In Dempster-Shafer evidence theory (DST) based classifier design, Dempster's combination (DC) rule is commonly used as a multi-attribute classifier to combine evidence collected from different attributes. The main aim of this paper is to present a classification method using a novel combination rule i.e., the evidence reasoning (ER) rule. As an improvement of the DC rule, the newly proposed ER rule defines the reliability and weight of evidence. The former indicates the ability of attribute or its evidence to provide correct assessment for classification problem, and the latter reflects the relative importance of evidence in comparison with other evidence when they need to be combined. The ER rule-based classification procedure is expatiated from evidence acquisition and estimation of evidence reliability and weight to combination of evidence. It is a purely data-driven approach without making any assumptions about the relationships between attributes and class memberships, and the specific statistic distributions of attribute data. Experiential results on five popular benchmark databases taken from University of California Irvine (UCI) machine learning database show high classification accuracy that is competitive with other classical and mainstream classifiers.

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Data classification using evidence reasoning rule

Dempster–Shafer evidence theory has been widely used in various fields of applications, because of the flexibility and effectiveness in modeling uncertainties without prior information. However, the existing evidence theory is insufficient to consider the situations where it has no capability to express the fluctuations of data at a given phase of time during their execution, and the uncertainty and imprecision which are inevitably involved in the data occur concurrently with changes to the phase or periodicity of the data. In this paper, therefore, a generalized Dempster–Shafer evidence theory is proposed. To be specific, a mass function in the generalized Dempster–Shafer evidence theory is modeled by a complex number, called as a complex basic belief assignment, which has more powerful ability to express uncertain information. Based on that, a generalized Dempster’s combination rule is exploited. In contrast to the classical Dempster’s combination rule, the condition in terms of the conflict coefficient between the evidences is released in the generalized Dempster’s combination rule. Hence, it is more general and applicable than the classical Dempster’s combination rule. When the complex mass function is degenerated from complex numbers to real numbers, the generalized Dempster’s combination rule degenerates to the classical evidence theory under the condition that the conflict coefficient between the evidences is less than 1. In a word, this generalized Dempster–Shafer evidence theory provides a promising way to model and handle more uncertain information. Thanks to this advantage, an algorithm for decision-making is devised based on the generalized Dempster–Shafer evidence theory. Finally, an application in a medical diagnosis illustrates the efficiency and practicability of the proposed algorithm.

Generalization of Dempster–Shafer theory: A complex mass function

Multiple attribute decision making (MADM) problems often consists of quantitative and qualitative attributes which can be assessed by numerical values and subjective judgments. Subjective judgments can be evaluated by linguistic variables, and both numerical values and subjective judgments can be accurate or uncertain. The evidential reasoning (ER) approach provides a process for dealing with MADM problems of both a quantitative and qualitative nature under uncertainty. The existing ER approach considers both benefit and cost attributes in the evidence combination process. In this paper, deviated interval and fixed interval attributes are introduced into ER based MADM approach and the frames of discernment for representing these two kinds of attributes are given. The transformation rules from the assessment values of deviated interval attributes to belief degrees in the ER structure are then studied. An ave-entropy based weight assignment method considering the risk preference of decision maker is also shown to deal with uncertain assessment situation, such as belief distribution with qualitative attribute and uncertain utility function. Some programming models to generate interval weights and utilities are constructed. The rationality and efficiency of the methods in supporting MADM problems are discussed. Two case studies are provided to demonstrate the applicability and validity of the proposed approaches and the potential in supporting MADM under uncertainty.

