ARITHMETIC OPERATIONS OF FUZZY FOCAL ELEMENTS IN EVIDENCE THEORY

Abstract

Evidence Theory is a branch of mathematics that concerns the combination of empirical evidence in an individual's mind in order to construct a coherent picture of reality. It is an important tool of uncertainty modelling when both epistemic and aleatory uncertainties are present in the problem under consideration. In the absence of empirical data, experts in related fields provide necessary information. The fundamental objects of this theory of evidence are called focal elements, and the primitive function associated with it is called basic probability assignment (bpa). Focal elements are usually crisp subsets of some universal set. However in certain situations focal elements may also be represented by fuzzy numbers. In this paper we propose methods to combine fuzzy focal elements and their corresponding basic probability assignment.