Characterization of almost filters and their fuzzifications of semigroups

Volume 35, Issue 4, pp 471--481 https://dx.doi.org/10.22436/jmcs.035.04.06

Publication Date: June 13, 2024 Submission Date: May 04, 2024 Revision Date: May 16, 2024 Accteptance Date: June 06, 2024

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Authors

P. Khamrot - Department of Mathematics, Faculty of Science and Agricultural Technology, Rajamangala University of Technology Lanna of Phitsanulok, Phitsanulok 65000, Thailand. R. Chinram - Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110, Thailand. Th. Gaketem - Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand.

Abstract

In this paper, we define and explore the properties and relationships of almost filters and fuzzy almost filters within semigroups. We examine whether the connection of two filters remains an almost filter in semigroups and verify if similar results hold within the framework of class fuzzifications. Furthermore, we investigate the connections between almost filters and fuzzy almost filters. We also define and demonstrate the characteristics of prime, semiprime, and strongly prime almost filters, including their applications as bi-filters in semigroups.

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Keywords

• Almost filter
• almost bi-filters
• fuzzy almost filters
• fuzzy almost bi-filters

MSC

•  20M10
•  03E72
•  08A72
•  18B40
•  20M12

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