In this paper some types of decomposable signed fuzzy measures have been presented. We discuss properties of 6-and ⊕decomposable signed fuzzy measures. We consider their relationship with bi-capacities.

The pseudometric generating property of non-additive set functions also plays an important role as the autocontinuity in fuzzy measure theory 2, 9]. A further research on this property has been presented in 4]. The aim of this paper is to prove the Egoroo's theorem and Lusin's theorem for measurable functions on metric spaces hold for those fuzzy measures with the exhaustivity and pseudometric ...

In this paper, we propose a fuzzy generalized ‘useful’ parametric mean length and bounds are obtained in terms of useful fuzzy measure. The bounds obtained are new and some known results are the particular cases of the proposed measure and bounds.

Distorted probabilities are an important family of fuzzy measures. In a recent paper we introduced m-dimensional distorted probabilities, which generalize the former and permit us to have a smooth transition from distorted probabilities to unconstrained ones. In this paper we introduce the union condition and the strict union condition, and we show that when these conditions hold for a fuzzy me...

In this paper, the well-known Egoroff’s theorem in classical measure theory is established on Sugeno fuzzy measure spaces. Taylor’s theorem, which concerns almost everywhere convergence of measurable function sequence in classical measure theory, is also generalized. The converse problem of the theorems are discussed, and a necessary and sufficient condition for the Egoroff’s theorem is obtaine...

and with the habitual changes in the case p = +∞. If I is a set then, l(I) denotes the Banach space L(I, ν),where ν is the counting measure. And if I is the set {1, ..., n}, the corresponding space is denoted ln . We will denote by H(X)the space of all analytic functions f : D −→ X such that ||f ||Hp(X) < +∞, with ||f ||Hp(X) = Sup {||fr||Lp(T;X) : 0 < r < 1} and fr(t) = f(rt), for all t ∈ T an...

We introduce a fuzzy metric on the set of probability measures on a fuzzy metric space. The construction is an analogue, in the realm of fuzzy metric spaces, of the Prokhorov metric on the set of probability measures on compact metric spaces. © 2011 Elsevier B.V. All rights reserved.