Distance and similarity measures for hesitant fuzzy sets
Information SciencesPublished 2 February 2011
Zeshui Xu, Meimei Xia
Citations1,110
SJR quartileQ1
SJR score1.80
SNIP1.98
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
A variety of distance measures for hesitant fuzzy sets are proposed, based on which the corresponding similarity measures can be obtained and can alleviate the influence of unduly large deviations on the aggregation results by assigning them low (or high) weights.
Abstract
In this paper, we propose a variety of distance measures for hesitant fuzzy sets, based on which the corresponding similarity measures can be obtained. We investigate the connections of the aforementioned distance measures and further develop a number of hesitant ordered weighted distance measures and hesitant ordered weighted similarity measures. They can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Several numerical examples are provided to illustrate these distance and similarity measures.
Keywords
Decision SciencesMathematicsEngineering
Fuzzy Sets and SystemsIntuitionistic fuzzy sets
16,153 Citations1986Krassimir Atanassov
Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
IEEE Transactions on Systems Man and CyberneticsOn ordered weighted averaging aggregation operators in multicriteria decisionmaking
7,125 Citations1988Ronald R. Yager
A type of operator for aggregation called an ordered weighted aggregation (OWA) operator is introduced and its performance is found to be between those obtained using the AND operator and the OR operator.
Mathematics in Science and Engineering/Mathematics in science and engineeringFuzzy Sets and Systems - Theory and Applications
6,430 Citations1980Didier Dubois, Henri Prade
International Journal of Intelligent SystemsHesitant fuzzy sets
1,617 Citations2010Vicenç Torra
It is proved that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set, and it is proved also that the operations proposed are consistent with the ones of intuitionist fuzzy sets when applied to the envelope.
Fuzzy Sets and SystemsDistances between intuitionistic fuzzy sets
1,587 Citations2000Eulalia Szmidt, Janusz Kacprzyk
It is shown that all three parameters describing intuitionistic fuzzy sets should be taken into account while calculating those distances between intuitionistically fuzzy sets.
On hesitant fuzzy sets and decision
1,194 Citations2009Vicenç Torra, Yasuo Narukawa
Fuzzy Sets and SystemsA method of inference in approximate reasoning based on interval-valued fuzzy sets
1,071 Citations1987Marian B. Gorzałczany
This method allows a formal, fuzzy representation to be built for verbal decision algorithms and can have an effective computer representation.
WORLD SCIENTIFIC eBooksMetric Spaces of Fuzzy Sets: Theory and Applications
880 Citations1994Phil Diamond, Peter E. Kloeden
Pattern Recognition LettersNew similarity measures of intuitionistic fuzzy sets and application to pattern recognitions
847 Citations2002Deng‐Feng Li, Cheng Chuntian
The definition of the degree of similarity between IFSs is introduced and several new similarity measures between I FSs are proposed and corresponding proofs are given.
Information SciencesIntuitionistic preference relations and their application in group decision making☆
838 Citations2007Zeshui Xu
This paper develops an approach to group decision making based on intuitionistic preference relations and an approach based on incomplete intuitionism preference relations respectively, in which the intuitionistic fuzzy arithmetic averaging operator and intuitionism fuzzy weighted arithmetic averagingoperator are used to aggregate intuitionistic preferences.
OmegaDeviation measures of linguistic preference relations in group decision making
742 Citations2004Zhigang Xu
A theoretic basis has been established for the application of linguistic preference relations in group decision making with the shown weighted combination of A1,A2,...,Am is linguistic preference relation.
International Journal of General SystemsON THE THEORY OF BAGS
709 Citations1986Ronald R. Yager
The bag structure as a set-like object in which repeated elements are significant and the operation of selecting elements from a bag based upon their membership in a set is introduced.
European Journal of Operational ResearchMulti-criteria decision-making methods based on intuitionistic fuzzy sets
650 Citations2006Huawen Liu, Guojun Wang
A series of new score functions are defined for multi-criteria decision-making problem based on the intuitionistic fuzzy point operators and the evaluation function and their effectiveness and advantage are illustrated by examples.
Fuzzy Sets and SystemsDistances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric
620 Citations2003Przemysław Grzegorzewski
New methods for measuring distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets, based on the Hausdorff metric, are suggested.
