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Categories of Alexandrov L-Fuzzy Pre-uniformities, L-Approximation Operators and Alexandrov L-Fuzzy Topologies
International Journal of Fuzzy Logic and Intelligent Systems 2019;19(1):28-39
Published online March 25, 2019
© 2019 Korean Institute of Intelligent Systems.

Yong Chan Kim1, A. A. Ramadan2, and Seok Jong Lee3

1Department of Mathematics, Gangneung-Wonju National University, Gangneung, Korea, 2Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt, 3Department of Mathematics, Chungbuk National University, Cheongju, Korea
Correspondence to: Seok Jong Lee (sjl@cbnu.ac.kr)
Received January 18, 2019; Revised March 10, 2019; Accepted March 13, 2019.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper investigates relationships among Alexandrov L-fuzzy pre-uniformities, Alexandrov L-fuzzy topologies, L-lower approximation operators and L-upper approximation operators. It also presents an adjointness between the category of Alexandrov L-fuzzy pre-uniform spaces and reflexive L-fuzzy relations. In addition, it shows that the category of Alexandrov L-fuzzy pre-uniform spaces and the category of L-lower (respectively, upper) approximation spaces are isomorphic.
Keywords : Complete residuated lattice, Alexandrov fuzzy topology, Lower approximation operator, Upper approximation operator, Alexandrov fuzzy pre-uniformity