Generalized Ideals of BCK/BCI-Algebras Based on Fuzzy Soft Set Theory

Muhiuddin, G.; Al-Kadi, Deena; Shum, K. P.; Alanazi, Abdulaziz M.

doi:10.1155/2021/8869931

Cited by 7 publications

(3 citation statements)

References 24 publications

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“…For other symbols, applications, and concepts, the reader is advised to refer [20][21][22][23][24][25][26][27][28][29][30].…”

Section: Preliminariesmentioning

confidence: 99%

Generalized Ideals of BCK/BCI-Algebras Based on MQHF Soft Set with Application in Decision Making

Alshayea,

Alsager

2023

Journal of Mathematics

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The purpose of this study is to generalize the concept of Q -hesitant fuzzy sets and soft set theory to Q -hesitant fuzzy soft sets. The Q -hesitant fuzzy set is an admirable hybrid property, specially developed by the new generalized hybrid structure of hesitant fuzzy sets. Our goal is to provide a formal structure for the m -polar Q -hesitant fuzzy soft (MQHFS) set. First, by combining m-pole fuzzy sets, soft set models, and Q -hesitant fuzzy sets, we introduce the concept of MQHFS and apply it to deal with multiple theories in B C K / B C I -algebra. We then develop a framework including MQHFS subalgebras, MQHFS ideals, closed MQHFS ideals, and MQHFS exchange ideals in B C K / B C I -algebras. Furthermore, we prove some relevant properties and theorems studied in our work. Finally, the application of MQHFS-based multicriteria decision-making in the Ministry of Health system is illustrated through a recent case study to demonstrate the effectiveness of MQHFS through the use of horizontal soft sets in decision-making.

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“…For other symbols, applications, and concepts, the reader is advised to refer [20][21][22][23][24][25][26][27][28][29][30].…”

Section: Preliminariesmentioning

confidence: 99%

Generalized Ideals of BCK/BCI-Algebras Based on MQHF Soft Set with Application in Decision Making

Alshayea,

Alsager

2023

Journal of Mathematics

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“…Muhiuddin and all. In 2021 apply fuzzy soft set theory to investigate commutative ideals in BCK-algebras [8,9]. Their research, published in the International Journal of Advanced and Applied Sciences, provides insights into this specific algebraic context.…”

Section: Introductionmentioning

confidence: 99%

M-polar Q-hesitant Anti-fuzzy Set in BCK/BCI-algebras

Alshayea,

Alsager

2024

Eur. J. Pure Appl. Math.

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The main objective of this paper is to effectively define a new concept of the fabulous fuzzy set theory that is called m-polar Q-hesitant anti-fuzzy set and apply it to the BCK/BCI-algebras. The m-polar Q-hesitant anti-fuzzy set is an astonishing development of the combination between the m-polar fuzzy set and the Q-hesitant fuzzy set. However, we introduce knowledge of the m-polar Q-hesitant anti-fuzzy subalgebra, m-polar Q-hesitant anti-fuzzy ideal, closed m-polar Q-hesitant anti-fuzzy ideal, m-polar Q hesitant anti-fuzzy commutative ideal, m-polar Q-hesitant anti-fuzzy implicative ideal, and m-polar Q-hesitant anti-fuzzy positive implicative of BCK/BCI- algebras. In addition, we investigate several theorems, examples, and properties of these notions.

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“…Furthermore, recent years have seen extensive research driven by the potential applications of fuzzy sets across diverse domains. Jun et al notably applied fuzzy soft set theory to BCK/BCIalgebras [24], while Muhiuddin et al explored generalized ideals of BCK/BCI-Algebras based on fuzzy soft set theory [30], making significant strides in this area [31].…”

Section: Introductionmentioning

confidence: 99%

n-polar Z-hesitant Complementary Fuzzy Soft Set in BCK/BCI-Algebras

Alsager,

2023

MJMS

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This paper introduces an innovative concept known as n-polar Z-hesitant Anti-Fuzzy Soft Sets (MZHAFSs) within the framework of BCK/BCI-algebras. Soft set theory originates in the captivating field of fuzzy set theory. Our approach is a harmonious synthesis of n-polar anti-fuzzy set theory, soft set models, and Z-hesitant anti-fuzzy sets, skillfully applied within the framework of BCK/BCI-algebras. This effort leads to the introduction of a new variant of fuzzy sets termed MZHAFSs (n-polar Z-hesitant anti-fuzzy soft sets) in the context of BCK/BCI-algebras. Additionally, we elucidate the concept of n-polar Z-hesitant anti-fuzzy soft sets to provide a comprehensive understanding. Furthermore, we introduce and define various related concepts, including n-polar Z-hesitant anti-fuzzy soft subalgebras, n-polar Z-hesitant anti-fuzzy soft ideals, n-polar Z-hesitant anti-fuzzy soft closed ideals, and n-polar Z-hesitant anti-fuzzy soft commutative ideals, and establish meaningful connections between them. We also present and rigorously prove several theorems that are pertinent to these newly introduced notions.

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Generalized Ideals of BCK/BCI-Algebras Based on Fuzzy Soft Set Theory

Abstract: In the present paper, using Lukaswize triple-valued logic, we introduce the notion of α , β -intuitionistic fuzzy soft ideal of BCK … Show more

Cited by 7 publications

References 24 publications

Generalized Ideals of BCK/BCI-Algebras Based on MQHF Soft Set with Application in Decision Making

Generalized Ideals of BCK/BCI-Algebras Based on MQHF Soft Set with Application in Decision Making

M-polar Q-hesitant Anti-fuzzy Set in BCK/BCI-algebras

n-polar Z-hesitant Complementary Fuzzy Soft Set in BCK/BCI-Algebras

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