Fuzzy Aggregation Operators Research Articles

Neutrality geometric aggregation operators based on cubic q-rung orthopair fuzzy sets and their applications in multiple attribute group decision-making problems

Cubic q-rung orthopair fuzzy set (Cq-ROFS) is a hybrid set that can hold much more information to handle data uncertainties. It provides more space for decision makers (DMs) to describe their opinion in the multi-attribute group decision-making (MAGDM). In order to involve neutral character to discuss the neutral values assigned by decision-makers, in this paper, some cubic q-rung orthopair fuzzy aggregation operators based on neutrality operation are proposed, such as the cubic q-rung orthopair fuzzy weighted neutrality geometric (Cq-ROFWNG) operator, the cubic q-rung orthopair fuzzy ordered weighted neutrality geometric (Cq-ROFOWNG) operator, the cubic q-rung orthopair fuzzy hybrid neutrality geometric (Cq-ROFHNG) operator. Meanwhile, some properties of these operators are discussed. Further, we develop a novel MAGDM approach based on the proposed operators in a cubic q-rung orthopair fuzzy environment. Finally, numerical examples are provided to demonstrate the effectiveness and superiority of the proposed method through a detailed comparison with existing methods.

Interval-valued fermatean fuzzy Aczel-Alsina geometric aggregation operators and their applications to group decision-making

Developing new aggregation operators on various classes of fuzzy sets and their generalizations is important in modelling real-life decision-making problems. Interval-valued Fermatean fuzzy sets (IVFFs) generalize the idea of interval-valued Pythagorean fuzzy sets (IVPFS) play a crucial role in modelling problems involving inadequate information. Decision-making problems modelled using IVFFNs require different score functions and aggregation operators on the set of IVFFNs. This study mainly focuses on establishing a few interval-valued Fermatean fuzzy (IVFF) aggregation operators by integrating the Aczel-Alsina (AA) operations to deal with group decision-making (GDM) problems. In this work, first, we discuss various Aczel-Alsina-based IVFF operations such as AA sum, AA product, and AA scalar multiplication for proposing a few new aggregation operators for the IVFF environment based on the new IVFF operations. Secondly, we introduce a few operators, including the interval-valued Fermatean fuzzy Aczel-Alsina (IVFFAA) weighted geometric operator, the IVFFAA ordered weighted geometric (IVFFAAOWG) operator, and the IVFFAA hybrid geometric (IVFFAAHG) operator. Various important properties such as idempotency, boundness, and monotonicity have also been studied. Thirdly, we establish multi-criteria group decision-making (MCGDM) method for solving real-life decision-making problems. Fourthly, we solve a model GDM problem to show the applicability and efficacy of our proposed MCGDM method, which utilizes the IVFFAAWG operator. Further, a sensitivity analysis is performed to ensure better performance, and finally, a comparative study of our method is done by comparing our proposed MCGDM approach with different existing methods.

Development of Aczel-Alsina t-norm based linear Diophantine fuzzy aggregation operators and their applications in multi-criteria decision-making with unknown weight information

Aczel-Alsina t-norm and t-conorm are intrinsically flexible and endow Aczel-Alsina aggregation operators with greater versatility and robustness in the aggregation process than operators rooted in other t-norms and t-conorm families. Moreover, the linear Diophantine fuzzy set (LD-FS) is one of the resilient extensions of the fuzzy sets (FSs), intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PyFSs), and q-rung orthopair fuzzy sets (q-ROFSs), which has acquired prominence in decision analysis due to its exceptional efficacy in resolving ambiguous data. Keeping in view the advantages of both LD-FSs and Aczel-Alsina aggregation operators, this article aims to establish Aczel-Alsina operation rules for LD-FSs, such as Aczel-Alsina sum, Aczel-Alsina product, Aczel-Alsina scalar multiplication, and Aczel-Alsina exponentiation. Based on these operation rules, we expose the linear Diophantine fuzzy Aczel-Alsina weighted average (LDFAAWA) operator, and linear Diophantine fuzzy Aczel-Alsina weighted geometric (LDFAAWG) operator and scrutinize their distinctive characteristics and results. Additionally, based on these aggregation operators (AOs), a multi-criteria decision-making (MCDM) approach is designed and tested with a practical case study related to forecasting weather under an LD-FS setting. The developed model undergoes a comparative analysis with several prevailing approaches to demonstrate the superiority and accuracy of the proposed model. Besides, the influence of the parameter Λ on the ranking order is successfully highlighted.

