Network


Latest external collaboration on country level. Dive into details by clicking on the dots.

Hotspot


Dive into the research topics where Claudi Alsina is active.

Publication


Featured researches published by Claudi Alsina.


Archive | 2006

Associative functions : triangular norms and copulas

Claudi Alsina; Maurice J Frank; Berthold Schweizer

The functional equation of associativity is the topic of Abels first contribution to Crelles Journal. Seventy years later, it was featured as the second part of Hilberts Fifth Problem, and it was solved under successively weaker hypotheses by Brouwer (1909), Cartan (1930) and Aczel (1949). In 1958, B Schweizer and A Sklar showed that the “triangular norms” introduced by Menger in his definition of a probabilistic metric space should be associative; and in their book Probabilistic Metric Spaces, they presented the basic properties of such triangular norms and the closely related copulas. Since then, the study of these two classes of functions has been evolving at an ever-increasing pace and the results have been applied in fields such as statistics, information theory, fuzzy set theory, multi-valued and quantum logic, hydrology, and economics, in particular, risk analysis.This book presents the foundations of the subject of associative functions on real intervals. It brings together results that have been widely scattered in the literature and adds much new material. In the process, virtually all the standard techniques for solving functional equations in one and several variables come into play. Thus, the book can serve as an advanced undergraduate or graduate text on functional equations.


Journal of Mathematical Analysis and Applications | 1983

On Some Logical Connectives for Fuzzy Sets Theory

Claudi Alsina; E Trillas; L Valverde

INTRODUCTION It was proved by Bellman and Giertz [2] that, under reasonable hypotheses (especially distributivity), the only truth-functional logical connectives for fuzzy sets are the usual min and max. The following easy argument proves that distributivity, monotonicity and boundary conditions are essential assumptions: x = F(x, 1) = F(x, G(l, 1)) = G(F(x, l), F(x, 1)) = G(x, x), max(x, Y) = G(max(x, Y), max(x, Y>> > G(x, Y> > max(G(x, 01, G(O, Y)) = ma+, Y), i.e., G(x, y) = max(x, y). Here F and G are, respectively, functions from (0, l]


Aequationes Mathematicae | 1992

On the definition of a probabilistic normed space

Claudi Alsina; B. Schweizer; A. Sklar

SummaryIn this paper we give a new definition of a probabilistic normed space. This definition, which is based on a characterization of normed spaces by means of a betweenness relation, includes the earlier definition of A. N. Šerstnev as a special case and leads naturally to the definition of the principal class of probabilistic normed spaces, the Menger spaces.


Statistics & Probability Letters | 1993

On the characterization of a class of binary operations on distribution functions

Claudi Alsina; Roger B. Nelsen; Berthold Schweizer

We characterize the class of binary operations \/o on distribution functions which are both induced pointwise, in the sense that the value of \/o(F, G) at g is a function of F(t) and G(t) (e.g. mixtures), and derivable from functions on random variables (e.g. convolution).


Fuzzy Sets and Systems | 1985

On a family of connectives for fuzzy sets

Claudi Alsina

Abstract In this paper we find the general solution of the functional equation S ∗ (T(x, y), T(x, N(y))) = x , where S ∗ is a t-conorm, T is a t-norm and N is a strong negation on the unit interval. In particular the result yields a family of connectives for fuzzy sets.


IEEE Transactions on Fuzzy Systems | 2002

On the law [p/spl and/q/spl rarr/r]=[(p/spl rarr/r)V(q/spl rarr/r)] in fuzzy logic

Enric Trillas; Claudi Alsina

This paper deals with the logical equivalence of the classical propositional calculus [p/spl and/q/spl rarr/r]=[(p/spl rarr/r)V(q/spl rarr/r)]. This equality seems to play a central role in a recent discussion around a paper of Combs and Andrews (1998). After reconsidering the equivalence in lattices, its validity in the standard theories of fuzzy sets endowed with an implication operator is studied.


soft computing | 1999

On contradiction in fuzzy logic

Enric Trillas; Claudi Alsina; Joan Jacas

Abstract We clarify which space of functions in [0, 1]E would be reasonable in fuzzy logic in order to avoid self-contradiction.


Archive | 1985

On the Stability of a Functional Equation Arising in Probabilistic Normed Spaces

Claudi Alsina

In this paper we solve for a given e > 0 the inequality


Archive | 2009

Norm derivatives and characterizations of inner product spaces

Claudi Alsina; Justyna Sikorska; M Santos Tomás


International Journal of General Systems | 2002

Searching for the roots of non-contradiction and excluded-middle

Enric Trillas; Claudi Alsina; Ana Pradera

{{\text{d}}_{\text{L}}}\left( {\tau \left( {F\left( {j/a} \right),F\left( {j/b} \right.} \right)} \right),F\left( {j/a + \left. b \right)} \right) \leqslant \varepsilon ,

Collaboration


Dive into the Claudi Alsina's collaboration.

Top Co-Authors

Avatar

Enric Trillas

Technical University of Madrid

View shared research outputs
Top Co-Authors

Avatar

Berthold Schweizer

University of Massachusetts Amherst

View shared research outputs
Top Co-Authors

Avatar

M Santos Tomás

Polytechnic University of Catalonia

View shared research outputs
Top Co-Authors

Avatar

M. S. Tomás

Polytechnic University of Catalonia

View shared research outputs
Top Co-Authors

Avatar
Top Co-Authors

Avatar

Eloy Renedo

Technical University of Madrid

View shared research outputs
Top Co-Authors

Avatar

Maurice J Frank

Illinois Institute of Technology

View shared research outputs
Top Co-Authors

Avatar

A. Sklar

Polytechnic University of Catalonia

View shared research outputs
Top Co-Authors

Avatar

Ana Pradera

King Juan Carlos University

View shared research outputs
Researchain Logo
Decentralizing Knowledge