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Author: Mustafa Demirci

Affiliation: Akdeniz University and Faculty of Sciences, Turkey

ISBN: 978-989-758-157-1

Keyword(s): Fuzzy Set, Fuzzy Logic, Fuzzy Topology, Quantale, Semi-Quantale, Category Theory, Adjoint Situation, Equivalence, Spatiality, Sobriety.

Related Ontology Subjects/Areas/Topics: Artificial Intelligence ; Computational Intelligence ; Fuzzy Systems ; Mathematical Foundations: Fuzzy Set Theory and Fuzzy Logic ; Soft Computing

Abstract: The present paper introduces M-fuzzy semi-quantales, fuzzifying semi-quantales, and (L,M)-quasi-fuzzy topological spaces, providing a common framework for (L,M)-fuzzy topological spaces of Kubiak and Sostak, ˇ L-quasi-fuzzy topological spaces of Rodabaugh and L-fuzzy topological spaces of Hohle and ¨ Sostak. In this ˇ paper, we set up a dual adjunction between the category of (L,M)-quasi-fuzzy topological spaces and the category of M-fuzzy semi-quantales, and then show that this adjunction includes a dual equivalence between the category of (L,M)-sober (L,M)-quasi-fuzzy topological spaces and the category of (L,M)-spatial M-fuzzy semi-quantales.

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Paper citation in several formats:
Demirci, M. (2015). Fuzzy Semi-Quantales, (L,M) Quasi-Fuzzy Topological Spaces and Their Duality.In Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (ECTA 2015) ISBN 978-989-758-157-1, pages 105-111. DOI: 10.5220/0005583601050111

@conference{fcta15,
author={Mustafa Demirci.},
title={Fuzzy Semi-Quantales, (L,M) Quasi-Fuzzy Topological Spaces and Their Duality},
booktitle={Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (ECTA 2015)},
year={2015},
pages={105-111},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005583601050111},
isbn={978-989-758-157-1},
}

TY - CONF

JO - Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: FCTA, (ECTA 2015)
TI - Fuzzy Semi-Quantales, (L,M) Quasi-Fuzzy Topological Spaces and Their Duality
SN - 978-989-758-157-1
AU - Demirci, M.
PY - 2015
SP - 105
EP - 111
DO - 10.5220/0005583601050111

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