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Authors: Abd El-latif, A.A.

Article Type: Research Article

Abstract: The aim of this paper is to introduce and study new classes of FP -multifunctions, called FP -lower (upper) irresolute and semi-irresolute, FP -presemi-open and FP -weak semi-open multifunctions, where the domain of these functions is a classical bitopological space with their values as arbitrary L -fuzzy sets in L -fuzzy bitopological space in view of Šostak’s sense. Also, we prove several characterizing theorems for these functions from different angles and we establish various properties of these multifunctions along with their mutual relationships.

Keywords: L-Fuzzy bitopological spaces, FP-upper(lower) irresolute multifunction, FP-presemi-open multifunction

DOI: 10.3233/JIFS-152486

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 6, pp. 3173-3180, 2017

Authors: Abd El-latif, A.A.

Article Type: Research Article

Abstract: Abd El-latif and Kim in [2 ], introduced the concepts of (L , M )-double fuzzy ideal and (L , M )-double fuzzy remote neighborhood systems, this paper is devoted to use these concepts to introduce and study the concept of pretopological fuzzy DR -convergence structure, and constructs the category PrFDRCS which contains TFDRCS as a bireflective subcategory. TFDRCS is shown as an isomorphic with (L , M )-TDFRN . Considering the relationship between the categories (L , M )-TDFRN and (L , M )-DFTML , it is proved that TFDRCS is isomorphic with (L , M )-DFTML . Also, …pretopological fuzzy DR -convergence spaces have been found to be characterized as a kind of (L , M )-double fuzzy remote neighborhood spaces, which is called an (L , M )- strong double fuzzy remote neighborhood space. Finally, it was proved that the category (L , M )-SDFRN is isomorphic with the category PrFDRCS . Show more

Keywords: Fuzzy DR-convergence, (L, M)-double fuzzy topological molecular lattice, (L, M)-double fuzzy remote neighborhood systems, (L, M)-double fuzzy ideal, isomorphic category

DOI: 10.3233/JIFS-16145

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 3, pp. 1513-1526, 2017

Authors: Abd El-latif, A.A.

Article Type: Research Article

Abstract: This paper is devoted to introduce and study new kinds of FP -multifunctions, namely FP -lower (upper) α -continuous, FP -lower (upper) almost α -continuous, and FP -lower (upper) weakly α -continuous multifunctions. Various properties of these multifunctions were investigated. We provided the relationships between these multifunctions and presented contrary examples. Finally, we gave the conditions which make these multifunctions equivalent.

Keywords: L-Fuzzy bitopological spaces, FP-lower (upper) α-continuous multifunctions, FP-lower (upper) almost α-continuous multifunctions, FP-lower (upper) weakly α-continuous multifunctions

DOI: 10.3233/JIFS-181791

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 1, pp. 953-964, 2019

Authors: Abd El-latif, A.A. | Khalaf, Mohammed M.

Article Type: Research Article

Abstract: In this paper, (2, M )-double fuzzifying topology as a generalized (2, M )-fuzzifying topology introduced by Höhle [7 ] is introduced. The relations between (2, M )-double fuzzy topology and (2, M )-double fuzzifying topology are studied. Also, we provided the definition of (2, M )-double fuzzifying preproximity structure. Not only that we studied the properties of these new notions, but we have also generated (2, M )-double fuzzifying topology from (2, M )-double fuzzifying preproximity. Finally, we introduced (2, M )-double fuzzifying preproximially continuous mapping which it used in more properties.

Keywords: (2, M)-double fuzzifying topology, (2, M)-double fuzzifying preproximity, double fuzzifying preproximally continuous mapping

DOI: 10.3233/JIFS-17691

Citation: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 4, pp. 4643-4655, 2018

Authors: Abd El-latif, A.A. | Kim, Yong Chan

Article Type: Research Article

Abstract: The aim of this paper is to introduce and study the notions of (L , M )-double fuzzy topological molecular lattice, (L , M )-double fuzzy remote neighborhood space, and to construct the category (L , M )-DFRN which contains (L , M )-TDFRN as a full subcategory. (L , M )-TDFRN is shown as an isomorphic with (L , M )-DFTML . Finally, the notion of (L , M )-double fuzzy ideal was introduced and the theory of (L , M )-double fuzzy ideal convergence in an (L , M )-double fuzzy topological molecular lattice was established.

Keywords: (L, M)-double fuzzy topological molecular lattice, (L, M)-double fuzzy remote neighborhood space, isomorphic category, (L, M)-double fuzzy ideal

DOI: 10.3233/IFS-152080

Citation: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 6, pp. 3321-3333, 2016