The notions of a -norm and of a fuzzy number are recalled. The law of large numbers for fuzzy numbers is defined. The fuzzy numbers, for which the law of large numbers holds, are investigated. The case when the law of large numbers is violated is studied.
This paper presents an approach to the problem of quantifying the inequality of a finite population with respect to a (social, economical, etc.) fuzzy-valued attribute. For this purpose, the fuzzy hyperbolic inequality index is introduced, and some properties extending the basic ones for real-valued attributes are examined.
Within the framework of discrete probabilistic uncertain reasoning a large literature exists justifying the maximum entropy inference process, , as being optimal in the context of a single agent whose subjective probabilistic knowledge base is consistent. In particular Paris and Vencovská completely characterised the inference process by means of an attractive set of axioms which an inference process should satisfy. More recently the second author extended the Paris-Vencovská axiomatic approach...
We introduce the concept of total coherence of a set-valued probability assessment on a family of conditional events. In particular we give sufficient and necessary conditions of total coherence in the case of interval-valued probability assessments. Some relevant cases in which the set-valued probability assessment is represented by the unitary hypercube are also considered.