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

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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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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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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Multi-Attribute Multi-Perception Decision-Making Based on Generalized T-Spherical Fuzzy Weighted Aggregation Operators on Neutrosophic Sets

Mathematics ◽

10.3390/math7090780 ◽

2019 ◽

Vol 7 (9) ◽

pp. 780 ◽

Cited By ~ 11

Author(s):

Quek ◽

Selvachandran ◽

Munir ◽

Mahmood ◽

Ullah ◽

...

Keyword(s):

Decision Making ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Aggregation Operators ◽

Neutrosophic Sets ◽

Operational Laws ◽

Fuzzy Aggregation ◽

Multi Attribute Decision Making ◽

Do So

The framework of the T-spherical fuzzy set is a recent development in fuzzy set theory that can describe imprecise events using four types of membership grades with no restrictions. The purpose of this manuscript is to point out the limitations of the existing intuitionistic fuzzy Einstein averaging and geometric operators and to develop some improved Einstein aggregation operators. To do so, first some new operational laws were developed for T-spherical fuzzy sets and their properties were investigated. Based on these new operations, two types of Einstein aggregation operators are proposed namely the Einstein interactive averaging aggregation operators and the Einstein interactive geometric aggregation operators. The properties of the newly developed aggregation operators were then investigated and verified. The T-spherical fuzzy aggregation operators were then applied to a multi-attribute decision making (MADM) problem related to the degree of pollution of five major cities in China. Actual datasets sourced from the UCI Machine Learning Repository were used for this purpose. A detailed study was done to determine the most and least polluted city for different perceptions for different situations. Several compliance tests were then outlined to test and verify the accuracy of the results obtained via our proposed decision-making algorithm. It was proved that the results obtained via our proposed decision-making algorithm was fully compliant with all the tests that were outlined, thereby confirming the accuracy of the results obtained via our proposed method.

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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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Decision-Making Approach under Pythagorean Fuzzy Yager Weighted Operators

Mathematics ◽

10.3390/math8010070 ◽

2020 ◽

Vol 8 (1) ◽

pp. 70 ◽

Cited By ~ 16

Author(s):

Gulfam Shahzadi ◽

Muhammad Akram ◽

Ahmad N. Al-Kenani

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Aggregation Operators ◽

Weighted Averaging ◽

Ordered Weighted Averaging ◽

Multi Attribute Decision Making ◽

Parametric Families

In fuzzy set theory, t-norms and t-conorms are fundamental binary operators. Yager proposed respective parametric families of both t-norms and t-conorms. In this paper, we apply these operators for the analysis of Pythagorean fuzzy sets. For this purpose, we introduce six families of aggregation operators named Pythagorean fuzzy Yager weighted averaging aggregation, Pythagorean fuzzy Yager ordered weighted averaging aggregation, Pythagorean fuzzy Yager hybrid weighted averaging aggregation, Pythagorean fuzzy Yager weighted geometric aggregation, Pythagorean fuzzy Yager ordered weighted geometric aggregation and Pythagorean fuzzy Yager hybrid weighted geometric aggregation. These tools inherit the operational advantages of the Yager parametric families. They enable us to study two multi-attribute decision-making problems. Ultimately we can choose the best option by comparison of the aggregate outputs through score values. We show this procedure with two practical fully developed examples.

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Interval-Valued Dual Hesitant Fuzzy Heronian Mean Aggregation Operators and their Application to Multi-Attribute Decision Making

International Journal of Computational Intelligence and Applications ◽

10.1142/s1469026818500050 ◽

2018 ◽

Vol 17 (01) ◽

pp. 1850005 ◽

Cited By ~ 7

Author(s):

Yuqi Zang ◽

Xiaodong Zhao ◽

Shiyong Li

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Aggregation Operators ◽

Hesitant Fuzzy Set ◽

Fuzzy Information ◽

New Approach ◽

Dual Hesitant Fuzzy Set ◽

Multi Attribute Decision Making ◽

Interval Valued ◽

Heronian Mean

The interval-valued dual hesitant fuzzy set (IVDHFS) can depict the imprecise, vague and indeterminate information and Heronian mean (HM) has the prominent characteristic of capturing the correlation of the aggregated arguments. In this paper, we investigate multi-attribute decision making (MADM) problems based on HM, in which the attribute values are assumed in the form of interval-valued dual hesitant fuzzy information. Firstly, we briefly present some concepts of IVDHFS and HM. Then, we propose the interval-valued dual hesitant fuzzy Heronian mean (IVDHFHM) operator and the interval-valued dual hesitant fuzzy geometric Heronian mean (IVDHFGHM) operator. We also prove that they satisfy some desirable properties. Further, we consider the importance of the input arguments and derive the interval-valued dual hesitant fuzzy weighted Heronian mean (IVDHFWHM) operator and the interval-valued dual hesitant fuzzy weighted geometric Heronian mean (IVDHFWGHM) operator, and then develop the procedure of MADM. Finally, an illustrate example is given to demonstrate the practicality and effectiveness of the new approach.

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Protraction of Einstein operators for decision-making under q-rung orthopair fuzzy model

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-201611 ◽

2020 ◽

pp. 1-20

Author(s):

Muhammad Akram ◽

Gulfam Shahzadi ◽

Sundas Shahzadi

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Intuitionistic Fuzzy Set ◽

Fuzzy Model ◽

Aggregation Operators ◽

Weighted Averaging ◽

Pythagorean Fuzzy Set ◽

Career Selection ◽

Ordered Weighted Averaging ◽

Multi Attribute Decision Making

An q-rung orthopair fuzzy set is a generalized structure that covers the modern extensions of fuzzy set, including intuitionistic fuzzy set and Pythagorean fuzzy set, with an adjustable parameter q that makes it flexible and adaptable to describe the inexact information in decision making. The condition of q-rung orthopair fuzzy set, i.e., sum of q th power of membership degree and nonmembership degree is bounded by one, makes it highly competent and adequate to get over the limitations of existing models. The basic purpose of this study is to establish some aggregation operators under the q-rung orthopair fuzzy environment with Einstein norm operations. Motivated by innovative features of Einstein operators and dominant behavior of q-rung orthopair fuzzy set, some new aggregation operators, namely, q-rung orthopair fuzzy Einstein weighted averaging, q-rung orthopair fuzzy Einstein ordered weighted averaging, generalized q-rung orthopair fuzzy Einstein weighted averaging and generalized q-rung orthopair fuzzy Einstein ordered weighted averaging operators are defined. Furthermore, some properties related to proposed operators are presented. Moreover, multi-attribute decision making problems related to career selection, agriculture land selection and residential place selection are presented under these operators to show the capability and proficiency of this new idea. The comparison analysis with existing theories shows the superiorities of proposed model.

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

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-211003 ◽

2021 ◽

pp. 1-19

Author(s):

Shouzhen Zeng ◽

Amina Azam ◽

Kifayat Ullah ◽

Zeeshan Ali ◽

Awais Asif

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Fuzzy Numbers ◽

Aggregation Operators ◽

Weighted Averaging ◽

Membership Degree ◽

Human Judgment ◽

Induction Method ◽

Fuzzy Aggregation ◽

The Impact

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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