Fuzzy Sets and SystemsEntropy, distance measure and similarity measure of fuzzy sets and their relations
572 Citations1992Xuecheng Liu
The axiom definitions of entropy, distance measure and similarity measure of fuzzy sets are systematically given and basic relations between these measures are discussed.
Pattern Recognition LettersSimilarity measures of intuitionistic fuzzy sets based on Hausdorff distance
571 Citations2004Wen‐Liang Hung, Miin‐Shen Yang
A method to calculate the distance between IFSs on the basis of the Hausdorff distance is presented and this distance is used to generate a new similarity measure that is well suited to use with linguistic variables.
Fuzzy Optimization and Decision MakingGeneralized OWA Aggregation Operators
566 Citations2004Ronald R. Yager
The ordered weighted averaging operator is extended to a provide a new class of operators called the generalized OWA (GOWA) operators, which add to the OWA operator an additional parameter controlling the power to which the argument values are raised.
Pattern Recognition LettersDistance measure between intuitionistic fuzzy sets
528 Citations2005Weiqiong Wang, Xiaolong Xin
The axiom definition of distance measure between intuitionistic fuzzy sets (IFSs) is introduced and some distance measures are proposed and corresponding proofs are given.
Pattern Recognition LettersSimilarity measures on intuitionistic fuzzy sets
504 Citations2003Zhizhen Liang, Pengfei Shi
The proposed similarity measures can provide a useful way for measuring IFSs more effectively and are more reasonable than some existing similarity measures in general cases.
International Journal of Intelligent SystemsGeneralized aggregation operators for intuitionistic fuzzy sets
476 Citations2009Hua Zhao, Zeshui Xu +2 more
This paper develops some new generalized aggregation operators, such as generalized intuitionistic fuzzy weighted averaging operator, generalized intuitionistic fuzzy ordered weighted averaging operator, generalized intuitionistic fuzzy hybrid averaging operator, generalized interval‐valued intuitionistic fuzzy weighted averaging operator, and generalized interval‐valued intuitionistic fuzzy hybrid average operator.
Information SciencesClustering algorithm for intuitionistic fuzzy sets
454 Citations2008Zeshui Xu, Jian Chen +1 more
This paper defines the concepts of association matrix and equivalent association matrix, and introduces some methods for calculating the association coefficients of IFSs, and proposes a clustering algorithm for IFS's, which is extended to cluster interval-valued intuitionistic fuzzy sets (IVIFSs).
Information SciencesChoquet integrals of weighted intuitionistic fuzzy information
437 Citations2009Zeshui Xu
The Choquet integral is used to propose some intuitionistic fuzzy aggregation operators that not only consider the importance of the elements or their ordered positions, but also can reflect the correlations among the elements and theirordered positions.
Fuzzy Optimization and Decision MakingSome similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making
423 Citations2007Zeshui Xu
The similarity measures are developed and the notions of positive ideal intuitionistic fuzzy set and negative ideal intuitionist fuzzy set are defined and applied to multiple attribute decision making under intuitionists fuzzy environment.
RECERCAT (Consorci de Serveis Universitaris de Catalunya)
417 Citations2009José M. Merigó, Anna M. Gil‐Lafuente
The induced generalized ordered weighted averaging (IGOWA) operator is a new aggregation operator that generalizes the OWA operator, including the main characteristics of both the generalized OWA and the induced OWA operators.
Pattern Recognition LettersOn the Dengfeng–Chuntian similarity measure and its application to pattern recognition
403 Citations2003H. B. Mitchell
This paper illustrates the application of the modified similarity measure on a simple pattern recognition problem and shows how a simple modification of the Dengfeng-Chuntian operator may correct this problem.
International Journal of Uncertainty Fuzziness and Knowledge-Based SystemsAN OVERVIEW OF DISTANCE AND SIMILARITY MEASURES OF INTUITIONISTIC FUZZY SETS
368 Citations2008Zeshui Xu, Jiayi Chen
This paper utilizes geometric distance model to define some continuous distance and similarity measures for IFSs, which are the various combinations and generalizations of the weighted Hamming distance, the weighted Euclidean distance and the weighted Hausdorff distance.
Information SciencesA comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets
349 Citations2008Dongrui Wu, Jerry M. Mendel
A new ranking method and a new similarity measure for IT2 FSs are proposed and the results are useful in understanding the uncertainties associated with linguistic terms and hence how to use them effectively in survey design and linguistic information processing.
