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Volume 14
Issue 13
10.3390/math14132332
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Article

Topological Structures of Fuzzy Modal Logics Based on Residuated Lattices

by
Yong Chan Kim
1 and
Young-Hee Kim
2,*
1
Department of Mathematics, Kangwon National University, Gangneung 25457, Republic of Korea
2
Ingenium College, Kwangwoon University, Seoul 01897, Republic of Korea
*
Author to whom correspondence should be addressed.
Mathematics 2026, 14(13), 2332; https://doi.org/10.3390/math14132332
Submission received: 29 May 2026 / Revised: 22 June 2026 / Accepted: 27 June 2026 / Published: 1 July 2026
Versions Notes

Abstract

The purpose of this paper is to interpret fuzzy Kripke models as fuzzy information systems with objects and attributes. We introduce topological structures (interior, closure operators, Alexandrov pretopologies, Alexandrov precotopologies, fuzzy rough set) to the formulas of fuzzy Kripke models based on complete residuated lattices. We study the relations of possible worlds as objects and formulas as attributes in a fuzzy information system. Using the properties of residuated and Galois connections, we can obtain fuzzy concept lattices and formal fuzzy concept lattices. We give their examples.
Keywords: complete residuated lattices; fuzzy Kripke model; fuzzy modal logics; residuated (Galois) connections; interior (closure) operators; (formal) fuzzy concept lattices complete residuated lattices; fuzzy Kripke model; fuzzy modal logics; residuated (Galois) connections; interior (closure) operators; (formal) fuzzy concept lattices

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MDPI and ACS Style

Kim, Y.C.; Kim, Y.-H. Topological Structures of Fuzzy Modal Logics Based on Residuated Lattices. Mathematics 2026, 14, 2332. https://doi.org/10.3390/math14132332

AMA Style

Kim YC, Kim Y-H. Topological Structures of Fuzzy Modal Logics Based on Residuated Lattices. Mathematics. 2026; 14(13):2332. https://doi.org/10.3390/math14132332

Chicago/Turabian Style

Kim, Yong Chan, and Young-Hee Kim. 2026. "Topological Structures of Fuzzy Modal Logics Based on Residuated Lattices" Mathematics 14, no. 13: 2332. https://doi.org/10.3390/math14132332

APA Style

Kim, Y. C., & Kim, Y.-H. (2026). Topological Structures of Fuzzy Modal Logics Based on Residuated Lattices. Mathematics, 14(13), 2332. https://doi.org/10.3390/math14132332

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