Abstract
The evidence theory is ascribed to a specific kind of uncertainty. In this theory, uncertainty refers to the fact that the element of our interest (the true world) may be included in subsets of other similar elements (possible worlds). In the original evidence theory, the estimates of the basic probability masses for the focal elements are given in an unambiguous form. In practice, to obtain such estimates is often difficult or even impossible. In such a situation, the relevant estimates are given in the interval or fuzzy form. The goal of the paper is to present and analyse the calculation procedures for determination of the belief functions and plausibility functions in the evidence theory for cases when the initial estimates are given in the interval or fuzzy form.
Highlights
TO THE EVIDENCE THEORY AND ITS EXTENSIONSIn this paper, we determine the ignorance as the situation where the necessary information is either missing, insufficient or presented in inappropriate form
The evidence theory has been developed to handle a specific type of uncertainty: the entity of interest can be in subsets of a universal set
The degree of certainty that a given entity is located in a concrete focal element is evaluated by the value of the basic probability mass given to this focal element
Summary
Abstract – The evidence theory is ascribed to a specific kind of uncertainty. In the original evidence theory, the estimates of the basic probability masses for the focal elements are given in an unambiguous form. To obtain such estimates is often difficult or even impossible In such a situation, the relevant estimates are given in the interval or fuzzy form. The goal of the paper is to present and analyse the calculation procedures for determination of the belief functions and plausibility functions in the evidence theory for cases when the initial estimates are given in the interval or fuzzy form. Keywords – Belief function, data incompleteness, evidence theory, frame of discernment, focal elements, fuzzy value, inaccuracy, interval probability, interval value, membership function, plausibility function, probability mass, uncertainty
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