A new type of the hybrid algebra between Abelian groups and UP (BCC)-algebras: UP (BCC)-modules

Volume 31, Issue 4, pp 403--432 http://dx.doi.org/10.22436/jmcs.031.04.05

Publication Date: May 24, 2023 Submission Date: April 04, 2023 Revision Date: April 27, 2023 Accteptance Date: May 10, 2023

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Authors

Ch. Polhinkong - Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. K. Ngenkokkruad - Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. R. Chinram - Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. P. Julatha - Department of Mathematics, Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand. A. Iampan - Fuzzy Algebras and Decision-Making Problems Research Unit, Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand.

Abstract

The goal of this study is to introduce the concept of a new type of the hybrid algebra between Abelian groups and UP (BCC)-algebras: UP (BCC)-modules. We introduce the concept of fuzzy UP (BCC)-submodules of UP (BCC)-modules and provide properties and find the necessary and sufficient conditions for this concept. We define fuzzy sets in UP (BCC)-modules of many forms, supplying their properties and their relation to fuzzy UP (BCC)-submodules. We also define and study the fuzzy UP (BCC)-submodule generated by a set of fuzzy sets in UP (BCC)-modules, as well as provide for their properties and their relation to fuzzy UP (BCC)-submodules. Finally, we apply the concept of fuzzy UP (BCC)-ideals of UP (BCC)-algebras while providing properties and find the results of the composition and the product between fuzzy UP (BCC)-ideals and fuzzy UP (BCC)-submodules.

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Keywords

• UP (BCC)-algebra
• UP (BCC)-module
• fuzzy UP (BCC)-ideal
• fuzzy UP (BCC)-submodule

MSC

•  03G25
•  06D99
•  08A72

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