A Reliability Analysis Method of Accelerated Performance Degradation Based on Bayesian Strategy

2020

Int J Intell Syst

Because of the superiority in dealing with uncertainty expression, Dempster-Shafer theory (D-S theory) is widely used in decision theory. In D-S theory, the basic probability assignment (BPA) is the basis and core. Recently, some researchers represent BPA on a N -dimension frame of discernment (FOD) as 2 N -dimension vector in Descartes coordinate system. This representation treats a BPA as a point in the 2 N -dimensional space. A new vector and geometry interpretation of BPA is proposed in this paper.The BPA on a N -dimension FOD is represented as N -dimension vector with parameters in this method.Then BPA is expressed as subset of N -dimension Cartesian space rather than a point. The proposed method is a new way to represent BPA with vector and geometry. The essence of this method is to convert BPA to probability distribution with parameters.The applications of this representation method in D-S theory have been studied. Based on this method, problems in D-S theory can be solved, which include the fusion of BPAs, the distance between BPAs, the correspondence between BPA and probability, and the entropy of BPAs.basic probability assignment, data fusion, dempster-shafer theory, distance, entropy Dempster-Shafer theory (D-S theory), 1,2 as an important and widely used uncertain reasoning method, has been receiving increasingly attention. 3,4 D-S theory assigns probabilities to the power set of events, so it can effectively deal with uncertainty and unknown problems. Because of the effectiveness in pattern recognition, 5,6 decision making, 7,8,9,10,11,12 reasoning, 13,14,15 and uncertainty analysis, 16,17,18,19 D-S theory has been applied in various fields. 20,21,22,23 In D-S theory, A complete set of incompatible basic hypotheses is called a frame of discernment (FOD), which represents all possible answers to a problem. The degree of trust assigned to each subset of FOD is called the basic probability assignment (BPA). Since the N -dimension FOD has 2 N subsets, some researchers represent the BPA as 2 N -dimension vector in Descartes coordinate system. 24,25 A BPA is a point in the 2 N -dimensional space in this representation method.Based on the idea of converting BPA to probability distribution (PD), a new interpretation of D-S theory is proposed in this paper. The BPA on a N -dimension FOD is represented as N -dimension vector with parameters in this method. Each dimension indicates a hypothesis in FOD. In fact, BPA is represented as a subset of N -dimension space rather than a point because of the variable parameters. In this way, BPAs have an intuitive vector and geometry representation. Based on this representation method, several problems in D-S theory have been studied, which include the fusion of BPAs, the distance between BPAs, the correspondence between BPA and probability, and the entropy of BPAs. The example shows that our method provides a new way to solve these basic problems of D-S theory, and can get reasonable results.Combination of BPAs from different information sources is a major problem in D...

Section: Preliminariesmentioning

confidence: 99%

A vector and geometry interpretation of basic probability assignment in Dempster‐Shafer theory

Luo

2020

Int J Intell Syst

“…Dealing with uncertainty is an open issue and many tools are presented to address this issue 44–47 . Many math models such as network analysis, 48–51 risk and reliability analysis, 52–54 visible graph, 55 and fuzzy sets 56–60 . IFS is an extension of the classical fuzzy sets, which has been used in a wide scope of application 61–65 .…”

Section: Preliminariesmentioning

confidence: 99%

Entailment for intuitionistic fuzzy sets based on generalized belief structures

Xue

2020

Int J Intell Syst

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...

“…where α(j) is an index function and y α(j) is the jth largest element in (1) and H j = {y α(i) for i = 1 to j} is subset of 2 Y .…”

Section: Choquet Integralmentioning

confidence: 99%

“…In the real world, there are many uncertainties and unreliabilities [1][2][3][4]. In order to deal with the uncertainties [5][6][7], many mathematical theories are proposed, such as Bayesian network [8], hyper structures [9], fuzzy sets (FS) [10][11][12], hesitant fuzzy subalgebras [13], D-S evidence theory [14][15][16], information quality [17,18], Z-number [19,20], D-number [21], entropy [22,23] and belief structure [24] and are applied in many fields [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Refined Expected Value Decision Rules under Orthopair Fuzzy Environment

Xue

2020

Mathematics

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.