Evaluation method based on fuzzy relations between Dempster-Shafer belief structure

Abstract

Many relations in the real world can be described by mathematical language. Fuzzy set theory can transform human language into mathematical language and use membership degree function to describe relations between events. Dempster–Shafer evidence theory provides basic probability assignment (BPA), which can describe the occurrence rate of attributes in basic events. Based on the known membership degree function and BPA distribution, a new evaluation method is proposed in this paper to analyze decision making. Given the relations among relevant events, which are expressed by BPA distribution and membership degree function, the relations among basic events and top event can be obtained. The Dempster's combination rule and pignistic probability transformation are used to transform BPA distribution into probability distribution. The belief measure is applied to deal with these fuzzy relations. Some numerical examples are given in this paper to illustrate the proposed evaluation methodology.

Generating Z-number based on OWA weights using maximum entropy

“…In real applications, how to deal with uncertainty in decision making is still an open issue. [11][12][13][14][15] Many uncertainty information processing models based on the relative math tools, such as fuzzy sets, 16,17 D numbers, [18][19][20] and evidence theory, [21][22][23] are presented and adopted in practical engineering. Among these models, Z numbers is efficient to represent the reliability of uncertain information and can be defined as follows.…”

Evidential Model Validation under Epistemic Uncertainty

“…As an extension to Bayesian theory, the Dempster-Shafer (D-S) evidence theory [14] uses basic probability assignment (BPA) to quantify evidence and uncertainty [17,[22][23][24][25][26]. Compared with probability, BPA has the advantage of efficient modeling of unknown information [27]. D-S evidence theory models how the uncertainty of a given hypothesis or discourse diminishes as groups of BPAs accumulate during the reasoning process [27][28][29][30].…”

“…Compared with probability, BPA has the advantage of efficient modeling of unknown information [27]. D-S evidence theory models how the uncertainty of a given hypothesis or discourse diminishes as groups of BPAs accumulate during the reasoning process [27][28][29][30]. The effectiveness of this method has been demonstrated in many fields.…”

Engine fault diagnosis based on sensor data fusion considering information quality and evidence theory

“…2 In real system, a larger quantity of information can be obtained from all kinds of sensors that detect the concrete values. Consequently, it is necessary for decision-makers to get rational result by considering all the complicated information [11][12][13][14][15] whose certainty maybe very high or low. And some methods of information fusion 16 used in fault diagnosis and other fields have been proposed, such as Kalman Filter, [17][18][19] neural network, [20][21][22] and fuzzy logic.…”