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

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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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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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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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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Dependent Interval 2-Tuple Linguistic Aggregation Operators and Their Application to Multiple Attribute Group Decision Making

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488514500366 ◽

2014 ◽

Vol 22 (05) ◽

pp. 717-735 ◽

Cited By ~ 29

Author(s):

Hu-Chen Liu ◽

Qing-Lian Lin ◽

Jing Wu

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Aggregation Operators ◽

Decision Makers ◽

Weighted Averaging ◽

Linguistic Variables ◽

Preference Information ◽

Operational Laws ◽

Multiple Attribute

Consider the various types of uncertain preference information provided by the decision makers and the importance of determining the associated weights for the aggregation operator, the multiple attribute group decision making (MAGDM) methods based on some dependent interval 2-tuple linguistic aggregation operators are proposed in this paper. Firstly some operational laws and possibility degree of interval 2-tuple linguistic variables are introduced. Then, we develop a dependent interval 2-tuple weighted averaging (DITWA) operator and a dependent interval 2-tuple weighted geometric (DITWG) operator, in which the associated weights only depend on the aggregated interval 2-tuple arguments and can relieve the influence of unfair arguments on the aggregated results by assigning low weights to them. Based on the DITWA and the DITWG operators, some approaches for multiple attribute group decision making with interval 2-tuple linguistic information are proposed. Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approaches.

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INTERVAL-VALUED INTUITIONISTIC FUZZY ORDERED PRECISE WEIGHTED AGGREGATION OPERATOR AND ITS APPLICATION IN GROUP DECISION MAKING

Technological and Economic Development of Economy ◽

10.3846/20294913.2013.869516 ◽

2014 ◽

Vol 20 (4) ◽

pp. 648-672 ◽

Cited By ~ 13

Author(s):

Wei Zhou ◽

Jian Min He

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Scale Invariance ◽

Group Decision ◽

Aggregation Operator ◽

Aggregation Operators ◽

Weighted Averaging ◽

Intuitionistic Fuzzy ◽

Fuzzy Aggregation ◽

Interval Valued

An important research topic related to the theory and application of the interval-valued intuitionistic fuzzy weighted aggregation operators is how to determine their associated weights. In this paper, we propose a precise weight-determined (PWD) method of the monotonicity and scale-invariance, just based on the new score and accuracy functions of interval-valued intuitionistic fuzzy number (IIFN). Since the monotonicity and scale-invariance, the PWD method may be a precise and objective approach to calculate the weights of IIFN and interval-valued intuitionistic fuzzy aggregation operator, and a more suitable approach to distinguish different decision makers (DMs) and experts in group decision making. Based on the PWD method, we develop two new interval-valued intuitionistic fuzzy aggregation operators, i.e. interval-valued intuitionistic fuzzy ordered precise weighted averaging (IIFOPWA) operator and interval-valued intuitionistic fuzzy ordered precise weighted geometric (IIFOPWG) operator, and study their desirable properties in detail. Finally, we provide an illustrative example.

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Complex pythagorean fuzzy aggregation operators based on confidence levels and their applications

Mathematical Biosciences and Engineering ◽

10.3934/mbe.2022050 ◽

2021 ◽

Vol 19 (1) ◽

pp. 1078-1107

Author(s):

Tahir Mahmood ◽

◽

Zeeshan Ali ◽

Kifayat Ullah ◽

Qaisar Khan ◽

...

Keyword(s):

Decision Making ◽

Sensitivity Analysis ◽

Comparative Analysis ◽

Aggregation Operators ◽

Weighted Averaging ◽

Confidence Levels ◽

Ordered Weighted Averaging ◽

Operational Laws ◽

Fuzzy Aggregation ◽

Multi Attribute Decision Making

<abstract> <p>The most important influence of this assessment is to analyze some new operational laws based on confidential levels (CLs) for complex Pythagorean fuzzy (CPF) settings. Moreover, to demonstrate the closeness between finite numbers of alternatives, the conception of confidence CPF weighted averaging (CCPFWA), confidence CPF ordered weighted averaging (CCPFOWA), confidence CPF weighted geometric (CCPFWG), and confidence CPF ordered weighted geometric (CCPFOWG) operators are invented. Several significant features of the invented works are also diagnosed. Moreover, to investigate the beneficial optimal from a large number of alternatives, a multi-attribute decision-making (MADM) analysis is analyzed based on CPF data. A lot of examples are demonstrated based on invented works to evaluate the supremacy and ability of the initiated works. For massive convenience, the sensitivity analysis and merits of the identified works are also explored with the help of comparative analysis and they're graphical shown.</p> </abstract>