IEEE Transactions on Systems Man and CyberneticsImage Enhancement Using Smoothing with Fuzzy Sets
338 Citations1981
A model for grey-tone image enhancement using the concept of fuzzy sets is suggested and the reduction of the "index of fuzziness" and "entropy" for different enhanced outputs (corresponding to different values of fuzzifiers) is demonstrated.
Expert Systems with ApplicationsA fuzzy multicriteria methodology for selection among energy alternatives
323 Citations2010Cengiz Kahraman, İ̇hsan Kaya
A fuzzy multicriteria decision-making methodology is suggested for the selection among energy policies, based on the analytic hierarchy process (AHP) under fuzziness, which determines the best energy policy for Turkey.
Fuzzy Sets and SystemsRelationship between similarity measure and entropy of interval valued fuzzy sets
321 Citations2005Wenyi Zeng, Hongxing Li
Knowledge-Based SystemsInduced generalized intuitionistic fuzzy operators
299 Citations2010Zeshui Xu, Meimei Xia
Choquet integral and Dempster-Shafer theory of evidence are applied to aggregate inuitionistic fuzzy information and some new types of aggregation operators are developed, including the induced generalized intuitionistic fuzzy Choquet integral operators and induced generalized intuistic fuzzy Dem pster-shafer operators.
Pattern Recognition LettersSimilarity measures between intuitionistic fuzzy (vague) sets: A comparative analysis
278 Citations2006Yanhong Li, David L. Olson +1 more
Information SciencesNew decision-making techniques and their application in the selection of financial products
275 Citations2010José M. Merigó, Anna M. Gil‐Lafuente
A new approach is developed that uses the ordered weighted averaging (OWA) operator in the selection of financial products to manipulate the attitudinal character of previous methods based on distance measures, so that the decision maker can select financial products according to his or her degree of optimism.
Information SciencesA method based on distance measure for interval-valued intuitionistic fuzzy group decision making
259 Citations2009Zeshui Xu
Some relations and operations of interval-valued intuitionistic fuzzy numbers are introduced, some types of matrices are defined and a method based on distance measure for group decision making with interval-value intuitionistic fuzziness matrices is developed.
IEEE Transactions on Systems Man and CyberneticsAn approximate analogical reasoning approach based on similarity measures
256 Citations1988İ.B. Türkşen, Zhao Zhong
An approximate analogical reasoning schema (AARS) which exhibits the advantages of fuzzy set theory and analogical Reasoning in expert systems development is described and is compared with conventional expert systems and existing fuzzy expert systems.
International Journal of Approximate ReasoningIndicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets
247 Citations2000Humberto Bustince
The indicator of the grade of inclusion for interval-valued fuzzy sets is used as an element that selects from the diAerent methods of inference studied, the one that will be executed in each case.
Information SciencesPattern recognition using type-II fuzzy sets
227 Citations2004Helen Mitchell
With this new similarity measure, it is shown that type-II fuzzy sets provide us with a natural language for formulating classification problems in pattern recognition.
International Journal of Approximate ReasoningSimilarity measures of intuitionistic fuzzy sets based on Lp metric
219 Citations2006Wen‐Liang Hung, Miin‐Shen Yang
Several reasonable measures to calculate the degree of similarity between IFSs are proposed, in which the proposed measures are induced by L"p metric, and applied to analyze the behavior of decision making.
Information SciencesA vector similarity measure for linguistic approximation: Interval type-2 and type-1 fuzzy sets
195 Citations2007Dongrui Wu, Jerry M. Mendel
A vector similarity measure (VSM) is proposed for IT2 FSs, whose two elements measure the similarity in shape and proximity, respectively, which shows that the VSM gives more reasonable results than all other existing similarity measures for IT1 FSs for the linguistic approximation problem.
International Journal of Intelligent Systems
166 Citations2009
An algorithm to transform a dynamic influence net (DIN) into a dynamic Bayesian network (DBN) that enables a system analyst to capture a complex situation using a DIN and pick the best COA that maximizes the likelihood of achieving the desired effect.
International Journal of Intelligent SystemsInduced aggregation operators in decision making with the Dempster-Shafer belief structure
148 Citations2009José M. Merigó, Montserrat Casanovas
This study analyzes the induced aggregation operators, focusing on the aggregation step and examine some of its main properties, including the distinction between descending and ascending orders and different families of induced operators.
