A method to solve strategy based decision making problems with logarithmic T-spherical fuzzy aggregation framework

T-Spherical fuzzy set (TSFS) is an improved extension in fuzzy set (FS) theory that takes into account four angles of the human judgment under uncertainty about a phenomenon that is membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). The purpose of this manuscript is to introduce and investigate logarithmic aggregation operators (LAOs) in the layout of TSFSs after observing the shortcomings of the previously existing AOs. First, we introduce the notions of logarithmic operations for T-spherical fuzzy numbers (TSFNs) and investigate some of their characteristics. The study is extended to develop T-spherical fuzzy (TSF) logarithmic AOs using the TSF logarithmic operations. The main theory includes the logarithmic TSF weighted averaging (LTSFWA) operator, and logarithmic TSF weighted geometric (LTSFWG) operator along with the conception of ordered weighted and hybrid AOs. An investigation about the validity of the logarithmic TSF AOs is established by using the induction method and examples are solved to examine the practicality of newly developed operators. Additionally, an algorithm for solving the problem of best production choice is developed using TSF information and logarithmic TSF AOs. An illustrative example is solved based on the proposed algorithm where the impact of the associated parameters is examined. We also did a comparative analysis to examine the advantages of the logarithmic TSF AOs.

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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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Logarithmic Aggregation Operators of Picture Fuzzy Numbers for Multi-Attribute Decision Making Problems

Mathematics ◽

10.3390/math7070608 ◽

2019 ◽

Vol 7 (7) ◽

pp. 608 ◽

Cited By ~ 10

Author(s):

Saifullah Khan ◽

Saleem Abdullah ◽

Lazim Abdullah ◽

Shahzaib Ashraf

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Vital Role ◽

Aggregation Operators ◽

Weighted Averaging ◽

Fuzzy Decision Making ◽

Fuzzy Decision ◽

Picture Fuzzy Set ◽

Fuzzy Aggregation ◽

Multi Attribute Decision Making

The objective of this study was to create a logarithmic decision-making approach to deal with uncertainty in the form of a picture fuzzy set. Firstly, we define the logarithmic picture fuzzy number and define the basic operations. As a generalization of the sets, the picture fuzzy set provides a more profitable method to express the uncertainties in the data to deal with decision making problems. Picture fuzzy aggregation operators have a vital role in fuzzy decision-making problems. In this study, we propose a series of logarithmic aggregation operators: logarithmic picture fuzzy weighted averaging/geometric and logarithmic picture fuzzy ordered weighted averaging/geometric aggregation operators and characterized their desirable properties. Finally, a novel algorithm technique was developed to solve multi-attribute decision making (MADM) problems with picture fuzzy information. To show the superiority and the validity of the proposed aggregation operations, we compared it with the existing method, and concluded from the comparison and sensitivity analysis that our proposed technique is more effective and reliable.

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Evaluation of Investment Policy Based on Multi-Attribute Decision-Making Using Interval Valued T-Spherical Fuzzy Aggregation Operators

Symmetry ◽

10.3390/sym11030357 ◽

2019 ◽

Vol 11 (3) ◽

pp. 357 ◽

Cited By ~ 21

Author(s):

Kifayat Ullah ◽

Nasruddin Hassan ◽

Tahir Mahmood ◽

Naeem Jan ◽

Mazlan Hassan

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Intuitionistic Fuzzy Set ◽

Aggregation Operators ◽

Weighted Averaging ◽

Investment Policies ◽

Picture Fuzzy Set ◽

Fuzzy Aggregation ◽

Multi Attribute Decision Making ◽

Interval Valued

Expressing the measure of uncertainty, in terms of an interval instead of a crisp number, provides improved results in fuzzy mathematics. Several such concepts are established, including the interval-valued fuzzy set, the interval-valued intuitionistic fuzzy set, and the interval-valued picture fuzzy set. The goal of this article is to enhance the T-spherical fuzzy set (TSFS) by introducing the interval-valued TSFS (IVTSFS), which describes the uncertainty measure in terms of the membership, abstinence, non-membership, and the refusal degree. The novelty of the IVTSFS over the pre-existing fuzzy structures is analyzed. The basic operations are proposed for IVTSFSs and their properties are investigated. Two aggregation operators for IVTSFSs are developed, including weighted averaging and weighted geometric operators, and their validity is examined using the induction method. Several consequences of new operators, along with their comparative studies, are elaborated. A multi-attribute decision-making method in the context of IVTSFSs is developed, followed by a brief numerical example where the selection of the best policy, among a list of investment policies of a multinational company, is to be evaluated. The advantages of using the framework of IVTSFSs are described theoretically and numerically, hence showing the limitations of pre-existing aggregation operators.

