Decision-Making Approach Based on Generalized Aggregation Operators with Complex Single-Valued Neutrosophic Hesitant Fuzzy Set Information

A strategic decision-making technique can help the decision maker to accomplish and analyze the information in an efficient manner. However, in our real life, an uncertainty will play a dominant role during the information collection phase. To handle such uncertainties in the data, we present a decision-making algorithm under the single-valued neutrosophic (SVN) environment. The SVN is a powerful way to deal the information in terms of three degrees, namely, “truth,” “falsity,” and “indeterminacy,” which all are considered independent. The main objective of this study is divided into three folds. In the first fold, we state the novel concept of complex SVN hesitant fuzzy (CSVNHF) set by incorporating the features of the SVN, complex numbers, and the hesitant element. The various fundamental and algebraic laws of the proposed CSVNHF set are described in details. The second fold is to state the various aggregation operators to obtain the aggregated values of the considered CSVNHF information. For this, we stated several generalized averaging operators, namely, CSVNHF generalized weighted averaging, ordered weighted average, and hybrid average. The various properties of these operators are also stated. Finally, we discuss a multiattribute decision-making (MADM) algorithm based on the proposed operators to address the problems under the CSVNHF environment. A numerical example is given to illustrate the work and compare the results with the existing studies’ results. Also, the sensitivity analysis and advantages of the stated algorithm are given in the work to verify and strengthen the study.

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Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators With New Distance Measures

Mathematics ◽

10.3390/math6120280 ◽

2018 ◽

Vol 6 (12) ◽

pp. 280 ◽

Cited By ~ 21

Author(s):

Harish Garg ◽

Gagandeep Kaur

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Weight Vector ◽

Aggregation Operators ◽

Distance Measures ◽

Weighted Averaging ◽

Hesitant Fuzzy Set ◽

Maximum Deviation ◽

Dual Hesitant Fuzzy Set ◽

Deviation Method

Probabilistic dual hesitant fuzzy set (PDHFS) is an enhanced version of a dual hesitant fuzzy set (DHFS) in which each membership and non-membership hesitant value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. By emphasizing the advantages of the PDHFS and the aggregation operators, in this manuscript, we have proposed several weighted and ordered weighted averaging and geometric aggregation operators by using Einstein norm operations, where the preferences related to each object is taken in terms of probabilistic dual hesitant fuzzy elements. Several desirable properties and relations are also investigated in details. Also, we have proposed two distance measures and its based maximum deviation method to compute the weight vector of the different criteria. Finally, a multi-criteria group decision-making approach is constructed based on proposed operators and the presented algorithm is explained with the help of the numerical example. The reliability of the presented decision-making method is explored with the help of testing criteria and by comparing the results of the example with several prevailing studies.

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Probabilistic Interval-Valued Hesitant Fuzzy Information Aggregation Operators and Their Application to Multi-Attribute Decision Making

Algorithms ◽

10.3390/a11080120 ◽

2018 ◽

Vol 11 (8) ◽

pp. 120 ◽

Cited By ~ 11

Author(s):

Wenying Wu ◽

Ying Li ◽

Zhiwei Ni ◽

Feifei Jin ◽

Xuhui Zhu

Keyword(s):

Decision Making ◽

Information Aggregation ◽

Aggregation Operators ◽

Weighted Averaging ◽

Hesitant Fuzzy Set ◽

Fuzzy Information ◽

Proposed Model ◽

Multi Attribute Decision Making ◽

Definition Of ◽

Interval Valued

Based on the probabilistic interval-valued hesitant fuzzy information aggregation operators, this paper investigates a novel multi-attribute group decision making (MAGDM) model to address the serious loss of information in a hesitant fuzzy information environment. Firstly, the definition of probabilistic interval-valued hesitant fuzzy set will be introduced, and then, using Archimedean norm, some new probabilistic interval-valued hesitant fuzzy operations are defined. Secondly, based on these operations, the generalized probabilistic interval-valued hesitant fuzzy ordered weighted averaging (GPIVHFOWA) operator, and the generalized probabilistic interval-valued hesitant fuzzy ordered weighted geometric (GPIVHFOWG) operator are proposed, and their desirable properties are discussed. We further study their common forms and analyze the relationship among these proposed operators. Finally, a new probabilistic interval-valued hesitant fuzzy MAGDM model is constructed, and the feasibility and effectiveness of the proposed model are verified by using an example of supplier selection.

