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...

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 deenition of similarity as an operation. In this paper we develop a similarity measure, based on fuzzy logic, that exhibit several features that match experimental ndings in humans. The model is dub...

Risk analysis plays an important role in many application systems. The current researches prefer to use fuzzy set theory for risk analysis. In this paper, we present a new fuzzy risk analysis method based on generalized fuzzy numbers. Firstly, we define new arithmetic operations between generalized fuzzy numbers. Then, we propose a new method to measure the degree of similarity between generali...

To describe expert uncertainty, it is often useful to go beyond additive probability measures and use non-additive (fuzzy) measures. One of the most widely and successfully used class of such measures is the class of Sugeno λ-measures. Their success is somewhat paradoxical, since from the purely mathematical viewpoint, these measures are – in some reasonable sense – equivalent to probability me...