Hesitant Anti‐Fuzzy Soft Set in BCK‐Algebras

Alshehri, Halimah; Alshehri, N. O.

doi:10.1155/2017/3634258

Cited by 5 publications

(3 citation statements)

References 8 publications

(7 reference statements)

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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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“…The exploration of Multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals extends the traditional theory of ideals in BCK/BCI-algebras, offering more flexibility in handling uncertain and hesitant information. Moreover, the significance of our work lies in developing algorithms and methodologies for efficient identification and characterization of these novel ideals [2,8]. We demonstrate the practical applicability of these concepts through examples and case studies, showcasing their prowess in handling complex, uncertain information and aiding in effective problem-solving processes.…”

Section: Introductionmentioning

confidence: 99%

Multi-polar Q-hesitant Fuzzy Soft Implicative and Positive Implicative Ideals in BCK/BCI-algebras.

Alshayea

2024

Eur. J. Pure Appl. Math.

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This paper focuses on exploring restricted mathematical concepts within the domain of BCK/BCI-algebras, specifically delving into the intricate realm of Multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals. BCK and BCI-algebras are pivotal structures in mathematical logic and algebraic systems, finding widespread applications in fields like computer science and artificial intelligence. Our contribution lies in the introduction and thorough investigation of the innovative notions of multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals, uniquely tailored for BCK/BCI-algebras. These ideals exhibit exceptional flexibility in managing uncertain and hesitant information, serving as potent tools for modeling and solvingreal-world problems characterized by imprecise or incomplete data. This study rigorously defines and explores the foundational properties of multi-polar Q-hesitant fuzzy soft implicative ideals, underscoring their relevance and applicability within BCK/BCI-algebras. Additionally, we present the concept of positive implicative ideals, establishing their interconnectedness with multi-polar Q-hesitant fuzzy soft implicative ideals. Our investigation delves into these ideals’ algebraic and logical facets, offering valuable insights into their mutual interactions and significance within the context of BCK/BCI-algebras. To facilitate practical implementation, we develop algorithms and methodologies for identifying and characterizing multi-polar Q-hesitant fuzzy soft implicative and positive implicative ideals. These computational tools enable efficient decision-making in scenariosinvolving uncertainty. Through illustrative examples and case studies, we showcase the potential of these ideals in handling complex, uncertain information, demonstrating their efficacy in aiding problem-solving processes. This research contributes significantly to advancing BCK/BCI-algebra theory by introducing innovative mathematical structures that bridge the gap between fuzzy logic, soft computing, and implicative ideals. The proposed multi-polar Q-hesitant fuzzy soft implicativeand positive implicative ideals open new avenues for addressing real-world problems characterized by imprecision and uncertainty. As such, they represent a valuable addition to the field of algebraic structures and their applications.

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“…In recent years, research in the field of fuzzy sets and their applications has seen remarkable growth, with several pivotal contributions that have expanded our understanding of these mathematical structures. Notable among these works, are Q-fuzzy soft set [3], New types of hesitant fuzzy soft set ideals in BCK-algebras [8], hesitant anti-fuzzy soft set in BCK-algebras [9]. In addition to these, the literature is enriched with various other contributions, including a decisionmaking approach based on a multi Q-hesitant fuzzy soft multi-granulation rough model by Alsager et al [7].…”

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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Hesitant Anti‐Fuzzy Soft Set in BCK‐Algebras

Cited by 5 publications

References 8 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

Multi-polar Q-hesitant Fuzzy Soft Implicative and Positive Implicative Ideals in BCK/BCI-algebras.

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

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