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Multiple Attribute Group Decision-Making process based on Generalized Archimedean Linguistic Pythagorean Fuzzy Averaging Aggregation Operators

10.21203/rs.3.rs-266713/v1 ◽

2021 ◽

Author(s):

Rajkumar Verma ◽

Niti Mittal

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Real Life ◽

Aggregation Operators ◽

Weighted Averaging ◽

Pythagorean Fuzzy Set ◽

Multiple Attribute ◽

Fuzzy Aggregation ◽

Linguistic Scale Function

Abstract The linguistic Pythagorean fuzzy set (LPFS) is a prominent tool for comprehensively representing qualitative information data. Aggregation operators (AOs) play an essential role in multiple attribute group decision-making (MAGDM) problems. In the present manuscript, we define four new operational laws for linguistic Pythagorean fuzzy numbers (LPFNs) based on Archimedean t-norm and t-conorm. Paper also uses the linguistic scale function (LSF) in order to accommodate different semantic situations during the operational process. Next, we introduce some new generalized arithmetic AOs, including the generalized Archimedean linguistic Pythagorean fuzzy weighted averaging (GALPFWA) operator, the generalized Archimedean linguistic Pythagorean fuzzy ordered weighted averaging (GALPFOWA) operator, the generalized Archimedean linguistic Pythagorean fuzzy hybrid averaging (GALPFHA) operator along with their desirable properties. The developed AOs include several existing linguistic Pythagorean fuzzy aggregation operators as their particular and limiting cases. Finally, using the proposed AOs, a new approach for solving the MAGDM problem is given and illustrated with a real-life numerical example to demonstrate its flexibility and effectiveness.

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Application of the Bipolar Neutrosophic Hamacher Averaging Aggregation Operators to Group Decision Making: An Illustrative Example

Symmetry ◽

10.3390/sym11050698 ◽

2019 ◽

Vol 11 (5) ◽

pp. 698 ◽

Cited By ~ 2

Author(s):

Muhammad Jamil ◽

Saleem Abdullah ◽

Muhammad Yaqub Khan ◽

Florentin Smarandache ◽

Fazal Ghani

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Real Life ◽

Aggregation Operators ◽

Decision Makers ◽

Weighted Averaging ◽

Neutrosophic Set ◽

Ordered Weighted Averaging ◽

New Methods

The present study aims to introduce the notion of bipolar neutrosophic Hamacher aggregation operators and to also provide its application in real life. Then neutrosophic set (NS) can elaborate the incomplete, inconsistent, and indeterminate information, Hamacher aggregation operators, and extended Einstein aggregation operators to the arithmetic and geometric aggregation operators. First, we give the fundamental definition and operations of the neutrosophic set and the bipolar neutrosophic set. Our main focus is on the Hamacher aggregation operators of bipolar neutrosophic, namely, bipolar neutrosophic Hamacher weighted averaging (BNHWA), bipolar neutrosophic Hamacher ordered weighted averaging (BNHOWA), and bipolar neutrosophic Hamacher hybrid averaging (BNHHA) along with their desirable properties. The prime gain of utilizing the suggested methods is that these operators progressively provide total perspective on the issue necessary for the decision makers. These tools provide generalized, increasingly exact, and precise outcomes when compared to the current methods. Finally, as an application, we propose new methods for the multi-criteria group decision-making issues by using the various kinds of bipolar neutrosophic operators with a numerical model. This demonstrates the usefulness and practicality of this proposed approach in real life.

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A Robust q-Rung Orthopair Fuzzy Einstein Prioritized Aggregation Operators with Application towards MCGDM

Symmetry ◽

10.3390/sym12061058 ◽

2020 ◽

Vol 12 (6) ◽

pp. 1058 ◽

Cited By ~ 1

Author(s):

Muhammad Riaz ◽

Hafiz Muhammad Athar Farid ◽

Humaira Kalsoom ◽

Dragan Pamučar ◽

Yu-Ming Chu

Keyword(s):

