Yafei Song

A novel similarity measure on intuitionistic fuzzy sets with its applications

The intuitionistic fuzzy set, as a generation of Zadeh’ fuzzy set, can express and process uncertainty much better, by introducing hesitation degree. Similarity measures between intuitionistic fuzzy sets (IFSs) are used to indicate the similarity degree between the information carried by IFSs. Although several similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity, or provide counter-intuitive cases. In this paper, we first review several widely used similarity measures and then propose new similarity measures. As the consistency of two IFSs, the proposed similarity measure is defined by the direct operation on the membership function, non-membership function, hesitation function and the upper bound of membership function of two IFS, rather than based on the distance measure or the relationship of membership and non-membership functions. 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 counter-intuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating the difference between patterns.

Combination of interval-valued belief structures based on intuitionistic fuzzy set

Theory of belief function can be introduced to the interval set by defining interval-valued belief structures. The Dempster-Shafer (D-S) theory of evidence has been extended to combine interval-valued belief structures for decades. Although there already exist several combination approaches proposed by previous researchers, this problem has not been fully resolved so far. A novel combination of interval-valued belief structures is developed after analyzing existing irrational or suboptimal approaches. The novel combination approach is modeled based on intuitionistic fuzzy set, rather than nonlinear programming models, which are computational complicated. Numerical examples are implemented to illustrate the performance of the proposed novel approach.

Combination of unreliable evidence sources in intuitionistic fuzzy MCDM framework

In this paper, we consider the combination of unreliable evidence sources in multiple criteria decision making (MCDM) framework in intuitionistic fuzzy environment. In the intuitionistic fuzzy MCDM framework, evidence sources can be combined based on intuitionistic fuzzy aggregation operators when reliability factors are known. Generalized intuitionistic fuzzy aggregation operators are applied to combine evidence sources with intuitionistic fuzzy reliability factors. Discounting operation on unreliable evidence bodies is also extended to deal with uncertain reliability factors. Then we define a combination operation on intuitionistic fuzzy values to combine evidence bodies in the intuitionistic fuzzy MCDM model. Finally the estimation of the reliability factors without prior knowledge is studied. Our proposed evaluation method is based on the principle of self-assessment. It is implemented by the probabilistic comparison between intuitionistic fuzzy values. Moreover, the proposed evaluation method is independent of the dissimilarity measure between basic probability assignments. Numerical examples demonstrate the performance of our combination rules and reliability estimation method.

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

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.

A distance measure between intuitionistic fuzzy belief functions

Intuitionistic fuzzy (IF) evidence theory, as an extension of Dempster-Shafer theory of evidence to the intuitionistic fuzzy environment, is exploited to process imprecise and vague information. Since its inception, much interest has been concentrated on IF evidence theory. Many works on the belief functions in IF information systems have appeared. However, there is little research on the distance measure between IF belief functions despite the fact that distance measure in classical belief functions has received close attention. In this paper we mainly investigated the distance measure between IF belief functions based on the Euclidean distance between two column vectors. The similarity between focal elements is also taken into account. The distance and similarity measures between IF sets are investigated firstly. A new similarity measure between IF sets along with its properties and proofs is proposed. The positive definiteness of similarity matrix is investigated to guarantee the metric properties of the distance measure. Then a distance measure between IF belief functions is proposed. It is proved that the proposed distance measure is a metric distance. As is illustrated by examples, the distance measure is sensitive to the change of focal elements. Moreover, its applicability for classical belief functions is also demonstrated.

A new approach to construct similarity measure for intuitionistic fuzzy sets

The intuitionistic fuzzy set (IFS), as a generation of Zadeh’s fuzzy set, can express and process uncertainty much better. Similarity measures between IFSs are used to indicate the similarity degree between the information carried by IFSs. Although several similarity measures for IFSs have been proposed in previous studies, some of them cannot satisfy the axioms of similarity, or provide counterintuitive cases. In this paper, we first review several widely used similarity measures and then propose a new similarity measures. As the consistency of two IFSs, the proposed similarity measure is defined based on the direct operation on the membership function, non-membership function, hesitation function and the upper bound of membership function of two IFS, rather than based on the distance measure or the relationship of membership and non-membership functions. It proves that the proposed similarity measure satisfies 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. Experiments on medical diagnosis and cluster analysis are carried out to illustrate the applicability of the proposed similarity measure in practice.

Credibility decay model in temporal evidence combination

Data fusion in time domain is sequential and dynamic. Methods to deal with evidence conflict in spatial domain may not suitable in temporal domain. It is significant to determine the dynamic credibility of evidence in time domain. The Markovian requirement of time domain fusion is analyzed based on Dempsters combination rule and evidence discount theory. And the credibility decay model is presented to get the dynamic evidence credibility. Then the evidence is discounted by dynamic discount factor. Its illustrated that such model can satisfied the requirement of data fusion in time domain. Proper and solid decision can be made by this approach. The Markovian requirement of time domain fusion was analyzed.The credibility decay model was presented to get the dynamic evidence credibility.The evidence was discounted by dynamic discount factor.Illustrative example demonstrates the performance of this model.

An evidential view of similarity measure for Atanassov’s intuitionistic fuzzy sets

In this paper, the construction of similarity measures for Atanassovs intuitionistic fuzzy sets (AIFSs) is considered from the view of evidence theory. We define similarity measures for AIFSs in the framework of Dempster-Shafer evidence theory. The proposed similarity measures are applied to deal with pattern recognition and multiple criteria decision making problems. First, existing similarity measures for AIFSs are critically reviewed. Then we introduce the transformation from AIFSs to basic probability assignments (BPAs) in evidence theory. Based on Jousselmes distance measure and cosine similarity measure between BPAs, two similarity measures between AIFSs are proposed. A composite similarity measure is constructed following the proof of properties related to our proposed similarity measures. Then, we use some contrastive examples to illustrate that the proposed similarity measure between AIFSs can overcome the drawbacks of existing similarity measures. Finally, we apply the proposed similarity measures between AIFSs to deal with pattern recognition and multiple criteria decision making problems. It is demonstrated that our proposed similarity measures can provide compatible results compared to those results obtained based on previous measures.

How to measure non-specificity of intuitionistic fuzzy sets

In this paper, we address the problem of how to measure non-specificity for intuitionistic fuzzy sets. This problem is relevant to the construction of intuitionistic fuzzy uncertainty measure. Although there already exist many uncertainty measures for intuitionistic fuzzy sets, few of them can discriminate uncertainty degrees of crisp sets. In order to construct a unified uncertainty measure for intuitionistic fuzzy sets, non-specificity must be taken into account. Starting from the Hartley measure, which is related to the cardinality of a crisp set, we propose a non-specificity measure for intuitionistic fuzzy sets. Properties of the proposed non-specificity measure are also investigated. Illustrative examples are employed to show its performance.

Evidence combination based on credibility and separability

D-S evidence theory has been widely used in various fields of information fusion due to its efficiency in dealing with uncertain information. Unfortunately, combination of conflicting evidences with the classical Dempsters rule may produce the counter-intuitive results. In this paper, Definitions of correlation coefficient and credibility are first presented, followed by the introduction of evidence separability. A modified weighted factor determined by credibility and separability is then presented, which is then applied to average the basic probability assignment (BPA). Finally, the modified BPA is combined following the D-S rule. It is demonstrated the more reasonable combination results can be obtained by this method. Moreover, better convergence performance can be obtained.