽

Fuzzy Approximation ◽

Approximation Operators ◽

Intuitionistic Fuzzy Rough Sets ◽

Interval Valued

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The Parameter Reduction of Fuzzy Soft Sets Based on Soft Fuzzy Rough Sets

Advances in Fuzzy Systems ◽

10.1155/2013/197435 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 8

Author(s):

Zhiming Zhang

Keyword(s):

Set Theory ◽

Rough Sets ◽

Soft Set ◽

Fuzzy Soft Set ◽

Fuzzy Rough Sets ◽

Soft Sets ◽

Parameter Reduction ◽

Approximation Operators ◽

Rough Approximation ◽

Fuzzy Soft Sets

Fuzzy set theory, rough set theory, and soft set theory are three effective mathematical tools for dealing with uncertainties and have many wide applications both in theory and practise. Meng et al. (2011) introduced the notion of soft fuzzy rough sets by combining fuzzy sets, rough sets, and soft sets all together. The aim of this paper is to study the parameter reduction of fuzzy soft sets based on soft fuzzy rough approximation operators. We propose some concepts and conditions for two fuzzy soft sets to generate the same lower soft fuzzy rough approximation operators and the same upper soft fuzzy rough approximation operators. The concept of reduct of a fuzzy soft set is introduced and the procedure to find a reduct for a fuzzy soft set is given. Furthermore, the concept of exclusion of a fuzzy soft set is introduced and the procedure to find an exclusion for a fuzzy soft set is given.

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