scholarly journals Modified Expression to Evaluate the Correlation Coefficient of Dual Hesitant Fuzzy Sets and Its Application to Multi-Attribute Decision Making

2021 ◽  
Author(s):  
Akanksha Singh
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Real Life ◽  
Correlation Coefficients ◽  
Hesitant Fuzzy Set ◽  
Root Cause ◽  
Dual Hesitant Fuzzy Set ◽  
Multi Attribute Decision Making ◽  
Detailed Mathematical Analysis

The main objective of this paper is to understand all the existing correlation coefficients (CoCfs) to determine the relation and dependency between two variables of the fuzzy sets and its extensions for solving decision-making (DM) problems. To study the weighted CoCfs between two variables the environment chosen here is dual hesitant fuzzy set (DHFS) which is a generalization of a fuzzy set which considers the hesitant value of both the membership and non-membership elements of a set. Although there exists CoCfs for DHFS but a detailed mathematical analysis suggests that there exists some shortcomings in the existing CoCfs for DHFS. Thus, an attempt has been made to properly understand the root cause of the posed limitation in the weighted CoCfs for DHFS and hence, modified weighted CoCfs for DHFS has been proposed for solving DHFS multi-attribute decision making (MADM) problems i.e., DM problems in which rating value of each alternative over each criterion is represented by a DHFS in the real-life. Also, to validate the proposed expressions of weighted CoCfs for solving DHFS MADM problems, an existing real-life problem is evaluated and a systematic comparison of the solution is presented for clarification.

scholarly journals A Novel Multi-Attribute Group Decision-Making Approach in the Framework of Proportional Dual Hesitant Fuzzy Sets

2019 ◽  
Vol 9 (6) ◽  
pp. 1232 ◽  
Author(s):  
Zia Bashir ◽  
Yasir Bashir ◽  
Tabasam Rashid ◽  
Jawad Ali ◽  
Wei Gao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Group Decision ◽  
Traditional Approach ◽  
Hesitant Fuzzy Set ◽  
Flexible Tool ◽  
Dual Hesitant Fuzzy Set

Making decisions are very common in the modern socio-economic environments. However, with the increasing complexity of the social, today’s decision makers (DMs) face such problems in which they hesitate and irresolute to provide their views. To cope with these uncertainties, many generalizations of fuzzy sets are designed, among them dual hesitant fuzzy set (DHFS) is quite resourceful and efficient in solving problems of a more vague nature. In this article, a novel concept called proportional dual hesitant fuzzy set (PDHFS) is proposed to further improve DHFS. The PDHFS is a flexible tool composed of some possible membership values and some possible non-membership values along with their associated proportions. In the theme of PDHFS, the proportions of membership values and non-membership values are considered to be independent. Some basic operations, properties, distance measure and comparison method are studied for the proposed set. Thereafter, a novel approach based on PDHFSs is developed to solve problems for multi-attribute group decision-making (MAGDM) in a fuzzy situation. It is totally different from the traditional approach. Finally, a practical example is given in order to elaborate the proposed method for the selection of the best alternative and detailed comparative analysis is given in order to validate the practicality.

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 Multi-Attribute Decision-Making Approach Based on Dual Hesitant Fuzzy Information Measures and Their Applications

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 786 ◽  
Author(s):  
Huiping Chen ◽  
Guiqiong Xu ◽  
Pingle Yang
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Hesitant Fuzzy Set ◽  
Information Measures ◽  
Extended Technique ◽  
Dual Hesitant Fuzzy Set ◽  
Entropy Measures ◽  
Multi Attribute Decision Making

Combining the ideas and advantages of intuitionistic fuzzy set (IFS) and hesitant fuzzy set (HFS), dual hesitant fuzzy set (DHFS) could express uncertain and complex information given by decision makers (DMs) in a more flexible manner. By virtue of the existing measure methods, elements in DHFSs should be of equal length and thus some values must be added into the shorter elements according to the risk preference of DMs. The extension of values will increase the subjectivity of decision-making to some extent, and different extension methods may produce different results. In order to address this issue, we first propose several new forms of distance and similarity measures without adding values. Subsequently, according to the proposed distance and similarity measures, two entropy measures are presented from the viewpoints of complementary set and the fuzziest set, respectively. Furthermore, based on the new distance and entropy measures, an extended technique for order preference by similarity to an ideal solution (TOPSIS) method is proposed for dealing with multi-attribute decision-making problems in the context of DHFS. Finally, two practical examples are analyzed to show the validity and applicability of the proposed method.

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

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 280 ◽  
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.

scholarly journals Jaccard and Dice Similarity Measures Based on Novel Complex Dual Hesitant Fuzzy Sets and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-25
Author(s):  
Tahir Mahmood ◽  
Ubaid Ur Rehman ◽  
Zeeshan Ali ◽  
Ronnason Chinram
Keyword(s):  
Similarity Measure ◽  
Fuzzy Set ◽  
Real Life ◽  
Similarity Measures ◽  
Hesitant Fuzzy Set ◽  
The Novel ◽  
Dual Hesitant Fuzzy Set ◽  
Life Problems ◽  
Novel Approach ◽  
Operational Laws

Complex dual hesitant fuzzy set (CDHFS) is a combination of two modifications, called complex fuzzy set (CFS) and dual hesitant fuzzy set (DHFS). CDHFS makes two degrees, called membership valued and nonmembership valued in the form of a finite subset of a unit disc in the complex plane, and is a capable method to solve uncertain and unpredictable information in real-life problems. The goal of this study is to describe the notion of CDHFS and its operational laws. The novel approach of the complex interval-valued dual hesitant fuzzy set (CIvDHFS) and its fundamental laws are also described and defended with the help of an example. Further, the vector similarity measures (VSMs), weighted vector similarity measures (WVSMs), hybrid vector similarity measure, and weighted hybrid vector similarity measure are additionally explored. These similarity measures (SM) are applied to the environment of pattern recognition and medical diagnosis to assess the capability and feasibility of the interpreted measures. We additionally solved some numerical examples utilizing the established measures. We examine the dependability and validity of the proposed measures by comparing them with some existing measures. The advantages, comparative analysis, and graphical portrayal of the investigated interpreted measures and existing measures are additionally described in detail.

scholarly journals Decision-Making Approach under Pythagorean Fuzzy Yager Weighted Operators

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 70 ◽  
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.

Correlation coefficients for T-spherical fuzzy sets and their applications in clustering and multi-attribute decision making

2019 ◽  
Vol 24 (3) ◽  
pp. 1647-1659 ◽  
Author(s):  
Kifayat Ullah ◽  
Harish Garg ◽  
Tahir Mahmood ◽  
Naeem Jan ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Correlation Coefficients ◽  
Multi Attribute Decision Making
Sign in / Sign up

Export Citation Format

Share Document