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...

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.

As a measure of information shared between two fuzzy pattern vectors, the fuzzy information proximity measure (FIPM) plays an important part in fuzzy pattern recognition, fuzzy clustering analysis and fuzzy approximate reasoning. In this paper, two novel FIPMs are set up. Firstly, an axiom theory about the FIPM is given, and different expressions of the FIPM are discussed. A new FIPM is then pr...

With complex multimedia data, we see the emergence of database systems in which the fundamental operation is similarity assessment. Before database issues can be addressed, it is necessary to give a definition of similarity as an operation. In this paper we study several models proposed in the psychological literature to explain the characteristics of human similarity assessment, and discuss th...

We study completely decomposable torsion-free abelian groups of the form GS := ⊕n∈SQpn for sets S ⊆ ω. We show that GS has a decidable copy if and only if S is Σ2 and has a computable copy if and only if S is Σ 0 3.