Fuzzy Sets and SystemsContinuous generalized OWA operator and its application to decision making
134 Citations2010Ligang Zhou, Huayou Chen
This paper presents a new class of operators called the continuous generalized ordered weighted averaging (C-GOWA) operators, which extends the continuous ordering weighted averaging operator, and generalizes the previous approaches by using Choquet integral and quasi-arithmetic means.
Fuzzy Sets and SystemsRemarks on basics of fuzzy sets and fuzzy multisets
124 Citations2005Sadaaki Miyamoto
Two remarks on basic aspects of fuzzy sets are given and notation for the @a-cuts and a commutative property in the extension principle are given.
Computers & Mathematics with ApplicationsOn similarity and inclusion measures between type-2 fuzzy sets with an application to clustering
112 Citations2008Miin‐Shen Yang, Der-Chen Lin
This paper defines similarity and inclusion measures between type-2 fuzzy sets, discusses their properties and also considers the relationships between them, and combines the proposed similarity measures with Yang and Shih's clustering method.
Fuzzy Sets and SystemsCluster analysis based on fuzzy relations
107 Citations2001Miin‐Shen Yang, Hsing-Mei Shih
In this paper, cluster analysis based on fuzzy relations is investigated and Tamura’s max-min n-step procedure is extended to all types of max-t compositions, and the topic of incomplete data via max-T compositions is discussed.
IEEE Transactions on Fuzzy SystemsNorms Induced from OWA Operators
103 Citations2009Ronald R. Yager
It is shown that the functional generation of the weights of an OWA norm requires the weight generating function have a non-positive second derivative.
Fuzzy Sets and SystemsFuzzy input-output controllers are universal approximators
101 Citations1993James J. Buckley, Yoichi Hayashi
It is shown that a fuzzy input-output controller can approximate, to any degree of accuracy, a continuous fuzzy system.
Computer science workbenchSoft Computing and Human-Centered Machines
98 Citations2000Zhiqiang Liu, Sadaaki Miyamoto
F fuzzy set theory - analysis and extensions methods in hard and fuzzy clustering soft-competitive learning paradigms aggregation operations for fusing fuzzy information fuzzy gated neural networks in pattern recognition soft computing technique in kansei (emotional) information processing.
Computer science workbenchMultisets and Fuzzy Multisets
98 Citations2000Sadaaki Miyamoto
Multisets, also called bags, are relatively unknown to researchers, partly because it has weaker mathematical properties and has been considered that applications are relatively limited.
Information SciencesA modified Hausdorff distance between fuzzy sets
96 Citations1999B.B. Chaudhuri
A modified metric is proposed which contains a single term representing geometric distance only; which reduces to the classical Hausdorff distance when the fuzzy sets are crisp; and which is relatively insensitive to noise.
Fuzzy Optimization and Decision MakingLearning Weights in the Generalized OWA Operators
92 Citations2005Gleb Beliakov
This paper discusses identification of parameters of generalized ordered weighted averaging (GOWA) operators from empirical data and develops optimization techniques which allow one to fit such operators to the observed data.
Lecture notes in computer scienceIntuitionistic Fuzzy Sets in Intelligent Data Analysis for Medical Diagnosis
88 Citations2001Eulalia Szmidt, Janusz Kacprzyk
This article proposes a new approach for medical diagnosis by employing intuitionistic fuzzy sets, and points out advantages of this new concept over the method proposed by De, Biswas and Roy where the max-min-max rule was used.
John Wiley & Sons, Inc. eBooksMultistage Fuzzy Control: A Prescriptive Approach
67 Citations1997Janusz Kacprzyk
This authoritative book explains the essential principles of fuzzy logic and describes both the theoretical and practical advantages of the new model-based, prescriptive approach to improve the efficiency of fuzzy control systems.
Data & Knowledge EngineeringSimilarity-based ranking and query processing in multimedia databases
59 Citations2000K. Selçuk Candan, Wen‐Syan Li +1 more
An algorithm to efficiently process queries with unordered fuzzy predicates (sub-queries) is developed, which benefits from the statistical properties of the semantics proposed in this paper.
Computer Engineering and ScienceBidirectional Approximate Reasoning Based on Weighted Similarity Measures of Vague Sets
13 Citations2002Wang Tian
This paper introduces a new weighted similarity measure for vague sets and proposes a method for determining the similarity direction, which improves the accuracy and applicability of approximate reasoning, and also provides a useful tool for approximate reasoning in intelligent systems.