This paper demonstrates that it is possible to relax the commitment to numeric degrees of belief while retaining the desirable features of the Bayesian approach for representing and changing states of belief. We first present an abstract representation of states of belief and an associated notion of conditionalization that subsume their Bayesian counterparts. Next, we provide some symbolic and ...

We fix once and for all a positive integer n. Unless we say otherwise, Ω will be an open subset of R. We let N; P; Z; Q; R; C be the set of nonnegative integers; the set of positive integers; the ring of integers; the field of rational numbers; the field of real numbers; and the field of complex numbers, respectively. Whenever a ∈ R and 0 < r <∞ we let U(a, r) = {x ∈ R : |x− a| < r} and B(a, r)...

One can prove the following propositions: (2) For all real numbers a, b, r such that 0 ¬ r and r ¬ 1 and a ¬ b holds a ¬ (1 − r) · a + r · b and (1 − r) · a + r · b ¬ b. (3) For all real numbers a, b such that a ­ 0 and b > 0 or a > 0 and b ­ 0 holds a + b > 0. (4) For all real numbers a, b such that −1 ¬ a and a ¬ 1 and −1 ¬ b and b ¬ 1 holds a · b ¬ 1. (5) For all real numbers a, b such that ...

for any lacunary sequence $theta = (k_{r})$, we define the concepts of $s_{theta}-$limit point and $s_{theta}-$cluster point of a sequence of fuzzy numbers $x = (x_{k})$. we introduce the new sets  $lambda^{f}_{s_{theta}}(x)$, $gamma^{f}_{s_{theta}}(x)$ and prove some inclusion relaions between these and the sets $lambda^{f}_{s}(x)$, $gamma^{f}_{s}(x)$ introduced in ~cite{ayt:slpsfn} by aytar [...

in this paper, by using a new approach on distance between two fuzzy numbers, we construct a new ranking system for fuzzy number which is very realistic and also matching our intuition as the crisp ranking system on r.