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 A Novel Approach of Complex Dual Hesitant Fuzzy Sets and Their Applications in Pattern Recognition and Medical Diagnosis

2021 ◽  
Vol 2021 ◽  
pp. 1-31
Author(s):  
Ubaid Ur Rehman ◽  
Tahir Mahmood ◽  
Zeeshan Ali ◽  
Thammarat Panityakul
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Reliability And Validity ◽  
Hesitant Fuzzy Set ◽  
Dual Hesitant Fuzzy Set ◽  
Novel Approach ◽  
Operational Laws ◽  
Interval Valued

Complex dual hesitant fuzzy set (CDHFS) is an assortment of complex fuzzy set (CFS) and dual hesitant fuzzy set (DHFS). In this manuscript, the notion of the CDHFS is explored and its operational laws are discussed. The new methodology of the complex interval-valued dual hesitant fuzzy set (CIvDHFS) and its necessary laws are introduced and are also defensible with the help of examples. Further, the antilogarithmic and with-out exponential-based similarity measures, generalized similarity measures, and their important characteristics are also developed. These similarity measures are applied in the environment of pattern recognition and medical diagnosis to evaluate the proficiency and feasibility of the established measures. We also solved some numerical examples using the established measures to examine the reliability and validity of the proposed measures by comparing these with existing measures. To strengthen the proposed study, the comparative analysis is made and it is conferred that the proposed study is much more superior to the existing studies.

A New Similarity Measure of Picture Fuzzy Sets And Application in pattern recognition

2020 ◽  
pp. 5-18
Author(s):  
Ngoc Minh Chau, Nguyen Thi Lan, Nguyen Xuan Thao ◽  
Keyword(s):  
Pattern Recognition ◽  
Fault Diagnosis ◽  
Fuzzy Sets ◽  
Steam Turbine ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Similarity Measures ◽  
The Novel ◽  
Picture Fuzzy Set ◽  
Picture Fuzzy Sets

In this paper, we propose some novel similarity measures between picture fuzzy sets. The novel similarity measure is constructed by combining negative functions of each degree membership of picture fuzzy set. We apply them in several pattern recognition problems. Finally, we apply them to find the fault diagnosis of the steam turbine.

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 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 Distance and Similarity Measures Including New Hesitant Degree on Hesitant Fuzzy Set

2019 ◽  
Vol 8 (4) ◽  
pp. 9117-9125
Keyword(s):  
Fuzzy Set ◽  
Satisfactory Result ◽  
Distance Measure ◽  
Real Life ◽  
Similarity Measures ◽  
Hesitant Fuzzy Set ◽  
Satisfactory Outcome

Hesitant degree plays an important role for finding the distance and similarity measures between two objects. Many researchers have developed many distance and similarity measures so far but in real life some situations arises where these measures fail to achieve the satisfactory result. In this paper, a new hesitant degree is introduced in the distance and similarity measures so that the limitations which are found can be easily handled with a satisfactory outcome. Finally, the validity of the proposed distance measure is illustrated with a suitable example..

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 A Decision Framework under a Linguistic Hesitant Fuzzy Set for Solving Multi-Criteria Group Decision Making Problems

2018 ◽  
Vol 10 (8) ◽  
pp. 2608 ◽  
Author(s):  
R. Krishankumar ◽  
K. Ravichandran ◽  
J. Premaladha ◽  
Samarjit Kar ◽  
Edmundas Zavadskas ◽  
...  
Keyword(s):  
Fuzzy Set ◽  
Group Decision ◽  
Healthcare Management ◽  
Decision Makers ◽  
Hesitant Fuzzy Set ◽  
Decision Framework ◽  
Qualitative Information ◽  
Proper Selection ◽  
Operational Laws ◽  
Criteria Weights

With fast-growing interest in sustainable healthcare management, proper selection and evaluation of hospitals become highly essential. Generally, experts/decision-makers (DMs) prefer qualitative information for rating objects. Motivated by this idea, in this paper, a linguistic hesitant fuzzy set (LHFS) is adopted for elicitation of preference information. The LHFS provides qualitative preferences of DMs as well as reflects their hesitancy, inconsistency, and vagueness. Motivated by the power of LHFS, in this paper we present a new decision framework that initially presents some operational laws and properties. Further, a new aggregation operator called simple linguistic hesitant fuzzy weighted geometry (SLHFWG) is proposed under the LHFS context that uses the strength of power operators. Some properties of SLHFWG are also investigated. Criteria weights are estimated using a newly proposed linguistic hesitant fuzzy statistical variance (LHFSV) method, and objects are ranked using the newly proposed linguistic hesitant fuzzy VIKOR (visekriterijumska optimizacijai kompromisno resenje) (LHFVIKOR) method, which is an extension of VIKOR under the LHFS context. The practicality and usefulness of the proposal are demonstrated by using a hospital evaluation example for sustainable healthcare management. Finally, the strengths and weaknesses of the proposal are realized by comparison with other methods.

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.

scholarly journals A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yafei Song ◽  
Xiaodan Wang ◽  
Lei Lei ◽  
Aijun Xue
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Axiomatic Definition

As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns.

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