### An Approach to Interval Fuzzy Probabilities

Tiago Da Cruz Asmus, Gracaliz Pereira Dimuro, Benjamin Bedregal
2015 Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology   unpublished
Fuzzy sets an logic have been largely applied used to the treatment of the uncertainty, vagueness and ambiguity found in the modeling of real problems. However, there may exist also the case when there is uncertainty related to the membership functions to be used in the modeling of fuzzy sets and fuzzy numbers, as there are many ways to define the shape of this kind of number. Thus, one can use, for example, the theory of interval fuzzy sets to address this uncertainty, considering different
more » ... eling of fuzzy numbers into a single interval fuzzy number. In this paper, we use interval fuzzy numbers to represent probabilities that are difficult to be estimated and where the modeling of fuzzy numbers is not trivial. To elaborate the calculation of probabilities, it will be introduced an approach based on one used by Buckley and Eslami, where the probabilities respect an arithmetic restriction. We discuss several properties of the proposed approach. Palavras-chave: Interval Fuzzy Logic, Interval Fuzzy Sets, Interval Fuzzy Probablities 1 For the lack of space, we omit some proofs of propositions and properties, which can be found in  .