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Multicriteria q-Rung Orthopair Fuzzy Decision Analysis: A Novel Approach Based on Archimedean Aggregation Operators with the Confidence Levels

10.21203/rs.3.rs-1059359/v1 ◽

2022 ◽

Author(s):

Yabin Shao ◽

Ning Wang ◽

Zengtai Gong

Keyword(s):

Decision Making ◽

Decision Maker ◽

Uncertain Data ◽

Aggregation Operators ◽

Weighted Averaging ◽

Confidence Levels ◽

Novel Approach ◽

Fuzzy Aggregation ◽

Multicriteria Group Decision Making ◽

The Impact

Abstract The confidence levels can reduce the influence of the unreasonable evaluation value was given by the decision maker on the decision-making results. The Archimedean t-norm and t-conorm (ATS) also have many advantages for the processing of uncertain data. Under this environment, the confidence q-rung orthopair fuzzy aggregation operators based on ATS is one of the most successful extensions of confidence q-rung orthopair fuzzy numbers (Cq-ROFNs) in which decrease the deviation caused by the subjective perspective of the decision maker in the multicriteria group decision-making (MCGDM) problems. In this paper, we propose weighted, ordered weighted averaging aggregation operators and weighted, ordered weighted geometric aggregation operators based on ATS, respectively. Moreover, the properties and four specific forms associated with aggregation operators are also investigated. In this study, a novel MCGDM approach is introduced by using the proposed operator. A reasonable example is proposed and compared the results which are obtained by our operators and that in existing literature, so as to verify the rationality and flexible of our method. From the study, we concluded that the proposed method can reduce the impact of extreme data, and makes decision-making results more reasonable by considering the attitudes of decision-makers.

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Linguistic Spherical Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

Mathematics ◽

10.3390/math7050413 ◽

2019 ◽

Vol 7 (5) ◽

pp. 413 ◽

Cited By ~ 19

Author(s):

Huanhuan Jin ◽

Shahzaib Ashraf ◽

Saleem Abdullah ◽

Muhammad Qiyas ◽

Mahwish Bano ◽

...

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Aggregation Operators ◽

Weighted Averaging ◽

Operational Laws ◽

Picture Fuzzy Set ◽

Fuzzy Aggregation ◽

Multi Attribute Decision Making

The key objective of the proposed work in this paper is to introduce a generalized form of linguistic picture fuzzy set, so-called linguistic spherical fuzzy set (LSFS), combining the notion of linguistic fuzzy set and spherical fuzzy set. In LSFS we deal with the vague and defective information in decision making. LSFS is characterized by linguistic positive, linguistic neutral and linguistic negative membership degree which satisfies the conditions that the square sum of its linguistic membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of linguistic spherical fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose linguistic spherical fuzzy weighted averaging and geometric operators based on spherical fuzzy numbers. Further, the proposed aggregation operators of linguistic spherical fuzzy number are applied to multi-attribute group decision-making problems. To implement the proposed models, we provide some numerical applications of group decision-making problems. In addition, compared with the previous model, we conclude that the proposed technique is more effective and reliable.

