A fuzzy-evidential hybrid inference engine for coronary heart disease risk assessment

Abstract

In many engineering problems, we encounter vagueness in information and uncertainty in decision making, so as these phenomena cause we could not reach to certain results for our proposed solution. In this paper, a novel inference engine named fuzzy-evidential hybrid inference engine has been proposed using Dempster–Shafer theory of evidence and fuzzy sets theory. This hybrid engine operates in two phases. In the first phase, it models the input information’s vagueness through fuzzy sets. In following, extracting the fuzzy rule set for the problem, it applies the fuzzy inference rules on the acquired fuzzy sets to produce the first phase results. At second phase, the acquired results of previous stage are assumed as basic beliefs for the problem propositions and in this way, the belief and plausibility functions (or the belief interval) are set. Gathering information from different sources, they provide us with diverse basic beliefs which should be fused to produce an integrative result. For this purpose, evidential combination rules are used to perform the information fusion. Having applied the proposed engine on the coronary heart disease (CHD) risk assessment, it has yielded 91.58% accuracy rate for its correct prediction. This hybrid engine models the information’s vagueness and decision making’s uncertainty precisely and through information fusion, provides more accurate results, so as it could be considered as an intelligent decision support system in diverse engineering problems.

Introduction

Vagueness, impreciseness and uncertainty are fundamental and indispensable aspects of knowledge, so as in many practical problems, the experts face vagueness in feature vectors and uncertainty in decision making. Essentially, a symptom is an uncertain indication of a phenomenon as it may or may not occur with it. In other words, uncertainty characterizes a relation between symptoms and phenomena (De et al., 2001, Han and Kamber, 2006, Straszecka, 2007). On the other hand, the feature vectors are usually vague. Hence, uncertainty regards the relation between symptoms and phenomena, whereas vagueness represents impreciseness in the feature vectors (Khatibi and Montazer, 2009, Straszecka, 2007).

Fuzzy sets (FSs), proposed by Zadeh (1965), as a framework to encounter uncertainty, vagueness and partial truth, represents a degree of membership for each member of the universe of discourse to a subset of it. Therefore, we have a spectrum of truth values. This theory establishes new logic, mathematics, operators, relations and systems to cope with vagueness and uncertainty in the problems (Zimmermann, 1996). In medical diagnosis, fuzzy sets are often applied to medical reasoning with an intent to model both uncertainty of a diagnosis and imprecision of symptoms. Diagnosis support systems operate on rules with fuzzy premises, which represent imprecise symptoms. During inference, fuzzy relations or implications are used, so conclusions are also represented in the form of fuzzy sets (Straszecka, 2007). From another point of view, Dempster–Shafer evidence theory generalizes Bayesian inference through proposing upper and lower bounds for the proposition’s truth value named belief and plausibility functions which expand the tolerance of evaluation results (Guan & Bell, 1991). Hence, coping efficiently with uncertainty leads us to more accurate decision making and this is considered as a fundamental challenge in medicine (Khatibi and Montazer, 2009, Straszecka, 2007).

Gathering information from different sources provides us with diverse perspectives on the problem, so as each of them results in complementary information and should be fused to produce an integrative result. For this purpose, information fusion techniques are proposed which refer to the synergistic aggregation of complementary and/or redundant observations and measurements to provide us with more reliable and complete information (Altincay and Demirekler, 2003, Cremer et al., 2001, Guan and Bell, 1991, Milisavljevic et al., 2003). Among various methods for information fusion, evidential combination rules in evidence theory are very popular and show successful results in diverse applications (Guan & Bell, 1991).

In this paper, a novel hybrid inference engine has been designed using evidence and fuzzy set theories. This engine establishes a two-phase inference through modeling problem’s vagueness and uncertainty, so as the problem’s data are represented with fuzzy sets and then, based on the fuzzy rule base, the first phase would be completed by fuzzy inference rules. In next phase, the results from previous stage are interpreted as basic beliefs, so as the belief and plausibility functions are calculated for the problem propositions which yield the belief interval as the final output of the system. Also, the acquired information from different sources which are characterized as basic beliefs are fused through evidential combination rules. This complementary stage in second phase enables us to perform information fusion in the proposed system. This hybrid engine has been examined in the coronary heart disease (CHD) risk assessment problem and the experimental results are illustrated and analyzed.

This paper is organized as follows. In Section 2, fundamental concepts of Dempster–Shafer evidence theory are represented and then, information fusion and evidential combination rules for this purpose are discussed. In Section 3, the fuzzy-evidential hybrid inference engine is designed which has been examined in the coronary heart disease risk assessment in the last section.