Resource allocation strategy selection for 5G network by using multi-attribute decision-making approach based on tangent trigonometric bipolar fuzzy aggregation operators

Resource allocation strategy selection for 5G network by using multi-attribute decision-making approach based on tangent trigonometric bipolar fuzzy aggregation operators

Complex Pythagorean Normal Interval-Valued Fuzzy Aggregation Operators for Solving Medical Diagnosis Problem

This paper presents a new methodology for solving multiple-attribute decision-making problems (MADMs) using a complex Pythagorean normal interval-valued fuzzy set (CPNIVFS), which is an extended concept of a complex Pythagorean fuzzy set. Four types of different aggregating operations (AOs), including CPNIVF weighted averaging (CPNIVFWA), CPNIVF weighted geometric (CPNIVFWG), generalized CPNIVFWA (CGPNIVFWA), and generalized CPNIVFWG (CGPNIVFWG), are discussed. The scoring function, accuracy function, and operational laws of the CPNIVFS are defined. Algebraic structures, such as associative, distributive, idempotent, bounded, commutativity, and monotonicity properties, are also shown to be satisfied by complex Pythagorean normal interval-valued fuzzy numbers. Furthermore, an algorithm is proposed to solve the MADM problems based on the defined AOs. The proposed approach is then used for a medical diagnosis problem about brain tumors because computer science and machine tool technology are among the most important components of brain tumor research. The five types of brain tumors diagnosed in these patients are gliomas, meningiomas, metastases, embryonal tumors, and ependymomas. Several types of treatments are available, which are often combined as part of an overall treatment plan. Brain tumors can be treated in various ways, including surgery, radiation therapy, chemotherapy, immunotherapy, and clinical trials. Based on the comparisons and options gathered, the most suitable treatment can be chosen. In this regard, it is evident that the value of the integer ⅁\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Game $$\\end{document} plays a significant role in determining the model. The candidate models under consideration can be validated by comparing them with the previously proposed ones. The proposed technique is compared with the existing method to demonstrate its superiority and validity, and the results conclude that the former is more reliable and effective than the latter. Finally, the criteria are evaluated by expert assessments to determine the most appropriate options.

Group decision-making algorithm with sine trigonometric r,s,t-spherical fuzzy aggregation operators and their application

r, s, t-spherical fuzzy (r, s, t-SPF) sets provide a robust framework for managing uncertainties in decision-making, surpassing other fuzzy sets in their ability to accommodate diverse uncertainties through the incorporation of flexible parameters r, s, and t. Considering these characteristics, this article explores sine trigonometric laws to enhance the applicability and theoretical foundation for r, s, t-SPF setting. Following these laws, several aggregation operators (AOs) are designed for aggregation of the r, s, t-SPF data. Meanwhile, the desired characteristics and relationships of these operators are studied under sine trigonometric functions. Furthermore, we build a group decision-making algorithm for addressing multiple attribute group decision-making (MAGDM) problems using the developed AOs. To exemplify the applicability of the proposed algorithm, we address a practical example regarding laptop selection. Finally, parameter analysis and a comprehensive comparison with existing operators are conducted to uncover the superiority and validity of the presented AOs.

Exploring complex n,m-rung orthopair fuzzy aggregation operators for enhanced multi-attribute decision making

Exploring complex n,m-rung orthopair fuzzy aggregation operators for enhanced multi-attribute decision making

Green knowledge management capability assessment based on interval-valued intuitionistic Fuzzy EWM-TOPSIS-Sort-B

As an emerging concept in knowledge management (KM), green knowledge management plays a crucial role in the sustainable development of enterprises. A reasonable assessment of an enterprise’s green knowledge management capabilities can help the company effectively manage the embedded green knowledge within its operational processes, thereby achieving self-reinforcement of competitive advantages for the enterprise. Therefore, this paper proposes a multi-criteria classification method based on interval-valued intuitionistic fuzzy entropy weight method-TOPSIS-Sort-B (EWM-TOPSIS-Sort-B) to assess the green knowledge management capabilities of enterprises. In this method, expert assessments are expressed using interval-valued intuitionistic fuzzy sets. A new entropy weight method is introduced into TOPSIS-Sort-B to determine the weights of various evaluation indicators, and TOPSIS-Sort-B is employed to classify and rate each evaluation scheme. It is worth noting that this paper has improved the TOPSIS-Sort-B method by not converting interval-valued intuitionistic fuzzy sets into precise values throughout the entire evaluation process, thus avoiding information loss. Finally, we applied a case of knowledge management capability assessment to validate the proposed method, and conducted sensitivity analysis and comparative analysis on this approach. The analysis results indicate that variations in the parameter ϑ of the interval-valued intuitionistic fuzzy aggregation operator lead to changes in criterion weights and the comprehensive evaluation matrix, resulting in unordered changes in the final classification results. Due to the absence of transformation of interval values in this study, compared to the four classification methods of TOPSISort-L, the classification results are more detailed, and the evaluation levels are more pronounced.