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Spherical uncertain linguistic Hamacher aggregation operators and their application on achieving consistent opinion fusion in group decision making

International Journal of Intelligent Computing and Cybernetics ◽

10.1108/ijicc-09-2020-0120 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Muhammad Qiyas ◽

Saleem Abdullah ◽

Muhammad Naeem

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Aggregation Operator ◽

Aggregation Operators ◽

Content Type ◽

Operational Laws ◽

Decision Making Problem ◽

Multi Attribute Decision Making ◽

New Type

PurposeThe aim of this research is to establish a new type of aggregation operator based on Hamacher operational law of spherical uncertain linguistic numbers (SULNs).Design/methodology/approachFirst, the authors define spherical uncertain linguistic sets and develop some operational laws of SULNs. Furthermore, the authors extended these operational laws to the aggregation operator and developed spherical uncertain linguistic Hamacher averaging and geometric aggregation operators.FindingsThe authors were limited in achieving a consistent opinion on the fusion in group decision-making problem with the SULN information.Originality/valueIn order to give an application of the introduced operators, the authors first constrict a system of multi-attribute decision-making algorithm.

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A New Ranking Methodology for Pythagorean Trapezoidal Uncertain Linguistic Fuzzy Sets Based on Einstein Operations

Symmetry ◽

10.3390/sym11030440 ◽

2019 ◽

Vol 11 (3) ◽

pp. 440 ◽

Cited By ~ 5

Author(s):

Arshad Khan ◽

Saleem Abdullah ◽

Muhammad Shakeel ◽

Faisal Khan ◽

Noor Amin ◽

...

Keyword(s):

Decision Making ◽

Group Decision ◽

Aggregation Operators ◽

Weighted Averaging ◽

Decision Making Process ◽

Ordered Weighted Averaging ◽

Operational Laws ◽

Multiple Attribute ◽

Fuzzy Aggregation ◽

Einstein Operations

In this article, we proposed new Pythagorean trapezoidal uncertain linguistic fuzzy aggregation information—namely, the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein weighted averaging (PTULFEWA) operator, the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein ordered weighted averaging (PTULFEOWA) operator, and the Pythagorean trapezoidal uncertain linguistic fuzzy Einstein hybrid weighted averaging (PTULFEHWA) operator—using the Einstein operational laws. We studied some important properties of the suggested aggregation operators and showed that the PTULFEHWA is more general than the other proposed operators, which simplifies these aggregation operators. Furthermore, we presented a multiple attribute group decision making (MADM) process for the proposed aggregation operators under the Pythagorean trapezoidal uncertain linguistic fuzzy (PTULF) environment. A numerical example was constructed to determine the effectiveness and practicality of the proposed approach. Lastly, a comparative analysis was performed of the presented approach with existing approaches to show that the proposed method is consistent and provides more information that may be useful for complex problems in the decision-making process.

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Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making

Symmetry ◽

10.3390/sym10110593 ◽

2018 ◽

Vol 10 (11) ◽

pp. 593 ◽

Cited By ~ 20

Author(s):

Hongran Zhang ◽

Runtong Zhang ◽

Huiqun Huang ◽

Jun Wang

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Intuitionistic Fuzzy Set ◽

Aggregation Operators ◽

Fuzzy Decision Making ◽

Good Ability ◽

Picture Fuzzy Set ◽

Fuzzy Aggregation ◽

Multi Attribute Decision Making ◽

Heronian Mean

As an extension of the intuitionistic fuzzy set (IFS), the recently proposed picture fuzzy set (PFS) is more suitable to describe decision-makers’ evaluation information in decision-making problems. Picture fuzzy aggregation operators are of high importance in multi-attribute decision-making (MADM) within a picture fuzzy decision-making environment. Hence, in this paper our main work is to introduce novel picture fuzzy aggregation operators. Firstly, we propose new picture fuzzy operational rules based on Dombi t-conorm and t-norm (DTT). Secondly, considering the existence of a broad and widespread correlation between attributes, we use Heronian mean (HM) information aggregation technology to fuse picture fuzzy numbers (PFNs) and propose new picture fuzzy aggregation operators. The proposed operators not only fuse individual attribute values, but also have a good ability to model the widespread correlation among attributes, making them more suitable for effectively solving increasingly complicated MADM problems. Hence, we introduce a new algorithm to handle MADM based on the proposed operators. Finally, we apply the newly developed method and algorithm in a supplier selection issue. The main novelties of this work are three-fold. Firstly, new operational laws for PFSs are proposed. Secondly, novel picture fuzzy aggregation operators are developed. Thirdly, a new approach for picture fuzzy MADM is proposed.

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