文档介绍：
Interval belief functions on intuitionistic fuzzy events and
their Choquet integral representations#
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ZHOU Hongjun*
(College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062)
Abstract: In the present paper we introduce interval belief functions on intuitionistic fuzzy events
(IF-events, for short) in a finite universe of discourse. The belief functions are constructed with respect
to Łukasiewicz connectives defined among IF-events and are consequently a generalization of the
existing (interval) probability theory on IF-events. Such construction makes it possible to embed this
theory into MV-algebras. It is also proved that the generalized belief functions have Choquet integral
representations.
Key words: IF-event; Belief function; Choquet integral
0 Introduction
As a generalization of the Bayesian theory of subjective probability, belief functions [1] are certain
non-additive real-valued set functions that represent our degree of belief in the occurrence of the (classical) events
based on the bodies of evidence.
The purpose of this paper is to generalize belief functions to intuitionistic fuzzy events (IF-events)
represented by intuitionistic fuzzy sets [2] (IF-sets) whose membership and non-membership functions are both
measurable functions on a measurable space. This is in the line of an increasing interest in