Decision Making ◽

Group Decision ◽

Real Life ◽

Aggregation Operators ◽

Weighted Averaging ◽

Membership Degree ◽

Smooth Approximation ◽

Life Circumstances ◽

Significant Mechanism ◽

Prioritized Aggregation Operators

A q-rung orthopair fuzzy set (q-ROFS) provides a significant mechanism for managing symmetrical aspects in real life circumstances. The renowned distinguishing feature of q-ROFS is that the sum of the qth powers to each membership degree (MD) and non-membership degree (NMD) is less than or equal 1, and therefore the comprehensive uncertain space for q-ROF information is broader. Numerous researchers have suggested several aggregation operators based on q-ROFSs. In order to discuss prioritized relationship in the criterion and a smooth approximation of q-ROF information, we introduced q-rung orthopair fuzzy Einstein prioritized weighted averaging (q-ROFEPWA) operator and q-rung orthopair fuzzy Einstein prioritized weighted geometric (q-ROFEPWG) operator. Additionally, we presented a multi-criteria group decision making (MCGDM) technique based on q-rung orthopair fuzzy Einstein prioritized aggregation operators. These operators can evaluate the possible symmetric roles of the criterion that express the real phenomena of the problem. In order to investigate characteristic of suggested operators regarding the symmetry of attributes and their symmetrical roles under q-ROF information, we presented an application of Einstein prioritized aggregation operators. Finally, by comparing it with some other established representative MCGDM models, an illustrative example is provided to check the feasibility, efficiency and supremacy of the proposed technique.

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A Decision-Making Approach Based on New Aggregation Operators under Fermatean Fuzzy Linguistic Information Environment

Axioms ◽

10.3390/axioms10020113 ◽

2021 ◽

Vol 10 (2) ◽

pp. 113

Author(s):

Rajkumar Verma

Keyword(s):

Decision Making ◽

Real Life ◽

Solution Process ◽

Evaluation Process ◽

Aggregation Operators ◽

Weighted Averaging ◽

Linguistic Information ◽

Operational Laws ◽

Linguistic Scale Function ◽

Fuzzy Linguistic

Fermatean fuzzy linguistic (FFL) set theory provides an efficient tool for modeling a higher level of uncertain and imprecise information, which cannot be represented using intuitionistic fuzzy linguistic (IFL)/Pythagorean fuzzy linguistic (PFL) sets. On the other hand, the linguistic scale function (LSF) is the better way to consider the semantics of the linguistic terms during the evaluation process. It is worth noting that the existing operational laws and aggregation operators (AOs) for Fermatean fuzzy linguistic numbers (FFLNs) are not valid in many situations, which can generate errors in real-life applications. The present study aims to define new robust operational laws and AOs under Fermatean fuzzy linguistic environment. To do so, first, we define some new modified operational laws for FFLNs based on LSF and prove some important mathematical properties of them. Next, the work defines several new AOs, namely, the FFL-weighted averaging (FFLWA) operator, the FFL-weighted geometric (FFLWG) operator, the FFL-ordered weighted averaging (FFLOWA) operator, the FFL-ordered weighted geometric (FFLOWG) operator, the FFL-hybrid averaging (FFLHA) operator and the FFL-hybrid geometric (FFLHG) operator under Fermatean fuzzy linguistic environment. Several properties of these AOs are investigated in detail. Further, based on the proposed AOs, a new decision-making approach with Fermatean fuzzy linguistic information is developed to solve group decision-making problems with multiple attributes. Finally, to illustrate the effectiveness of the present approach, a real-life supplier selection problem is presented where the evaluation information of the alternatives is given in terms of FFLNs. Compared to the existing methods, the salient features of the developed approach are (1) it can solve decision-making problems with qualitative information data using FFLNs; (2) It can consider the attitudinal character of the decision-makers during the solution process; (3) It has a solid ability to distinguish the optimal alternative.

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Dynamic hesitant fuzzy aggregation operators in multi-period decision making

Kybernetes ◽

10.1108/k-11-2013-0236 ◽

2014 ◽

Vol 43 (5) ◽

pp. 715-736 ◽

Cited By ~ 21

Author(s):

Ding-Hong Peng ◽

Hua Wang

Keyword(s):

Decision Making ◽

Decision Analysis ◽

Fuzzy Variable ◽

Real Life ◽

Multiple Criteria Decision Making ◽

Aggregation Operators ◽

Weighted Averaging ◽

Fuzzy Information ◽

Content Type ◽

Fuzzy Aggregation

Purpose – The purpose of this paper is to present some dynamic hesitant fuzzy aggregation operators to tackle with the multi-period decision-making problems where all decision information is provided by decision makers in hesitant fuzzy information from different periods. Design/methodology/approach – First, the notions and operational laws of the hesitant fuzzy variable are defined. Then, some dynamic hesitant fuzzy aggregation operators involve the dynamic hesitant fuzzy weighted averaging (DHFWA) operator, the dynamic hesitant fuzzy weighted geometric (DHFWG) operator, and their generalized versions are presented. Some desirable properties of these proposed operators are established. Furthermore, two linguistic quantifier-based methods are introduced to determine the weights of periods. Next, the paper extends the results to the interval-valued hesitant fuzzy situation. Furthermore, the authors develop an approach to solve the multi-period multiple criteria decision making (MPMCDM) problems. Finally, an illustrative example is given. Findings – The presented hesitant fuzzy aggregation operators are very suitable for aggregating the hesitant fuzzy information collected at different periods. The developed approach can solve the MPMCDM problems where all decision information takes the form of hesitant fuzzy information collected at different periods. Practical implications – The presented hesitant fuzzy aggregation operators and decision-making approach can widely apply to dynamic decision analysis, multi-stage decision analysis in real life. Originality/value – The paper presents the useful way to aggregate the hesitant fuzzy information collected at different periods in MPMCDM situations.