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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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Some Improved q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications to Multiattribute Group Decision-Making

Mathematical Problems in Engineering ◽

10.1155/2019/2036728 ◽

2019 ◽

Vol 2019 ◽

pp. 1-18 ◽

Cited By ~ 4

Author(s):

Lei Xu ◽

Yi Liu ◽

Haobin Liu

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Intuitionistic Fuzzy Set ◽

Aggregation Operator ◽

Aggregation Operators ◽

Weighted Averaging ◽

Pythagorean Fuzzy Set ◽

Fuzzy Aggregation

As a generalization of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), q-rung orthopair fuzzy set (q-ROFS) is a new concept in describing complex fuzzy uncertainty information. The present work focuses on the multiattribute group decision-making (MAGDM) approach under the q-rung orthopair fuzzy information. To begin with, some drawbacks of the existing MAGDM methods based on aggregation operators (AOs) are firstly analyzed. In addition, some improved operational laws put forward to overcome the drawbacks along with some properties of the operational law are proved. Thirdly, we put forward the improved q-rung orthopair fuzzy-weighted averaging (q-IROFWA) aggregation operator and improved q-rung orthopair fuzzy-weighted power averaging (q-IROFWPA) aggregation operator and present some of their properties. Then, based on the q-IROFWA operator and q-IROFWPA operator, we proposed a new method to deal with MAGDM problems under the fuzzy environment. Finally, some numerical examples are provided to illustrate the feasibility and validity of the proposed method.

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New Logarithmic Operational Laws-Based Complex q-Rung Orthopair Fuzzy Aggregation Operators and Their Application in Decision-Making Process

Complexity ◽

10.1155/2021/5540529 ◽

2021 ◽

Vol 2021 ◽

pp. 1-32

Author(s):

Harish Garg ◽

Zeeshan Ali ◽

Tahir Mahmood ◽

Sultan Aljahdali ◽

Habib Shah

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Aggregation Operators ◽

Unit Interval ◽

Weighted Averaging ◽

Decision Making Process ◽

The Real ◽

Fundamental Properties ◽

Operational Laws ◽

Fuzzy Aggregation

A complex q-rung orthopair fuzzy set (CQROFS) is one of the useful tools to handle the uncertainties in the data. The main characteristic of the CQROFS is that it handles the imprecise information in the data using the membership degrees such that the sum of the q-powers of the real parts (also for imaginary parts) of the membership and nonmembership degrees is restricted to the unit interval. Keeping the highlights of this set, in this study, we manifested some new logarithmic operational laws (LOLs) between the pairs of the CQROFSs and investigated their properties. Also, by using these proposed laws, we stated several averaging and geometric operators, namely, logarithmic complex q-rung orthopair fuzzy weighted averaging (LCQROFWA) and logarithmic complex q-rung orthopair fuzzy weighted geometric (LCQROFWG) operators and hence stated their fundamental properties. Later on, based on the suggested operators, a multiattribute decision-making (MADM) algorithm is acted to solve the decision-making problems. A numerical example has been considered to illustrate the approach and compare their obtained results with several of the existing studies’ results. Finally, the advantages of the suggested algorithms and operators are presented.

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Multi Criteria Group Decision Making Based On Q-Rung Orthopair Trapezoidal Hesitant Dombi Fuzzy Aggregation Operators

10.21203/rs.3.rs-328227/v1 ◽

2021 ◽

Author(s):

Aliya Fahmi ◽

Muhammad Aslam ◽

Rehan Ahmad

Keyword(s):

Decision Making ◽

Fuzzy Numbers ◽

Group Decision ◽

Uncertain Data ◽

Multiple Attribute Decision Making ◽

Aggregation Operators ◽

Weighted Averaging ◽

Multiple Attribute ◽

Fuzzy Aggregation ◽

Fuzzy Statistics

Abstract The paper determinations to present the impression of dombi aggregation operators for the q-rung orthopair trapezoidal hesitant dombi fuzzy numbers. The q-rung orthopair trapezoidal hesitant dombi fuzzy statistics is an imperative idea. On the other indicator, the association between the diverse combines of the qualities are well chronicled in rapports of dombi operators. Thus, possession these compensations of q-rung orthopair trapezoidal hesitant dombi fuzzy number, the impartial of this work is to describe numerous weighted averaging and geometric aggregation operators. The numerous possessions and the extraordinary cases of them are also derived. Further, the consequences of proposed new dombi aggregation operators are studied in view of some constraints. Finally, a multiple attribute decision making algorithm, based on the proposed operators, is established to solve the problems with uncertain data and exemplify with arithmetical instances. A relative assignment, domination check and discussion of the intentional approach are provided to authorize the methodology.

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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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