It was John Maynard Keynes [13] who first forcibly argued that probabilities cannot be simply ordered. There are cases, he argued, in which the probability of the hypothesis h can be regarded neither as greater than that of hypothesis k, nor less than that of hypothesis k, nor yet equal to that of hypothesis k. Although he did not provide a mathematical structure for his probability values, he ...

The aim of this work is to analyze the interval canonical representation for fuzzy QL-implications and automorphisms. Intervals have been used to model the uncertainty of a specialist’s information related to truth values in the fuzzy propositional calculus: the basic systems are based on interval fuzzy connectives. Thus, using subsets of the real unit interval as the standard sets of truth deg...

In this paper we introduce the notion of interval-valued (∈,∈ ∨qm̃)− fuzzy subquasigroups and present some of their properties. We characterize interval-valued (∈,∈ ∨qm̃)− fuzzy subquasigroups by their level subsets. The implication-based such new fuzzy subquasigroups are also established.

Payoffs in (bimatrix) games are usually not known precisely, but it is often possible to determine lower and upper bounds on payoffs. Such interval valued bimatrix games are considered in this paper. There are many questions arising in this context. First, we discuss the problem of existence of an equilibrium being common for all instances of interval values. We show that this property is equiv...

In this note the notion of interval-valued fuzzy B-algebras (briefly,i-v fuzzy B-algebras), the level and strong level B-subalgebra is introduced.Then we state and prove some theorems which determine the relationshipbetween these notions and B-subalgebras. The images and inverse images ofi-v fuzzy B-subalgebras are defined, and how the homomorphic images andinverse images of i-v fuzzy B-subalge...

In this work we extend to the interval-valued setting the notion of an overlap functions and we discuss a method which makes use of interval-valued overlap functions for constructing OWA operators with interval-valued weights. . Some properties of intervalvalued overlap functions and the derived interval-valued OWA operators are analysed. We specially focus on the homogeneity and migrativity pr...

In many engineering situations, we need to make decisions under uncertainty. In some cases, we know the probabilities pi of different situations i; these probabilities should add up to 1. In other cases, we only have expert estimates of the degree of possibility μi of different situations; in accordance with the possibility theories, the largest of these degrees should be equal to 1. In practic...

We introduce the concepts of IVF m-semiopen sets, IVF m-preopen sets, IVF m-semicontinuous mappings and IVF mprecontinuous mappings on interval-valued fuzzy minimal spaces. We investigate characterizations of IVF m-semicontinuous mappings and IVF m-precontinuous mappings and study properties of IVF m-semiopen sets and IVF m-preopen sets.

This paper provides inference methods for best linear approximations to functions which are known to lie within a band. It extends the partial identification literature by allowing the upper and lower functions defining the band to be any functions, including ones carrying an index, which can be estimated parametrically or non-parametrically. The identification region of the parameters of the b...