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Decision Making Methods Based on Fuzzy Aggregation Operators: Three Decades Review from 1986 to 2017

International Journal of Information Technology & Decision Making ◽

10.1142/s021962201830001x ◽

2018 ◽

Vol 17 (02) ◽

pp. 391-466 ◽

Cited By ~ 45

Author(s):

Abbas Mardani ◽

Mehrbakhsh Nilashi ◽

Edmundas Kazimieras Zavadskas ◽

Siti Rahmah Awang ◽

Habib Zare ◽

...

Keyword(s):

Decision Making ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Operator Theory ◽

Real Life ◽

Aggregation Operator ◽

Aggregation Operators ◽

Weighted Averaging ◽

Fuzzy Aggregation

In many real-life decision making (DM) situations, the available information is vague or imprecise. To adequately solve decision problems with vague or imprecise information, fuzzy set theory and aggregation operator theory have become powerful tools. In last three decades, DM theories and methods under fuzzy aggregation operator have been proposed and developed for effectively solving the DM problems and numerous applications have been reported in the literature. While various aggregation operators have been suggested and developed, there is a lack of research regarding systematic literature review and classification of study in this field. Regarding this, Web of Science database has been nominated and systematic and meta-analysis method called “PRISMA” has been proposed. Accordingly, a review of 312 published articles appearing in 33 popular journals related to fuzzy set theory, aggregation operator theory and DM approaches between July 1986 and June 2017 have been attained to reach a comprehensive review of DM methods and aggregation operator environment. Consequently, the selected published articles have been categorized by name of author(s), the publication year, technique, application area, country, research contribution and journals in which they appeared. The findings of this study found that, ordered weighted averaging (OWA) has been the highest frequently accessed more than other areas. This systematic review shows that the DM theories under fuzzy aggregation operator environment have received a great deal of interest from researchers and practitioners in many disciplines.

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Picture Hesitant Fuzzy Set and Its Application to Multiple Criteria Decision-Making

Symmetry ◽

10.3390/sym10070295 ◽

2018 ◽

Vol 10 (7) ◽

pp. 295 ◽

Cited By ~ 9

Author(s):

Rui Wang ◽

Yanlai Li

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Real Life ◽

Multiple Criteria Decision Making ◽

Service Selection ◽

Aggregation Operators ◽

Multiple Criteria ◽

Hesitant Fuzzy Set ◽

Web Service Selection ◽

Picture Fuzzy Set

To address the complex multiple criteria decision-making (MCDM) problems in practice, this article proposes the picture hesitant fuzzy set (PHFS) theory based on the picture fuzzy set and the hesitant fuzzy set. First, the concept of PHFS is put forward, and its operations are presented, simultaneously. Second, the generalized picture hesitant fuzzy weighted aggregation operators are developed, and some theorems and reduced operators of them are discussed. Third, the generalized picture hesitant fuzzy prioritized weighted aggregation operators are put forward to solve the MCDM problems that the related criteria are at different priorities. Fourth, two novel MCDM methods combined with the proposed operators are constructed to determine the best alternative in real life. Finally, two numerical examples and an application of web service selection are investigated to illustrate the effectiveness of the proposed methods. The sensitivity analysis shows that the different values of the parameter λ affect the ranking of alternatives, and the proposed operators are compared with several existing MCDM methods to illustrate their advantages.

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Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽

10.3390/axioms10030145 ◽

2021 ◽

Vol 10 (3) ◽

pp. 145

Author(s):

Yun Jin ◽

Zareena Kousar ◽

Kifayat Ullah ◽

Tahir Mahmood ◽

Nimet Yapici Pehlivan ◽

...

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Evaluation Process ◽

Aggregation Operators ◽

Weighted Averaging ◽

Membership Degree ◽

Operational Laws ◽

Multi Attribute Decision Making ◽

Interval Valued ◽

Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

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