Combinative distance-based assessment method using linguistic T-spherical fuzzy aggregation operators and its application to multi-attribute group decision-making

Clean energy has become a hot topic worldwide because of the continuous rise in the climate's temperature. Reduced air pollution is only one of the many economic and environmental advantages of clean energy. An effective contractor with experience and knowledge in clean energy projects is always required to handle the complicated process of planning, implementing, and maintaining the new clean energy infrastructure. Contractor selection for renewable energy projects (REPs) is a multi-attribute group decision-making (MAGDM) problem. Linguistic T-spherical fuzzy set (LT-SFS) can be compatible with fuzzier information, and the contractor selection problem also has a lot of fuzzy information, which makes LT-SFS very suitable for contractor selection for REPs. Hence, the present work proposes a MAGDM methodology utilizing a combinative distance-based assessment (CODAS) method within the LT-SF context. For that, the Einstein and Frank t-norm and t-conorm has been used to define new and generalized operational laws for linguistic T-spherical fuzzy numbers. Then, the linguistic T-spherical fuzzy Einstein and linguistic T-spherical fuzzy Frank aggregation operators are proposed to integrate the information data provided by experts. Moreover, the proposed aggregation operators based-CODAS approach is designed to evaluate and rank the available alternatives. A real-life decision problem of selecting the best suitable contractor for a renewable energy project is solved to verify our suggested technique. Moreover, the sensitivity analysis is also carried out by changing the parameter's value to check the consistency of the rank order. Finally, the new model is compared with existing approaches to demonstrate its strength. The comparative analysis shows that the results of the suggested technique are more feasible and beneficial than those of existing approaches.

Group decision making based on cubic fermatean Einstein fuzzy weighted geometric operator

Cubic Fermatean fuzzy sets offer a flexible and powerful tool for decision-making, permitting decision-makers to incorporate uncertainty and reluctance into their decision-making process, and enabling them to make more informed and effective decisions in complex and uncertain situations. We present cubic fermatean fuzzy set and operational laws. We offer some cubic fermatean fuzzy numbers, as well as some cubic fermatean fuzzy aggregation operators, such as the cubic fermatean Einstein fuzzy weighted geometric operator, the cubic fermatean Einstein fuzzy ordered weighted geometric operator, and the cubic fermatean Einstein fuzzy hybrid weighted geometric operator. To demonstrate the solution to complicated real-life problems, an algorithm for the MADM problem is established under a system of cubic fermatean fuzzy information. To check the possibility of proposed aggregation approaches, we provided a numerical example to choose the desirable best options by using conceived approaches. To disclose the suppleness and applicability of designed methods, sensitive study, and comparative study are illustrated by complementary findings of existing methods with presently developed approaches.

A Review on Picture Fuzzy Aggregation Operators

Multiple Attribute Decision Making (MADM) is a fundamental concept in the scope of the decision sciences, serving as a structured method for evaluating and selecting the most appropriate alternative option from a pool of available alternatives. MADM methods have gained prominence over the years and are frequently applied in real-world scenarios. Nevertheless, decision-making in practical situations often involves information that is imprecise and uncertain, especially conflicting criteria or attributes. Therefore, Picture Fuzzy Sets (PFSs) and Aggregation Operators (AOs) have proven invaluable in effectively addressing decision challenges characterized by impression and uncertainty. During the past few years, various Picture Fuzzy Aggregation Operators (PFAOs) have been suggested and established but have not been thoroughly reviewed. The primary highlight of this research is to analyse as well as review the development and proposals surrounding PFAOs and their diverse applications within the decision-making paradigm. Regarding this, a review of 140 published articles from 2017 to 2022 appeared in 48 high-ranking journals cited from the "Scopus" and "Web of Science" databases. Other than that, all these articles have been classified by the nationalities of authors, publication year, published journal, research area, operators and methods. The findings of this study discovered that PFAOs have been increasingly applied for supporting decisions due to their frequent implications and applications in different managerial domains, either profit or non-profit organizations. This literature survey's significant contribution provides a platform for researchers to identify future dimensions of works as improvements for decision-making in picture fuzzy environments while also promoting future application of the approaches.

