Aczel-Alsina-based aggregation operators for intuitionistic hesitant fuzzy set environment and their application to multiple attribute decision-making process

Ali, Wajid; Shaheen, Tanzeela; Haq, Iftikhar Ul; Toor, Hamza; Akram, Faraz; Garg, Harish; Uddin, Md. Zia; Hassan, Mohammad Mehedi

doi:10.3934/math.2023916

Cited by 6 publications

(1 citation statement)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the future, we will explore novel aggregation operators for aggregating the information for 3WD based on DTRSs. We will further utilize our developed approach to improve the existing literature [54][55][56][57][58] and design the real application in artificial intelligence and data sciences.…”

Section: Discussionmentioning

confidence: 99%

An Improved Intuitionistic Fuzzy Decision-Theoretic Rough Set Model and Its Application

Ali,

Shaheen,

Toor

et al. 2023

Axioms

Self Cite

View full text Add to dashboard Cite

The Decision-Theoretic Rough Set model stands as a compelling advancement in the realm of rough sets, offering a broader scope of applicability. This approach, deeply rooted in Bayesian theory, contributes significantly to delineating regions of minimal risk. Within the Decision-Theoretic Rough Set paradigm, the universal set undergoes a tripartite division, where distinct regions emerge and losses are intelligently distributed through the utilization of membership functions. This research endeavors to present an enhanced and more encompassing iteration of the Decision-Theoretic Rough Set framework. Our work culminates in the creation of the Generalized Intuitionistic Decision-Theoretic Rough Set (GI-DTRS), a fusion that melds the principles of Decision-Theoretic Rough Sets and intuitionistic fuzzy sets. Notably, this synthesis bridges the gaps that exist within the conventional approach. The innovation lies in the incorporation of an error function tailored to the hesitancy grade inherent in intuitionistic fuzzy sets. This integration harmonizes seamlessly with the contours of the membership function. Furthermore, our methodology deviates from established norms by constructing similarity classes based on similarity measures, as opposed to relying on equivalence classes. This shift holds particular relevance in the context of aggregating information systems, effectively circumventing the challenges associated with the process. To demonstrate the practical efficacy of our proposed approach, we delve into a concrete experiment within the information technology domain. Through this empirical exploration, the real-world utility of our approach becomes vividly apparent. Additionally, a comprehensive comparative analysis is undertaken, juxtaposing our approach against existing techniques for aggregation and decision modeling. The culmination of our efforts is a well-rounded article, punctuated by the insights, recommendations, and future directions delineated by the authors.

show abstract

Section: Discussionmentioning

confidence: 99%

An Improved Intuitionistic Fuzzy Decision-Theoretic Rough Set Model and Its Application

Ali,

Shaheen,

Toor

et al. 2023

Axioms

Self Cite

View full text Add to dashboard Cite

show abstract

A Novel Framework of Pythagorean Fuzzy Dominance-Based Rough Sets and Analysis of Knowledge Reductions

Haq,

Shaheen,

Toor

et al. 2023

IEEE Access

Self Cite

View full text Add to dashboard Cite

The dominance-based rough set approach is crucial to the advancement of rough set theory. It gives a more thorough and adaptable framework for knowledge acquisition, information analysis, and DM. It is a means of expressing discrepancies resulting from the examination of the domains with specified preference rankings of the characteristics. This work seeks to extend the Rough set approach utilizing dominance relationships to a Pythagorean fuzzy setting. The lower and upper approximations of Pythagorean fuzzy dominance-based rough set are determined by using the constructive technique. Next, we examine the basic characteristics for the rough estimations relying on the Pythagorean fuzzy dominance. By combining Approximate Distribution Reductions with a Pythagorean fuzzy dominance-based rough set, reductions are prescribed in four distinct manners. Additionally, the discernibility matrices and theorems connected to these reductions are produced. Such findings are all Pythagorean fuzzy generalizations or extensions of the conventional rough set method relying on dominance. Finally, the conceptual ideas are supported with a numerical example.

show abstract

Intuitionistic Hesitant Fuzzy Partitioned Maclaurin Symmetric Mean Aggregation Operators-Based Algorithm and Its Application in Decision Making

Azeem,

Ali,

Ali

et al. 2023

IEEE Access

View full text Add to dashboard Cite

Intuitionistic hesitant fuzzy sets, which enable the representation of an element's membership and non-membership as a set of multiple possible values, offer significant utility in describing uncertainty in various aspects of people's daily lives. Fundamental mathematical techniques known as intuitionistic hesitant fuzzy aggregation operators are employed to merge multiple inputs into a single result based on predetermined criteria. However, conventional approaches that rely on classic intuitionistic hesitant fuzzy aggregation operators have faced criticism due to their limited understanding of criteria characterization. We introduce two novel operators, namely the intuitionistic hesitant fuzzy partitioned Maclaurin symmetric mean (IHFPMSM) and intuitionistic hesitant fuzzy weighted partitioned Maclaurin symmetric mean (IHFWPMSM), which draw inspiration from the partitioned Maclaurin symmetric mean concept. Subsequently, we thoroughly examine various characteristics and special cases of these operators. Building upon the IHFWPMSM operator, we propose a novel multiple-criteria decision-making (MCDM) method that effectively selects the most suitable alternative from a set of options. To demonstrate the effectiveness of our proposed approach, we discuss a systematic methodology for selecting the optimal location for shoe company construction. Lastly, we demonstrate the superior prevalence and effectiveness of the developed approach through comprehensive comparative and sensitivity analyses, surpassing the capabilities of existing approaches.INDEX TERMS Intuitionistic hesitant fuzzy set, Maclaurin symmetric mean, partitioned Maclaurin symmetric mean, multiple criteria decision-making.

show abstract

Aczel-Alsina-based aggregation operators for intuitionistic hesitant fuzzy set environment and their application to multiple attribute decision-making process

Cited by 6 publications

References 33 publications

An Improved Intuitionistic Fuzzy Decision-Theoretic Rough Set Model and Its Application

An Improved Intuitionistic Fuzzy Decision-Theoretic Rough Set Model and Its Application

A Novel Framework of Pythagorean Fuzzy Dominance-Based Rough Sets and Analysis of Knowledge Reductions

Intuitionistic Hesitant Fuzzy Partitioned Maclaurin Symmetric Mean Aggregation Operators-Based Algorithm and Its Application in Decision Making

Contact Info

Product

Resources

About