Evidential reasoning approach with multiple kinds of attributes and entropy-based weight assignment

This paper presents a new method for sensor dynamic reliability evaluation based on evidence theory and intuitionistic fuzzy sets when the prior knowledge is unknown. The dynamic reliability of sensors is evaluated based on supporting degree between basic probability assignments (BPAs) provided by sensors. First, the concept of asymmetric supporting degree is proposed. By transforming BPAs to intuitionistic fuzzy sets, supporting degree between BPAs is calculated based on intuitionistic fuzzy operations and similarity measure. Then the relationship between dynamic reliability and supporting degree is analyzed. The process of dynamic reliability evaluation is proposed. Finally, the proposed dynamic reliability evaluation is applied to evidence combination. A new evidence combination rule is proposed based on evidence discounting operation and Dempster’s rule. Comparative analysis on the performance of the proposed reliability evaluation method and evidence combination rule is carried out based on numerical examples. The proposed method for data fusion is also applied in target recognition to show its feasibility and validity.

Sensor dynamic reliability evaluation based on evidence theory and intuitionistic fuzzy sets

Dempster–Shafer evidence (DSE) theory, which allows combining pieces of evidence from different data sources to derive a degree of belief function that is a type of fuzzy measure, is a general framework for reasoning with uncertainty. In this framework, how to optimally manage the conflicts of multiple pieces of evidence in DSE remains an open issue to support decision making. The existing conflict measurement approaches can achieve acceptable outcomes but do not fully consider the optimization at the decision-making level using the novel measurement of conflicts. In this article, we propose a novel evidential correlation coefficient (ECC) for belief functions by measuring the conflict between two pieces of evidence in decision making. Then, we investigate the properties of our proposed evidential correlation and conflict coefficients, which are all proven to satisfy the desirable properties for conflict measurement, including nonnegativity, symmetry, boundedness, extreme consistency, and insensitivity to refinement. We also present several examples and comparisons to demonstrate the superiority of our proposed ECC method. Finally, we apply the proposed ECC in a decision-making application of motor rotor fault diagnosis, which verifies the practicability and effectiveness of our proposed novel measurement.

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A Novel Conflict Measurement in Decision-Making and Its Application in Fault Diagnosis

The optimal design of industrial alarm systems based on evidence theory

The invention relates to a rotating mechanical device fault diagnosis method capable of synthesizing multisource fault probability likelihood credibility. The rotating mechanical device fault diagnosis method capable of synthesizing the multisource fault probability likelihood credibility includes: performing interval partition on fault characteristic monitoring data obtained under different fault modes, and building a mapping relation list of fault characteristic parameters and fault types; calculating out a likelihood vector of occurrence of each fault mode; building an objective function according to a training sample set, obtaining a reliability factor by optimizing the objective function, using the reliability factor to amend the likelihood vectors, and generating diagnosis evidence; respectively figuring out activated diagnosis evidence of multiple fault characteristics after obtaining values of the multiple fault characteristics on line, and then synthesizing the activated diagnosis evidence, and obtaining the fault types corresponding to the fault characteristics obtained on line according to a synthesis result. The rotating mechanical device fault diagnosis method capable of synthesizing the multisource fault probability likelihood credibility does not perform a restriction or constraint on variation characteristics, forms, accuracy and the like of massive fault characteristic data when used to process the massive fault characteristic data, and thereby facilitates engineering realization.

Rotating mechanical device fault diagnosis method capable of synthesizing multisource fault probability likelihood credibility

This paper presents a belief rule inference method for controlling the system with uncertain parameters. It uses the belief rule base (BRB) to model nonlinear relationship between system deviation and its integral, differential (inputs) and the controlled variable (output), in which the antecedent and consequent attributes of rule are the referential values of the inputs and output respectively. For the rules activated by the inputs, the evidential reasoning (ER) algorithm is used to combine the belief structures of these rules so as to reason out the value of the controlled variable. Moreover, a nonlinear optimization strategy is given to enhance the accuracy of initial parameters of BRB. A representative experiment on the separately excited DC motor with uncertain parameters illustrates that the proposed method can give more accurate control actions than the classical fuzzy-PID control method.

http://ieeexplore.ieee.org/iel7/7547213/7553055/07554804.pdf

Shibao Li

Papers

The optimal design of industrial alarm systems based on evidence theory

Rotating mechanical device fault diagnosis method capable of synthesizing multisource fault probability likelihood credibility

A belief rule inference approach for controlling the system with uncertain parameters