Fuzzy lattice ordered group based on fuzzy partial ordering relation
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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.
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References
[1] Mahmoud Bakhshi, On fuzzy convex lattice-ordered subgroups, Iranian Journal of Fuzzy Systems, 10 (3) (2013), 159–172. https://www.sid.ir/EN/VEWSSID/J_pdf/90820130310.pdf Google Scholar
[2] Garrett Birkhoff, Lattice theory, volume 25, American Mathematical Soc., 1940. http://dx.doi.org/10.2307/2268183 Google Scholar
[3] Garrett Birkhoff, Lattice-ordered groups, The Annals of Mathematics, 43 (2) (1942), 298–331. http://dx.doi.org/10.2307/1968871 Google Scholar
[4] Inheung Chon, Fuzzy partial order relations and fuzzy lattices, Korean Journal of Mathematics 17 (4) (2009), 361–374. https://www.dbpia.co.kr/Journal/articleDetail?nodeId=NODE08985027 Google Scholar
[5] M. R. Darnell, Theory of lattice-ordered groups, volume 1. Marcel Dekker, 1995. Google Scholar
[6] Parimi Radha, Krishna Kishore and Dawit Cherinet Kifetew, Properties of generalised lattice ordered groups, (IJCSAM) International Journal of Computing Science and Applied Mathematics 7 (1) (2021), 25–27. http://dx.doi.org/10.12962/j24775401.v7i1.7778 Google Scholar
[7] Valeri ̆ı Matveevich Kopytov and N Ya Medvedev, The theory of lattice-ordered groups, volume 307. Springer Science & Business Media, 2013. Google Scholar
[8] Sileshe Gone Korma, Radhakrishna Kishore Parimi, and Dawit Chernet Kifetew, Homomorphism and isomorphism theorems on fuzzy lattices, Research in Mathematics 10 (1) (2023), 2255411. http://dx.doi.org/10.1080/27684830.2023.2255411 Google Scholar
[9] Ivan Mezzomo, Benjamin C Bedregal, and Regivan HN Santiago, Types of fuzzy ideals in fuzzy lattices, Journal of Intelligent & Fuzzy Systems 28 (2) (2015), 929–945. http://dx.doi.org/10.3233/ifs-141374 Google Scholar
[10] Radha Krishna Kishore Parimi, Generalised lattice ordered groups (gl-groups), International Journal of Algebra 7 (2) (2013), 63–68. http://dx.doi.org/10.12988/ija.2013.13006 Google Scholar
[11] Ursala Paul and Paul Isaac, Fuzzy lattice ordered g-modules, International Journal of Fuzzy System Applications (IJFSA) 8 (3) (2019), 94–107. http://dx.doi.org/10.4018/ijfsa.2019070104 Google Scholar
[12] GSVS Saibaba, L-fuzzy prime spectrum of l-groups, Annals of Fuzzy Mathematics and Informatics 12 (2) (2016), 175–191. http://www.afmi.or.kr/articles_in_%20press/2016-02/AFMI-H-151116-2/AFMI-H-151116-2.pdf Google Scholar
[13] G.S.V.Satya Saibaba, Fuzzy lattice ordered groups, Southeast Asian Bulletin of Mathematics 32 (2008), 749–766. Google Scholar
[14] G.S.V.Satya Saibaba, Fuzzy convex sub l-groups, Annals of Fuzzy Mathematics and Informatics 11 (2016), 989–1001. http://www.afmi.or.kr/papers/2016/Vol-11_No-06/PDF/AFMI-11-6(989-1001)-H-151116-1R1.pdf Google Scholar
[15] Branimir Sˇeˇselja, Andreja Tepavˇcevi ́c, and Mirna Udoviˇci ́c, Fuzzy ordered structures and fuzzy lattice ordered groups, Journal of Intelligent & Fuzzy Systems 27 (3) (2014), 1119–1127. http://dx.doi.org/10.3233/ifs-131075 Google Scholar
[16] Stuart A Steinberg, Lattice-ordered rings and modules, volume 1. Springer, 2010. http://dx.doi.org/10.1007/978-1-4419-1721-8 Google Scholar
[17] J Vimala, Fuzzy lattice ordered group, International Journal of Scientific and Engineering Research 5 (9) (2014), 58–60. Google Scholar
[18] Lotfi A Zadeh, Fuzzy sets, Information and Control 8 (2) (1965), 338–353. http://dx.doi.org/10.1016/s0019-9958(65)90241-x Google Scholar
[19] Lotfi A Zadeh, Similarity relations and fuzzy orderings, Information sciences 3 (2) (1971), 177–200. http://dx.doi.org/10.1016/s0020-0255(71)80005-1 Google Scholar