On intuitionistic gradation of openness

Mondal, Tapas Kumar; Samanta, Sourav

doi:10.1016/s0165-0114(01)00235-4

Cited by 98 publications

(50 citation statements)

References 24 publications

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“…The generalization of closed set reported by Abbas 2006 [7] and -closed by [8]. The goal of this article is to continue and to the allocation study of Fatimah et al [9,10]. Also, we will generalization the study of some properties of α m -closed sets in topological spaces by Milby [11], then we investigate the behavior of (p, q)-fuzzy -closed set and its various characterization, after that we introduce the concept of (p, q)-generalized fuzzy -closed set and it's complement (p, q)-generalized fuzzy -open.…”

Section: Introductionmentioning

confidence: 93%

(p,q) - Fuzzy αm-Closed Sets in Double Fuzzy Topological Spaces

Mohammed¹,

Abdullah²,

Obaid³

2018

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In this submitted article, we defined new notions of closed sets and called it (p, q)-fuzzy α m -closed sets in double fuzzy topological spaces. Also, we investigate some characterizations and properties of the sets mentioned above. As a result, we discussed some new and more general relationship between (p, q)-fuzzy α m -closed set and it's generalized which is called an (p, q)-generalized fuzzy α m -closed sets which was obtained and compared.

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Section: Introductionmentioning

confidence: 93%

(p,q) - Fuzzy αm-Closed Sets in Double Fuzzy Topological Spaces

Mohammed¹,

Abdullah²,

Obaid³

2018

djps

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“…Definition 1 (see [12,13] To answer the first question, we should know that double fuzzy sets and hence double fuzzy topological spaces deal with obscurities. In addition to that, we observed that the concept of double fuzzy topological spaces is a generalization of fuzzy topological spaces and classical topology.…”

Section: Preliminariesmentioning

confidence: 99%

“…Later Ç oker [11] defined intuitionistic fuzzy topology in Chang's sense. Then, Mondal and Samanta [12] introduced the intuitionistic gradation of openness of fuzzy sets. Gutiérrez García and Rodabaugh [13], in 2005, replaced the term "intuitionistic" and concluded that the most appropriate work is under the name "double.…”

Section: Introductionmentioning

confidence: 99%

Somewhat Slightly Generalized Double Fuzzy Semicontinuous Functions

Mohammed

Noorani

Ghareeb

2014

International Journal of Mathematics and Mathematical Sciences

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The aim of this paper is to introduce the concepts of somewhat slightly generalized double fuzzy semicontinuous functions and somewhat slightly generalized double fuzzy semiopen functions in double fuzzy topological spaces. Some interesting properties and characterizations of these functions are introduced and discussed. Furthermore, the relationships among the new concepts are discussed with some necessary examples.

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“…Atanassov and Gargov [2] introduced the concept of interval-valued intuitionistic fuzzy sets which is a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. Mondal and Samanta [8,14] introduced the concept of intuitionistic gradation of openness and defined intuitionistic fuzzy topological spaces. In [11], we defined interval-valued intuitionistic smooth topological spaces.…”

Section: Introductionmentioning

confidence: 99%