Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON TRIPOLAR FUZZY IDEALS IN ORDERED SEMIGROUPS

  • NUTTAPONG, WATTANASIRIPONG (Division of Applied Mathematics, Faculty of Science and Technology, Valaya Alongkorn Rajabhat University under the Royal Patronage) ;
  • NAREUPANAT, LEKKOKSUNG (Division of Mathematics, Faculty of Engineering, Ragamangala University of Technology Isan, Khon Kaen Campus) ;
  • SOMSAK, LEKKOKSUNG (Division of Mathematics, Faculty of Engineering, Ragamangala University of Technology Isan, Khon Kaen Campus)
  • Received : 2022.02.11
  • Accepted : 2022.09.17
  • Published : 2023.01.30
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Abstract

In this paper, we introduce the concept of tripolar fuzzy sub-semigroups, tripolar fuzzy ideals, tripolar fuzzy quasi-ideals, and tripolar fuzzy bi-ideals of an ordered semigroup and study some algebraic properties of them. Moreover, we prove that tripolar fuzzy bi-ideals and quasi-ideals coincide only in a particular class of ordered semigroups. Finally, we prove that every tripolar fuzzy quasi-ideal is the intersection of a tripolar fuzzy left and a tripolar fuzzy right ideal.

Keywords

Acknowledgement

We would like to express our sincere gratitude to the anonymous referee for their valuable comments and suggestions, which significantly improved the quality of this paper.

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