Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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FUZZY LATTICE ORDERED GROUP BASED ON FUZZY PARTIAL ORDERING RELATION

  • Received : 2023.09.24
  • Accepted : 2024.04.26
  • Published : 2024.06.30
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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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Acknowledgement

This work was supported by a research grant from Arba Minch University.

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