Fuzzy lattice ordered group based on fuzzy partial ordering relation
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In this paper, we introduce the concept of a fuzzy lattice ordered group, which is based on a fuzzy lattice that Chon developed in his paper "Fuzzy Partial Order Relations and Fuzzy Lattice". We will also discuss fuzzy lattice-ordered groups in detail, provide several results that are analogous to the classical theory of lattice-ordered groups, and characterize the relationship between a fuzzy lattice-ordered group using its level set and support. Moreover, we define the concepts of $fl$-subgroups, quotients, and cosets of $fl$-groups and obtain some fundamental results for these fuzzy algebraic structures.
Abstract
In this paper, we introduce the concept of a fuzzy lattice ordered group, which is based on a fuzzy lattice that Chon developed in his paper "Fuzzy Partial Order Relations and Fuzzy Lattice". We will also discuss fuzzy lattice-ordered groups in detail, provide several results that are analogous to the classical theory of lattice-ordered groups, and characterize the relationship between a fuzzy lattice-ordered group using its level set and support. Moreover, we define the concepts of $fl$-subgroups, quotients, and cosets of $fl$-groups and obtain some fundamental results for these fuzzy algebraic structures.
참고문헌 (19)
- Mahmoud Bakhshi, "On fuzzy convex lattice-ordered subgroups", Iranian Journal of Fuzzy Systems, 10(3), pp.159~172 (2013)
- Garrett Birkho, "Lattice theory, volume 25" (1940), American Mathematical Soc
- Garrett Birkho, "Lattice-ordered groups", The Annals of Mathematics, 43(2), pp.298~331 (1942)[DOI]
- Inheung Chon, "Fuzzy partial order relations and fuzzy lattices", Korean Journal of Mathematics, 17(4), pp.361~374 (2009)
- M. R. Darnell, "Theory of lattice-ordered groups, volume 1" (1995), Marcel Dekker
- Parimi Radha, "Properties of generalised lattice ordered groups", (IJCSAM) International Journal of Computing Science and Applied Mathemat-ics, 7(1), pp.25~27 (2021)[DOI]
- Valeriꠘꠕ Matveevich Kopytov, "The theory of lattice-ordered groups, volume 307" (2013), Springer Science & Business Media
- Sileshe Gone Korma, "Homomor-phism and isomorphism theorems on fuzzy lattices", Research in Mathematics, 10(1), pp.2255411~ (2023)[DOI]
- Ivan Mezzomo, "Types of fuzzy ideals in fuzzy lattices", Journal of Intelligent & Fuzzy Systems, 28(2), pp.929~945 (2015)[DOI]
- Radha Krishna Kishore Parimi, "Generalised lattice ordered groups(gl-groups)", International Journal of Algebra, 7(2), pp.63~68 (2013)[DOI]
- Ursala Paul, "Fuzzy lattice ordered g-modules", International Journal of Fuzzy System Applications(IJFSA), 8(3), pp.94~107 (2019)[DOI]
- GSVS Saibaba, "L-fuzzy prime spectrum of l-groups", Annals of Fuzzy Mathematics and Infor-matics, 12(2), pp.175~191 (2016)
- G.S.V.Satya Saibaba, "Fuzzy lattice ordered groups", Southeast Asian Bulletin of Mathematics, 32, pp.749~766 (2008)
- G.S.V.Satya Saibaba, "Fuzzy convex sub l-groups", Annals of Fuzzy Mathematics and Informatics, 11, pp.989~1001 (2016)
- Branimir Seselja, "Fuzzy ordered structures and fuzzy lattice ordered groups", Journal of Intelligent & Fuzzy Systems, 27(3), pp.1119~1127 (2014)[DOI]
- Stuart A Steinberg, "Lattice-ordered rings and modules, volume 1" (2010), Springer
- J Vimala, "Fuzzy lattice ordered group", International Journal of Scientic and Engineering Research, 5(9), pp.58~60 (2014)
- Lot A Zadeh, "Fuzzy sets", Information and Control, 8(2), pp.338~353 (1965)[DOI]
- Lot A Zadeh, "Similarity relations and fuzzy orderings", Information sciences, 3(2), pp.177~200 (1971)[DOI]