Geometric-arithmetic mean inequality for q-rung orthopair fuzzy Hamacher aggregations

The geometric-arithmetic mean inequality is undoubtedly the most important one in the area of information aggregation. Recently, some q-rung orthopair fuzzy aggregation operators were proposed based on the Hamacher operations. In this paper, we give a detailed theoretical and practical analysis of the developed Hamacher arithmetic and geometric operators for q-rung orthopair fuzzy values. First, we investigate the monotonicity of these Hamacher aggregation operators on q-rung orthopair fuzzy values with respect to the parameter within Hamacher operations. Then, we discuss the limiting cases of these q-rung orthopair fuzzy Hamacher aggregation operators as the parameter therein approaches to zero or infinity and give a new characterization of the boundedness of these aggregation operators. Subsequently, we establish the geometric-arithmetic mean inequality for q-rung orthopair fuzzy information based on Hamacher operations. Finally, we present a decision making method by use of these aggregation operators and apply it to the problem of enterprise resource planning system selection.

Multi-Attribute Group Decision-Making Problem Based On Q-Rung Orthopair Fuzzy Set Under Confidence Environment

Emergency decision-making for communities and countries is an important and critical tool. It improves the effectiveness and reliability to response emergencies which minimizes the rate of casualties, environmental damages and economic losses. In the event of emergency decision-making, the main issue is extreme imprecision, ambiguity, and fuzziness. This paper is devoted to the study of q‐rung orthopair fuzzy aggregation operators under the confidence levels and their applications to multiple-attribute group decision making (MAGDM) problems. The concept of q-rung orthopair fuzzy set (q-ROFS) is used as tool to describe undetermined information and is superior to the intuitionistic set (IFS) and Pythagorean fuzzy set (PFS). The distinguishing feature of the q-ROFS is that the sum of the q-th power of the membership degree and the q-th power of non-membership degree is bounded by 1. As a result, the range of uncertain information that it may describe is expanded. In this work, we focus on MAGDM problems under the fuzzy environment. First, based on aggregation operators some drawbacks of the already existing MAGDM methods are analyzed. Moreover, we present some modified operational laws and some of their properties to overcome these drawbacks. Next, related to q-ROFS fuzzy-weighted averaging (q-ICROFWA) and fuzzy-weighted power averaging (q-ICROFWPA) aggregation operator under confidence levels along with their properties are presented. By using these operators’ q-ICROFWA and q-ICROFWPA an advanced method is proposed to deal with MAGDM problems in fuzzy environment. At last, the validity and feasibility of this method is illustrated with some numerical examples.

Q-Rung orthopair fuzzy dynamic aggregation operators with time sequence preference for dynamic decision-making.

The q-rung orthopair fuzzy set (q-ROPFS) is a kind of fuzzy framework that is capable of introducing significantly more fuzzy information than other fuzzy frameworks. The concept of combining information and aggregating it plays a significant part in the multi-criteria decision-making method. However, this new branch has recently attracted scholars from several domains. The goal of this study is to introduce some dynamic q-rung orthopair fuzzy aggregation operators (AOs) for solving multi-period decision-making issues in which all decision information is given by decision makers in the form of "q-rung orthopair fuzzy numbers" (q-ROPFNs) spanning diverse time periods. Einstein AOs are used to provide seamless information fusion, taking this advantage we proposed two new AOs namely, "dynamic q-rung orthopair fuzzy Einstein weighted averaging (DQROPFEWA) operator and dynamic q-rung orthopair fuzzy Einstein weighted geometric (DQROPFEWG) operator". Several attractive features of these AOs are addressed in depth. Additionally, we develop a method for addressing multi-period decision-making problems by using ideal solutions. To demonstrate the suggested approach's use, a numerical example is provided for calculating the impact of "coronavirus disease" 2019 (COVID-19) on everyday living. Finally, a comparison of the proposed and existing studies is performed to establish the efficacy of the proposed method. The given AOs and decision-making technique have broad use in real-world multi-stage decision analysis and dynamic decision analysis.

