Search

In this paper, we show how the Kantorovich problem appears in many constructions in the theory of belief functions. We demonstrate this on several relations on belief functions such as inclusion, equality and intersection of belief functions. Using the Kantorovich problem we try to measure these relations and as the result we obtain various functionals like the Wasserstein distance on belief functions.

It is an important feature of a monotone measure that it is not additive in general. In the paper we propose the mathematical tool, based on canonical sequences of monotone measures, for analyzing additivity of monotone measures on subalgebras and give a way of generating such monotone measures. It turns out that the generating rule can be considered as an effect of a linear operator defined on the set of monotone measures. We also investigate in what cases the sequence of such operators behaves commutatively and preserve continuity properties from the generating monotone measure.

In the paper, we formalize the notion of contradiction between belief functions: we argue that belief functions are not contradictory if they provide non-contradictory models for decision-making. To elaborate on this idea, we take the decision rule from imprecise probabilities and show that sources of information described by belief functions are not contradictory iff the intersection of corresponding credal sets is not empty. We demonstrate that evidential conjunctive and disjunctive rules fit with this idea and they are justified in a probabilistic setting. In the case of contradictory sources of information, we analyze possible conjunctions and show how the result can be described by generalized credal sets. Based on generalized credal sets, we propose a measure of contradiction between information sources and find its axiomatics. We show how the contradiction correction can be produced based on generalized credal sets and how it can be done on sets of surely desirable gambles.

In the paper we investigate the criteria of choosing generalized Dempster-Shafer rules for aggregating sources whose information is represented by belief functions. The approach is based on measuring various types of uncertainty in information and we use for this purpose in particular linear imprecision indices. Some results concerning properties of such rules are also presented.

This work presents a fuzzy resource-constrained project scheduling problem that is one of the operational research problems that can be defined as a combinatorial NP-hard problem of constructing a special plan for performing a number of precedence related tasks subject to limited uncertain resources. It is relevant to use fuzzy numbers when activity durations rely on human estimations and due to lack of historical data there is no opportunity to predict them accurately. The goal is to construct a fuzzy heuristic-based approach to obtain a near optimal solution in a reasonable computational time.