An interpretation of focal elements as fuzzy sets

Abstract

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.

Combining knowledge from different sources

“…Membership functions for numerical variables can be found as triangular, trapezoidal or Gaussian functions based on some statistical parameters (Civanlar & Trussell, 1986; Rojas et al , 1998; Szczepaniak et al , 2000; Polat et al , 2006). The method of membership function design for the present algorithm is described in detail by Straszecka (2003, 2006a, 2006b). The algorithm of the bpa calculation is given in Figure 1.…”

Combining uncertainty and imprecision in models of medical diagnosis

“…It is still convenient that the value is identical for all the membership functions, e.g. 0.5 [33]. Hence, (x * , 0.5) and (x ** , 0.5) points resemble (a 0 , 0.5) and (d 0 , 0.5) points of the membership function in Fig.…”

“…Some classical methods of clustering (ISODATA [34], FUZZY ISODATA [3]) as well as fuzzy inference [9] in its basic Mamdani-like format have resulted in a classification error ranging from 8% to 50% [33] for a single diagnosis. Also, statistical and classical probabilitybased methods [7] have revealed a complex structure of data sets, although classification has been simplified into two separate processes of distinction between H and D 1 as well as between H and D 2 .…”

Interpretation of Sound Tomography Image for the Recognition of Ganoderma Infection Level in Oil Palm

“…In the same way, fuzzy sets were also used as an interpretation of focal elements by Straszecka in [23]. We suggest using the membership function obtained to initialize the mass function.…”