(p, q)-fuzzy aggregation operators and their applications to decision-making

(p, q)-fuzzy aggregation operators and their applications to decision-making

Confidence Levels Measurement of Mobile Phone Selection Using a Multiattribute Decision-Making Approach with Unknown Attribute Weight Information Based on T-Spherical Fuzzy Aggregation Operators

Advancement in mobile phone (MP) technology has revolutionized the lifestyle. In recent years, we observed that MP technology had been involved in almost all aspects of life, such as communication purposes, e-commerce, mobile baking, and social media connectivity. So, it becomes a hot research topic to select the best MP that fulfills the desired feathers requirement. In this paper, the expert’s familiarity with the examined objects is factored into the initial judgments under the T-spherical fuzzy sets (T-SFSs) environment. The T-SFS is the extension of the picture fuzzy (PF) set (PFS), which gives wider scope for finding the most precise options than existing fuzzy frameworks. The multiattribute decision-making (MADM) is a common and valuable method for aggregating information. For MADM, various aggregation operators (AOs) have been created over the years. The article introduces the newly proposed approach T-spherical fuzzy (T-SF) confidence level weighted averaging T−SFWAc and T-SF confidence level weighted geometric T−SFWGc. Also, some desired properties of AOs are discussed, and the T-SF entropy measure is introduced for selecting the weight criteria. A MADM framework is introduced, on the behalf of proposed operators. The proposed MADM framework is applied to solve the real-life example of consumers’ preferences to show effectiveness and practicality. Lastly, the developed framework is set side by side with other prevailing approaches to demonstrate the superiority and significance of other existing AOs.

Fuzzy Aggregation Operators

Fuzzy Aggregation Operators

Selection of Software Development Methodology by Employing a Multi-Criteria Decision-Making Approach Based on Logarithmic Bipolar Complex Fuzzy Aggregation Operators

Selection of Software Development Methodology by Employing a Multi-Criteria Decision-Making Approach Based on Logarithmic Bipolar Complex Fuzzy Aggregation Operators

Dynamic bipolar fuzzy aggregation operators: A novel approach for emerging technology selection in enterprise integration

<abstract> <p>Emerging technology selection is crucial for enterprise integration, driving innovation, competitiveness, and streamlining operations across diverse sectors like finance and healthcare. However, the decision-making process for technology adoption is often complex and fraught with uncertainties. Bipolar fuzzy sets offer a nuanced representation of uncertainty, allowing for simultaneous positive and negative membership degrees, making them valuable in decision-making and expert systems. In this paper, we introduce dynamic averaging and dynamic geometric operators under bipolar fuzzy environment. We also establish some of the fundamental crucial features of these operators. Moreover, we present a step by step mechanism to solve MADM problem under bipolar fuzzy dynamic aggregation operators. In addition, these new techniques are successfully applied for the selection of the most promising emerging technology for enterprise integration. Finally, a comparative study is conducted to show the validity and practicability of the proposed techniques in comparison to existing methods.</p> </abstract>

Linguistics complex intuitionistic fuzzy aggregation operators and their applications to plastic waste management approach selection

<p>Linguistic complex intuitionistic fuzzy aggregation operators are a novel idea for the description of intuitionistic fuzzy information, where linguistic complex concepts are used to describe membership and non-membership. This can convey the hazy information more clearly, and some findings on linguistic complex intuitionistic fuzzy aggregation operators have been attained. Nonetheless, several linguistic complex intuitionistic fuzzy aggregation operators in the literature are founded on conventional operational principles, which have certain limitations when used to multi-attribute group decision-making (MAGDM). In this study, we presented some improved operating rules based on linguistic complex intuitionistic fuzzy variables (LCIFVs) and changed their features to address these issues. Next, we created a few aggregation operators, such as the enhanced linguistic complex intuitionistic fuzzy weighted average (LCIFWA) and the linguistic complex intuitionistic fuzzy ordered weighted averaging (LCIFOWA) operator, to fuse the decision information represented by LCIFVs. We also demonstrated that they had a few favorable qualities. We introduced many novel approaches to address the MAGDM issues in the context of the linguistic complex intuitionistic fuzzy environment, based on the LCIFOWA and linguistic complex intuitionistic fuzzy ordered weighted geometric (LCIFOWG) operators. In short, we employed few real-world scenarios to demonstrate the viability and soundness of the suggested techniques through comparison with other approaches. This unique technique has been applied to plastic waste management selection, and the results are more accurate than the previously used materials and methods.</p>