scholarly journals Complex Fuzzy Power Aggregation Operators

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Bo Hu ◽  
Lvqing Bi ◽  
Songsong Dai
Keyword(s):  
Decision Making ◽  
Unit Disk ◽  
Fuzzy Set ◽  
Aggregation Operators ◽  
Rotational Invariance ◽  
Geometric Properties ◽  
New Approach ◽  
Complex Fuzzy Set ◽  
Fuzzy Aggregation

A complex fuzzy set is an extension of the fuzzy set, of which membership grades take complex values in the complex unit disk. We present two complex fuzzy power aggregation operators including complex fuzzy weighted power (CFWP) and complex fuzzy ordered weighted power (CFOWP) operators. We then study two geometric properties which include rotational invariance and reflectional invariance for these complex fuzzy aggregation operators. We also apply the new proposed aggregation operators to decision making and illustrate an example to show the validity of the new approach.

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

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 608 ◽  
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.

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

2018 ◽  
Vol 17 (01) ◽  
pp. 1850005 ◽  
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.

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

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 357 ◽  
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.

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

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.

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

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 593 ◽  
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.

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

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 413 ◽  
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.

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

2018 ◽  
Vol 17 (02) ◽  
pp. 391-466 ◽  
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.

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

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
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.

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

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 780 ◽  
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.

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

Complexity ◽  
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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