Aczel–Alsina aggregation operators and their application to intuitionistic fuzzy multiple attribute decision making

Senapati, Tapan; Chen, Guiyun; Yager, Ronald R.

doi:10.1002/int.22684

Cited by 137 publications

(80 citation statements)

References 53 publications

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“…√ n j=1 ωj (− log νj ) γ , which is consistent with [28,Theorem 2]. Applying Theorems 6.2-6.4, we know that [28, are direct corollaries of our results.…”

Section: Picture Fuzzy Interactional Aggregation Operatorssupporting

confidence: 89%

Picture Fuzzy Interactional Aggregation Operators via Strict Triangular Norms and Applications to Multi-Criteria Decision Making

Wu¹,

Zhu²,

Çaylı³

et al. 2022

Preprint

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The picture fuzzy set, characterized by three membership degrees, is a helpful tool for multi-criteria decision making (MCDM). This paper investigates the structure of the closed operational laws in the picture fuzzy numbers (PFNs) and proposes efficient picture fuzzy MCDM methods. We first introduce an admissible order for PFNs and prove that all PFNs form a complete lattice under this order. Then, we give some specific examples to show the non-closeness of some existing picture fuzzy aggregation operators. To ensure the closeness of the operational laws in PFNs, we construct a new class of picture fuzzy operators based on strict triangular norms, which consider the interaction between the positive degrees (negative degrees) and the neutral degrees. Based on these new operators, we obtain the picture fuzzy interactional weighted average (PFIWA) operator and the picture fuzzy interactional weighted geometric (PFIWG) operator. They are proved to be monotonous, idempotent, bounded, shift-invariant, and homogeneous. We also establish a novel MCDM method under the picture fuzzy environment applying PFIWA and PFIWG operators. Furthermore, we present an illustrative example for a clear understanding of our method. We also give the comparative analysis among the operators induced by six classes of famous triangular norms.

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“…√ n j=1 ωj (− log νj ) γ , which is consistent with [28,Theorem 2]. Applying Theorems 6.2-6.4, we know that [28, are direct corollaries of our results.…”

Section: Picture Fuzzy Interactional Aggregation Operatorssupporting

confidence: 89%

Picture Fuzzy Interactional Aggregation Operators via Strict Triangular Norms and Applications to Multi-Criteria Decision Making

Wu¹,

Zhu²,

Çaylı³

et al. 2022

Preprint

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“…Aczel and Alsina [27] first introduced a new pair of TN and TCN which is more flexible than the other TN and TCN mentioned above. Since the Aczel-Alsina TN and TCN have a great impact due to the variableness of involved parameters, Senapati et al [28][29] recently developed Aczel-Alsina AOs for a framework of IFSs and also for interval-valued IFSs (IVIFSs), and then applied them to solve the MADM problems, and Senapati [30] considered Aczel-Alsina AOs based on PFSs with application to MADM.…”

Section: Introductionmentioning

confidence: 99%

Aczel-Alsina Aggregation Operators on T-Spherical Fuzzy (TSF) Information With Application to TSF Multi-Attribute Decision Making

et al. 2022

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Aczel-Alsina t-norm (TN) and t-conorm (TCN) were proposed by Aczel and Alsina in 1982 where they are more flexible than the other TN and TCN. Since Aczel-Alsina TN and TCN have a great impact due to the variableness of involved parameters, they have good applications in multi-attribute decision making (MADM) under fuzzy sets (FSs) construction. Recently, Senapati et al. (2022) developed Aczel-Alsina aggregation operators (AOs) under intuitionistic FSs (IFSs) and interval-valued IFSs (IVIFSs) with their applications in solving IFS and IVIFS MADM problems. We know that T-spherical FSs (TSFSs) are a recently developed approach to uncertain information with less information loss and more reliability than IFSs and IVIFSs. In this paper, we develop these AOs on TSFSs as a new approach to solve MADM problems by using Aczel-Alsina TN and Aczel-Alsina TCN under T-spherical fuzzy (TSF) information. Furthermore, the basic operations of TSF numbers (TSFNs) are developed and exemplified. Based on these operations, two types of AOs, i.e. TSF Aczel-Alsina weighted average (TSFAAWA), and TSF Aczel-Alsina weighted geometric (TSFAAWG) operators, are introduced and investigated. The reliability and accuracy of the newly developed AOs are tested numerically and theoretically by the induction methods. To further give applications and also study the sensitivity of these TSF Aczel-Alsina operators, the problem of project evaluation using these proposed operators is comprehensively observed. The results obtained by using these TSF Aczel-Alsina operators are compared with some previously existing AOs of TSFSs. According to comparison results, we observe the reliability and efficiency of the proposed methods.

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“…Wang et al 32 recommended a histogram equalization fusion optimization technique on the Aczel–Alsina triangular norm (AA

t

‐norm) to broaden the spacing of pretenders while simultaneously narrowing the distance of legitimate. Recently, Senapati et al 33 introduced intuitionistic fuzzy Aczel–Alsina aggregation operators and utilized them in MADM methodology. The main goal of such an interesting article is to show some aggregation operations under IVIF information called IVIF Aczel‐ Alsina aggregations for establishing the specific priority of decisions when using decision‐making approaches.…”

Section: Introductionmentioning

confidence: 99%

Novel Aczel–Alsina operations‐based interval‐valued intuitionistic fuzzy aggregation operators and their applications in multiple attribute decision‐making process

Senapati

Chen

Mesiar

et al. 2021

Int J of Intelligent Sys

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In the creation of better multiple attribute decisionmaking (MADM) patterns to address the ambiguity in the expanding sophisticated of expert systems, the hypothesis of interval-valued intuitionistic fuzzy sets has proven to be an effective and advantageous technique. We employ Aczel-Alsina operations to remedy the MADM issue, wherein all data supplied by decisionmakers is conveyed as interval-valued intuitionistic fuzzy (IVIF) decision matrices with all components described by an IVIF number (IVIFN). This allows us to satisfy much more demands from fuzzy decisionmaking concerns (IVIFN). In the framework of IVIFNs, we primarily describe several novel Aczel-Alsina operations. On the basis of these operations, we construct several novel IVIF aggregation operators, such as the IVIF Aczel-Alsina weighted averaging operator, the IVIF Aczel-Alsina order weighted averaging operator, and IVIF Aczel-Alsina hybrid averaging operator. We built up several features of such operators. We recommend an MADM technique dependent on the advanced IVIF aggregation operators.To demonstrate the effectiveness of the developed technique, we present an overview of research scientist

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Aczel–Alsina aggregation operators and their application to intuitionistic fuzzy multiple attribute decision making

Cited by 137 publications

References 53 publications

Picture Fuzzy Interactional Aggregation Operators via Strict Triangular Norms and Applications to Multi-Criteria Decision Making

Picture Fuzzy Interactional Aggregation Operators via Strict Triangular Norms and Applications to Multi-Criteria Decision Making

Aczel-Alsina Aggregation Operators on T-Spherical Fuzzy (TSF) Information With Application to TSF Multi-Attribute Decision Making

Novel Aczel–Alsina operations‐based interval‐valued intuitionistic fuzzy aggregation operators and their applications in multiple attribute decision‐making process

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