Multiple-Attribute Decision Making Based on the Probabilistic Dominance Relationship with Fuzzy Algebras

Baklouti, Amir

doi:10.3390/sym15061188

Cited by 4 publications

(5 citation statements)

References 40 publications

(40 reference statements)

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“…the IFMST. Finally, we reached the solution set of arcs E = {(4,3), (3,2), (3,8), (8,6), (6,5), (6,7), and (7,1)} for the problem. A graphical illustration of the final solution is given in Figure 4, where red lines are used to emphasize the chosen arcs.…”

Section: Discussionmentioning

confidence: 99%

“…The authors solved the problem using the VIKOR model, in which the evaluation results of the alternatives were circular intuitionistic fuzzy sets. Baklouti [6] evaluated a multi-attribute decision-making problem. For such problems, Baklouti proposed a novel ranking method for IFNs based on the probabilistic dominance relationship between IFNs and fuzzy algebras.…”

Section: Introductionmentioning

confidence: 99%

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Defuzzification of Non-Linear Pentagonal Intuitionistic Fuzzy Numbers and Application in the Minimum Spanning Tree Problem

Mert

2023

Symmetry

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In recent years, with the variety of digital objects around us becoming a source of information, the fields of artificial intelligence (AI) and machine learning (ML) have experienced very rapid development. Processing and converting the information around us into data within the framework of the information processing theory is important, as AI and ML techniques need large amounts of reliable data in the training and validation stages. Even though information naturally contains uncertainty, information must still be modeled and converted into data without neglecting this uncertainty. Mathematical techniques, such as the fuzzy theory and the intuitionistic fuzzy theory, are used for this purpose. In the intuitionistic fuzzy theory, membership and non-membership functions are employed to describe intuitionistic fuzzy sets and intuitionistic fuzzy numbers (IFNs). IFNs are characterized by the mathematical statements of these two functions. A more general and inclusive definition of IFN is always a requirement in AI technologies, as the uncertainty introduced by various information sources needs to be transformed into similar IFNs without neglecting the variety of uncertainty. In this paper, we proposed a general and inclusive mathematical definition for IFN and called this IFN a non-linear pentagonal intuitionistic fuzzy number (NLPIFN), which allows its users to maintain variety in uncertainty. We know that AI technology implementations are performed in computerized environments, so we need to transform the IFN into a crisp number to make such IFNs available in such environments. Techniques used in transformation are called defuzzification methods. In this paper, we proposed a short-cut formula for the defuzzification of a NLPIFN using the intuitionistic fuzzy weighted averaging based on levels (IF-WABL) method. We also implemented our findings in the minimum spanning tree problem by taking weights as NLPIFNs to determine the uncertainty in the process more precisely.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Defuzzification of Non-Linear Pentagonal Intuitionistic Fuzzy Numbers and Application in the Minimum Spanning Tree Problem

Mert

2023

Symmetry

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“…Tan, Wu, Shi, and Zhao studied granulation selection and decision-making using multigranulation rough sets over two universes [22]. In their study, Baklouti et al [23][24][25] explored the decision-making process regarding selling or leasing used vehicles considering energy types, potential demand for leasing, and expected maintenance costs. These works showcase the application of mathematical modeling, optimization, and decision-making techniques in addressing sustainability challenges in different fields.…”

Section: Introductionmentioning

confidence: 99%

Exploring Roughness in Left Almost Semigroups and Its Connections to Fuzzy Lie Algebras

Assiry,

Baklouti

2023

Symmetry

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This paper explores the concept of Generalized Roughness in LA-Semigroups and its applications in various mathematical disciplines. We highlight the fundamental properties and structures of Generalized Roughness, examining its relationships with Fuzzy Lie Algebras, Order Theory, Lattice Structures, Algebraic Structures, and Categorical Perspectives. Moreover, we investigate the potential of mathematical modeling, optimization techniques, data analysis, and machine learning in the context of Generalized Roughness. Our findings reveal important results in Generalized Roughness, such as the preservation of roughness under the fuzzy equivalence relation and the composition of roughness sets. We demonstrate the significance of Generalized Roughness in the context of order theory and lattice structures, presenting key propositions and a theorem that elucidate its properties and relationships. Furthermore, we explore the applications of Generalized Roughness in mathematical modeling and optimization, highlighting the optimization of roughness measures, parameter estimation, and decision-making processes related to LA-Semigroup operations. We showcase how mathematical techniques can enhance understanding and utilization of LA-Semigroups in practical scenarios. Lastly, we delve into the role of data analysis and machine learning in uncovering patterns, relationships, and predictive models in Generalized Roughness. By leveraging these techniques, we provide examples and insights into how data analysis and machine learning can contribute to enhancing our understanding of LA-Semigroup behavior and supporting decision-making processes.

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“…Fuzzy Lie algebras are a unique and emerging area of research that introduces non-commutative structures into the realm of Lie algebras. For more detail about these structures, see [12][13][14]. By examining the deformations and cohomology spaces in parallel with the concepts from fuzzy Lie algebras, we aimed to establish a deeper connection between these two mathematical domains.…”

Section: Introductionmentioning

confidence: 99%

S-Embedding of Lie Superalgebras and Its Implications for Fuzzy Lie Algebras

Assiry,

Mansour,

Baklouti

2023

Axioms

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This paper performed an investigation into the s-embedding of the Lie superalgebra (→S1∣1), a representation of smooth vector fields on a (1,1)-dimensional super-circle. Our primary objective was to establish a precise definition of the s-embedding, effectively dissecting the Lie superalgebra into the superalgebra of super-pseudodifferential operators ( SψD⊙) residing on the super-circle S1|1. We also introduce and rigorously define the central charge within the framework of (→S1∣1), leveraging the canonical central extension of SψD⊙. Moreover, we expanded the scope of our inquiry to encompass the domain of fuzzy Lie algebras, seeking to elucidate potential connections and parallels between these ostensibly distinct mathematical constructs. Our exploration spanned various facets, including non-commutative structures, representation theory, central extensions, and central charges, as we aimed to bridge the gap between Lie superalgebras and fuzzy Lie algebras. To summarize, this paper is a pioneering work with two pivotal contributions. Initially, a meticulous definition of the s-embedding of the Lie superalgebra (→S1|1) is provided, emphasizing the representationof smooth vector fields on the (1,1)-dimensional super-circle, thereby enriching a fundamental comprehension of the topic. Moreover, an investigation of the realm of fuzzy Lie algebras was undertaken, probing associations with conventional Lie superalgebras. Capitalizing on these discoveries, we expound upon the nexus between central extensions and provide a novel deformed representation of the central charge.

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Multiple-Attribute Decision Making Based on the Probabilistic Dominance Relationship with Fuzzy Algebras

Cited by 4 publications

References 40 publications

Defuzzification of Non-Linear Pentagonal Intuitionistic Fuzzy Numbers and Application in the Minimum Spanning Tree Problem

Defuzzification of Non-Linear Pentagonal Intuitionistic Fuzzy Numbers and Application in the Minimum Spanning Tree Problem

Exploring Roughness in Left Almost Semigroups and Its Connections to Fuzzy Lie Algebras

S-Embedding of Lie Superalgebras and Its Implications for Fuzzy Lie Algebras

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