Gradation of openness: fuzzy topology

Chattopadhyay, Kausik; Hazra, R. N.; Samanta, Sourav

doi:10.1016/0165-0114(92)90329-3

Cited by 143 publications

(81 citation statements)

References 2 publications

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“…A definition of type-2 m-topology is introduced which will be called m2-topology. The relevance of this approach in fuzzy setting have been done by A.Sostak [21], M. S. Ying [24], U. Höhle and A.Sostak [14], T. Kubiak [15], and Hazra, Chattopadhyay and Samanta [5,11]. In brief, in this paper, we have defined a notion of an m2-topological space by introducing a count of openness of an mset, m2-cotopological space by introducing a count of closedness of an mset.…”

Section: [78]mentioning

confidence: 99%

On type-2 m-topological spaces

Nazmul

2017

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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Abstract. In the present paper, we define a notion of an m2-topological space by introducing a count of openness of a multiset (mset in short) and study the properties of m2-subspaces, mgp-maps etc. Decomposition theorems involving m-topologies and m2-topologies are established. The behaviour of the functional image and functional preimage of an m2-topologies, the continuity of the identity mapping and a constant mapping in m2-topologies are also examined.

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Section: [78]mentioning

confidence: 99%

On type-2 m-topological spaces

Nazmul

2017

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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“…Chang [1] defined fuzzy topological spaces using fuzzy sets. In [2], Chattopadhyay, Hazra and Samanta introduced the smooth topological space which is a generalization of a fuzzy topological space. In [5], we introduced the concept of fuzzy -minimal space which is an extension of the smooth topological space.…”

Section: Intorductionmentioning

confidence: 99%

A Note On Fuzzy r-M Precontinuity And Fuzzy r-Minimal Compactness On Fuzzy r-Minimal Spaces

민원근¹,

김영기²

2011

Journal of Korean Institute of Intelligent Systems

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fuzzy r-minimal 공간에서 fuzzy r-  preopen 함수의 개념을 소개하며 fuzzy r- pre-연속 함수, fuzzy r-  preopen 함수와 여러 종류의 fuzzy r-minimal 컴팩트성과의 관계에 대하여 조사한다. AbstractIn this paper, we introduce and study the concept of fuzzy r-  preopen mappings between fuzzy r-minimal spaces.We also investigate the relationships among fuzzy r- precontinuous mappings, fuzzy r-  -preopen mappings and several types of fuzzy r-minimal compactness.Key Words : fuzzy r-minimal preopen, fuzzy r-M continuous, fuzzy r- precontinuous, fuzzy r-minimal precompact, fuzzy r-  -preopen mappings IntorductionThe concept of fuzzy set was introduced by Zadeh [7]. Chang [1] defined fuzzy topological spaces using fuzzy sets. In [2], Chattopadhyay, Hazra and Samanta introduced the smooth topological space which is a generalization of a fuzzy topological space. In [5], we introduced the concept of fuzzy -minimal space which is an extension of the smooth topological space. The concepts of fuzzy -open sets and fuzzy -M continuous mappings are also introduced and studied. In [3], We introduced the concepts of fuzzy -minimal preopen sets and fuzzy -M precontinuous mappings, which are generalizations of fuzzy -minimal open sets and fuzzy -M continuous mappings, respectively. Yoo et al. introduced the concepts of fuzzy -minimal compactness, almost fuzzy -minimal compactness and nearly fuzzy -minimal compactness on fuzzy  -minimal spaces in [6]. In this paper, we introduce and study the concept of fuzzy -  -preopen mapping between fuzzy -minimal spaces. We also investigate the relationships among fuzzy -M precontinuous mappings, fuzzy -  -preopen mappings and several types of fuzzy r-minimal compactness. In particular, in Theorem 3.11, we will show that: If a mapping    →  is fuzzy -M precontinuous and fuzzy -  -preopen on two -FMS's, and If  is a nearly fuzzy -minimal precompact set, then () is a nearly fuzzy -minimal compact set.

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“…Chattopadhyay et. al [3,4] have redefined the similar concept. In [15,5] Ramadan gave a similar definition namely "Smooth fuzzy topology" for lattice L = [0, 1], it has been developed in many direction [7,9,10,12,13,17].…”

Section: Introductionmentioning

confidence: 99%

On Fuzzy Bitopological Spaces in Šostak's Sense (Ii)

Ramadan¹,

Abbas²,

El-Latif³

2010

Communications of the Korean Mathematical Society

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Abstract. In this paper, we have use a fuzzy bitopological space (X, τ 1 , τ 2 ) to create a family τ s ij which is a supra fuzzy topology on X. Also, we introduce and study the concepts of r − (τ i , τ j )-generalized fuzzy regular closed, r − (τ i , τ j )-generalized fuzzy strongly semi-closed and r − (τ i , τ j )-generalized fuzzy regular strongly semi-closed sets in fuzzy bitopological space in the sense ofŠostak. Also, these classes of fuzzy subsets are applied for constructing several type of fuzzy closed mapping and some type of fuzzy separation axioms called fuzzy binormal, fuzzy mildly binormal and fuzzy almost pairwise normal.

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Gradation of openness: fuzzy topology

Cited by 143 publications

References 2 publications

On type-2 m-topological spaces

On type-2 m-topological spaces

A Note On Fuzzy r-M Precontinuity And Fuzzy r-Minimal Compactness On Fuzzy r-Minimal Spaces

On Fuzzy Bitopological Spaces in Šostak's Sense (Ii)

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