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Interior and closure operators on generalized co-residuated lattices

김용찬|오주목
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2022.04|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제23권 제2호|pp. 129-144|DOI 10.30948/afmi.2022.23.2.129

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키워드

Rough setsGeneralized co-residuated latticesRight (left) distance functionsRight (left) closure (interior) operatorsVarious connections

초록

In this paper, we introduce the notions and properties of generalized co-residuated lattices as a non-commutative algebraic structure. We define right and left distance functions. In particular, we study the relations between various operators and various connections. We give their examples.

Abstract

In this paper, we introduce the notions and properties of generalized co-residuated lattices as a non-commutative algebraic structure. We define right and left distance functions. In particular, we study the relations between various operators and various connections. We give their examples.

참고문헌 (11)

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  5. G. Georgescu, "Non-dual fuzzy connections", Arch. Math. Log, 43, pp.1009~1039 (2004)
  6. M. C. Zheng, "Coresiduated lattice with applications", Fuzzy systems and Mathematics, 19, pp.1~6 (2005)
  7. Z. Pawlak, "Rough sets", Internat. J. Comput. Inform. Sci, 11, pp.341~356 (1982)
  8. Z. Pawlak, "Rough sets: Theoretical Aspects of Reasoning about Data, System Theory, Knowl-edge Engineering and Problem Solving" (1991), Kluwer Academic Publishers
  9. Q. Junsheng, "On (; &)-fuzzy rough sets based on residuated and co-residuated lattices", Fuzzy Sets and Systems, 336, pp.54~86 (2018)
  10. 고정미, "Preserving Maps and Approximation Operators in Complete Co-Residuated Lattices", 한국지능시스템학회 논문지, 30(5), pp.331~340 (2020), 한국지능시스템학회[DOI]
  11. J. M. Oh, "Distance functions, upper approximation operators and Alexandrov fuzzy topologies", Journal of Intelligent and Fuzzy Systems, 40(6), pp.11915~11925 (2021)

관련 논문AI추천

Various systems, operators and distance functions on generalized co-residuated latticesJu-Mok Oh기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2025 · 제29권 제1호$L$-fuzzy bi-closure systems and $L$-fuzzy bi-closure operators고정미, 김용찬강원경기수학회 · 한국수학논문집2019 · 제27권 제2호TWO TYPES OF ALGEBRAIC STRUCTURES BASED ON GENERALIZED RESIDUATED LATTICES김영희, 박진원강원경기수학회 · 한국수학논문집2024 · 제32권 제4호Generalizations of Zadeh powerset operators in complete co-residuated lattices김용찬, 오주목기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2022 · 제23권 제3호Left and Right Coresiduated Lattices오주목한국수학교육학회 · 이론수학과 교직수학2024 · 제31권 제4호Adjunctions and Galois connections in complete co-residuated latticesJu-Mok Oh, Yong Chan Kim기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2021 · 제22권 제3호

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