A new divergence measure for belief functions in D–S evidence theory for multisensor data fusion

Entailment for measure-based belief structures can extend the possible probability value range of variables on a space and obtain more information from variables. However, if the variable space comes from intuitionistic fuzzy sets, the classical entailment for measure-based belief structures will not work in this issue. To deal with this situation, we propose the entailment for intuitionistic fuzzy sets based on generalized belief structures in this paper to apply the entailment for measure based belief structures on space, which is made up of non-membership degree, membership degree and hesitancy degree of a given intuitionistic fuzzy sets. Numerical examples are mentioned to prove the effectively and flexibility of this proposed entailment model. The experimental results indicate that the proposed algorithm can extend the possible probability value range of variables of space efficiently and obtain more information from intuitionistic fuzzy sets.belief function, Dempster-Shafer evidence theory, entailment, generalized belief structures, intuitionistic fuzzy sets | INTRODUCTIONIn real life, there are a lot of uncertainties in the real world. To address the uncertainties, many mathematical theories are proposed, such as probability theory, 1 fuzzy sets (FS), 2 Dempster-Shafer evidence theory, 3,4 intuitionistic fuzzy sets (IFS), 5,6 information quality, 7-11 Z-number, 12 fuzzy reasoning, 13-15 D-number, 16-18 entropy function, [19][20][21][22] and belief structure. 23,24 Among these theories and models, the IFS 25 considering the degree of hesitancy, membership, and nonmembership of objects, can deal with the uncertainties more flexibly and accurately, which has been used in many fields widely, 26 such as the uncertainty decision making, 27,28 pattern recognition 29 and so on.Recently, Yager proposed the entailment for measure based belief structures with a space, which has the promising aspect. 30 However, what the entailment for measure-based belief structures for a given IFS is still an open issue to be addressed. This paper proposes entailment for intuitionistic fuzzy sets based on generalized belief structures, which treats hesitancy degree, non-membership degree and membership degree of a given intuitionistic fuzzy set as three variables in a space X . Assume V takes its value in the X and is an uncertain variable. If g 1 and g 2 be two generalized belief structures on X and g 2 contains g 1 , then the belief of the statement that V is true based on g 2 will be smaller than that of the statement that V is true based on g 1 and the plausibility of the statement that V is true based on g 2 will be bigger than that of the statement that V is true based on g 1 .The remain of this paper is structured as follows. Section 2 introduces the preliminary. Section 3 presents the entailment for intuitionistic fuzzy sets based on generalized belief structures. Section 4 illustrates the flexibility and accuracy of the entailment for intuitionistic fuzzy sets based on generalized belief structures. Section 5 summarizes the...

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“…Evidence theory is widely used and generalized 69–73 . Given a space

Y

, the definition of generalized belief structure is defined as follows.…”

Section: Preliminariesmentioning

confidence: 99%

Entailment for intuitionistic fuzzy sets based on generalized belief structures

Xue

Deng

2020

Int J Intell Syst

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“…To deal with uncertainty, many tools and models have been proposed [41][42][43][44], such as fuzzy sets [45,46], basic probability assignment [47,48], rough sets [49], ordered weighted average operator [50], entropy [51][52][53][54], game theory [55,56] and complex networks [57][58][59][60][61][62]. In this section, some relative definitions are briefly introduced, such as refined expected value [40], measure [63,64] and Choquet integral [65].…”

Section: Preliminariesmentioning

confidence: 99%

Refined Expected Value Decision Rules under Orthopair Fuzzy Environment

Xue

Deng

2020

Mathematics

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Refined expected value decision rules can refine the calculation of the expected value and make decisions by estimating the expected values of different alternatives, which use many theories, such as Choquet integral, PM function, measure and so on. However, the refined expected value decision rules have not been applied to the orthopair fuzzy environment yet. To address this issue, in this paper we propose the refined expected value decision rules under the orthopair fuzzy environment, which can apply the refined expected value decision rules on the issues of decision making that is described in the orthopair fuzzy environment. Numerical examples were applied to verify the availability and flexibility of the new refined expected value decision rules model. The experimental results demonstrate that the proposed model can apply refined expected value decision rules in the orthopair fuzzy environment and solve the decision making issues with the orthopair fuzzy environment successfully.

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“…The counter-intuitive results may be obtained when information is highly conflicted [53]. Hence, many methods are proposed to address this issue [54]- [56]. The weighted average method is proposed by Deng et al based on Murphy's average method and Jousselme distance [57]- [59].…”

Section: A Dempster-shafer Evidence Theorymentioning

confidence: 99%

An Improved Expression for Information Quality of Basic Probability Assignment and Its Application in Fault Diagnosis

Li¹

2020

Preprint

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<div>Information quality is widely used in many applications. However, how to measure infor </div><div>mation quality in basic probability assignment accurately is still an open issue. Generalized expression for </div><div>information quality is an effective method to measure information quality in basic probability assignment. </div><div>Nevertheless, the counter-intuitive results may be obtained when statements are of intersection. To address </div><div>this issue, a new expression for information quality of basic probability assignment is proposed in this paper </div><div>considering the frame of discernment and the inflfluence of intersection among statements which can cause </div><div>changes of uncertainty. Numerical examples are illustrated to demonstrate the effectiveness of the proposed </div><div>method. In addition, an application in fault diagnosis is used to show the effectiveness of the proposed </div><div>method. </div>

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A new divergence measure for belief functions in D–S evidence theory for multisensor data fusion

Cited by 225 publications

References 42 publications

Entailment for intuitionistic fuzzy sets based on generalized belief structures

Entailment for intuitionistic fuzzy sets based on generalized belief structures

Refined Expected Value Decision Rules under Orthopair Fuzzy Environment

An Improved Expression for Information Quality of Basic Probability Assignment and Its Application in Fault Diagnosis

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