Ewa Straszecka

Combining uncertainty and imprecision in models of medical diagnosis

The paper presents a unified fuzzy-probabilistic framework for modeling processes of medical diagnosis. The two basic concepts of the Dempster-Shafer theory, i.e. focal elements and a basic probability assignment, correspond to disease symptoms and the significance of an individual symptom in the diagnosis, respectively. The belief computation is related to diagnostic inference. The final conclusion of the inference is the diagnosis with the greatest belief value. Fuzzy sets are used to describe focal elements. It is shown how their membership functions and basic probability assignments are estimated on the basis of experimental data. The interpretation of focal elements as fuzzy sets along with individual consideration of evidence imprecision and uncertainty of diagnosis are the essential new aspects of the presented method. Experimental studies have demonstrated the superiority of the proposed approach over some other modeling alternatives.

An interpretation of focal elements as fuzzy sets

This article proposes defining focal elements in the Dempster‐Shafer theory as fuzzy sets in an application to medical diagnosis support. Membership functions for medical parameters of “fuzzy” nature are constructed. A diagnosis support consists of Bel measure calculation only for these focal elements that have membership function values grater than a “truth” threshold. Coherence between membership function shapes and the truth threshold is shown and a new way of membership function designing is proposed. An extension of the “truth” threshold for nonfuzzy focal elements is proposed that make a unification of symptoms interpretation during diagnosis support possible.

Medical Knowledge Representation in Terms of IF-THEN Rules and the Dempster-Shafer Theory

The paper proposes a method of knowledge and certainty representation that is an alternative to fuzzy reasoning and classical probability based techniques. It makes possible to represent symptoms of different nature and is acceptable for physicians. The proposed solutions are based on the Dempster-Shafer theory of evidence, still, different definition for focal elements is proposed and specific method of basic probability assignment calculation for symptoms is suggested. It has been shown on examples of thyroid gland diseases diagnosis support that the method is efficient and numerically easy.

Interpretation of Medical Symptoms Using Fuzzy Focal Elements

In medical diagnosis symptoms often differ in nature varying form linguistic information trough numerical values to crisp statements. Hence, unification of their interpretation during diagnosis support is difficult. The authors propose the diagnosis support using an extension of the Dempster-Shafer theory for fuzzy focal elements. Performance of the method depends on the membership function shapes. The paper provides indications for imprecise symptom representation and its membership function determination. The problems are discussed for thyroid gland diseases. Conclusions helpful in diagnosis support are formulated.

Medical diagnosis support using uncertainty and imprecision measures

An algorithm of medical diagnosis support is proposed. It is based on the Dempster-Shafer theory of evidence, still the theory is extended for fuzzy focal elements. Definitions of the basic probability assignment as well as of belief and plausibility measures for the extension are provided The proposed method makes it possible to interpret simultaneously numerous symptoms of different nature: crisp, fuzzy or parameters of undetermined domains. General rules of medical knowledge can be adapted to population dependencies. The algorithms performance is verified for the thyroid gland diseases problem using data from an Internet base, simulated patient cases and real patient database. Accuracy of suggested diagnoses is considerably better for the proposed algorithm than for reference methods. The presented solutions are numerically easy and close to knowledge representation that is used in medical handbooks.

A model of a diagnostic rule in the dempster-shafer theory

In the paper a model of a rule in medical diagnosis is proposed. The Dempster-Shafer theory of evidence and fuzzy sets are implemented in the rule representation. The basic probability assignment describes certainty of the rule. Fuzzy sets model the rule premises. The diagnosis is indicated by the belief and the plausibility measures. Thresholds are used to adjust the significance of the rules and quality of observations. The suggested methods are verified for databases of thyroid gland diseases: the database found in the Internet and individually gathered data, as well as simulated data and the iris plants database.

Extracting easily interpreted diagnostic rules

Abstract Diagnosis support systems are often disregarded because of their high costs, complicated inference and inability to modify the knowledge base. The aim of this work is to propose a method that helps to resolve these problems by extracting diagnostic rules that can be easily interpreted and verified by experts. The rules can be obtained from data, even if the latter are imperfect, which is usual in medical databases. Next, intuitively clear reasoning is suggested to elaborate on the diagnosis. Rules are focal elements in the framework of the Dempster–Shafer theory. They include fuzzy sets in their premises. Thus, a measure of imprecision as a fuzzy membership function and a measure of uncertainty as the basic probability value are used. Moreover, a rule selection algorithm and a rule evaluation method that prevent some of the imperfections of the existing methods are proposed. Particular attention is paid to the evaluation of the extracted rule set according to its reliability and clarity for a human user. Experimental results obtained for popular medical data sets demonstrate the advantages of the proposed approach. For each data set, simple and readable rule sets are determined. They provide comparable or better results than the approaches published so far.

On Advantages of a Fuzzy Approach to a Diagnosis Support

In the paper the problem of norm limits of laboratory tests used in probabilistic and fuzzy approach to diagnosis support is discussed. The fuzzy approach is proposed as the Dempster-Shafer theory extended for fuzzy focal elements. A simple diagnostic problem is simulated for the both approaches and results are commented. Conclusions from the simulation are used to determine the set of rules for a benchmark database. Both the simulation and calculations for the benchmark confirm that a fuzzy interpretation of norm limits can improve a diagnosis.

Matching Knowledge and Evidence in a Model of Medical Diagnosis

The Dempster-Shafer theory extended for fuzzy focal elements can be used to build a flexible model of medical diagnosis. Yet, quality of an inferred diagnosis depends on precision of matching knowledge with evidence (patient’s findings). The paper provides definitions of matching precision and suggests methods of the most adequate use of available information about symptoms. The methods are illustrated by an example and tests of an Internet database.

Defining Membership Functions

The chapter presents basic concepts and methods used in defining membership functions of fuzzy sets. Usual problems of fuzzy set applications connected with the universe of discourse, shape, and accuracy of membership functions as well as with their acquisition are discussed. An example of a fuzzy set application to a medical score test modelling is given. In the example a modified Takagi-Sugeno algorithm of fuzzy identification is described. Conclusions about present customs and suggestions of future trends in defining membership functions close the study.