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Similarity in fuzzy reasoning.

Frank Klawonn, Juan Luis Castro (1995)

Mathware and Soft Computing

Fuzzy set theory is based on a `fuzzification' of the predicate in (element of), the concept of membership degrees is considered as fundamental. In this paper we elucidate the connection between indistinguishability modelled by fuzzy equivalence relations and fuzzy sets. We show that the indistinguishability inherent to fuzzy sets can be computed and that this indistinguishability cannot be overcome in approximate reasoning. For our investigations we generalize from the unit interval as the basis...

S-implications and R -implications on a finite chain

Margarita Mas, Miquel Monserrat, Joan Torrens (2004)

Kybernetika

This paper is devoted to the study of two kinds of implications on a finite chain L : S -implications and R -implications. A characterization of each kind of these operators is given and a lot of different implications on L are obtained, not only from smooth t-norms but also from non smooth ones. Some additional properties on these implications are studied specially in the smooth case. Finally, a class of non smooth t-norms including the nilpotent minimum is characterized. Any t-norm in this class...

Singular fractional linear systems and electrical circuits

Tadeusz Kaczorek (2011)

International Journal of Applied Mathematics and Computer Science

A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least...

Singular Perturbations For Heart Image Segmentation Tracking

J. Pousin (2009)

Mathematical Modelling of Natural Phenomena

In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

Dryanov, Dimiter (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.We characterize Paley-Wiener-Schwartz space of entire functions as a union of three-parametric linear normed subspaces determined by the type of the entire functions, their polynomial asymptotic on the real line, and the index p ≥ 1 of a Sobolev type Lp-summability on the real line with an appropriate weight function. An entire function belonging to a sub-space of the decomposition is exactly recovered by a sampling series, locally...

Sobre el parámetro complejidad lineal y los filtros no lineales de segundo orden.

Amparo Fúster Sabater, Luis J. García Villalba (2000)

Revista Matemática Complutense

A new method of analysing the linear complexity of 2nd-order nonlinear filterings of m-sequences that is based on the concept of regular coset is present. The procedure considers any value of the LFSR's length, L, (prime or composite number). Emphasis is on the geometric interpretation of the regular cosets which produce degeneracies in the linear complexity of the filtered sequence. Numerical expressions to compute the linear complexity of such sequences are given as well as practical rules to...

Sobre el tamaño de muestra para experimentos aleatorios con imprecisión difusa.

M.ª Angeles Gil Alvarez, Pedro Gil Alvarez (1988)

Trabajos de Estadística

Statistical Inference deals with the drawing of conclusions about a random experiment on the basis of the information contained in a sample from it. A random experiment can be defined by means of the set of its possible outcomes (sample space) and the ability of observation of the experimenter. It is usually assumed that this ability allows the experimenter to describe the observable events as subsets of the sample space. In this paper, we will consider that the experimenter can only express the...

Some classes of divergence measures between fuzzy subsets and between fuzzy partitions.

Susana Montes, Pedro Gil (1998)

Mathware and Soft Computing

The aim of this paper is to present and study one important class of divergence measure between fuzzy subsets, and one important class of divergence measure between fuzzy partitions, each of them having some specific properties. In the first case, the divergence measure attempts to quantify the degree of difference between two fuzzy subsets ? and ? by comparing the fuzziness of both ? and ? with the fuzziness of the intermediate fuzzy subset. In the second case, we use this divergence between subsets...

Some decompositions of Bernoulli sets and codes

Aldo de Luca (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

A decomposition of a set X of words over a d -letter alphabet A = { a 1 , ... , a d } is any sequence X 1 , ... , X d , Y 1 , ... , Y d of subsets of A * such that the sets X i , i = 1 , ... , d , are pairwise disjoint, their union is X , and for all i , 1 ≤ i ≤ d , X i ∼ a i Y i , where ∼ denotes the commutative equivalence relation. We introduce some suitable decompositions that we call good, admissible, and normal. A normal decomposition is admissible and an admissible decomposition is good. We prove that a set is commutatively prefix if and only if it has a normal decomposition. In particular,...

Some decompositions of Bernoulli sets and codes

Aldo de Luca (2010)

RAIRO - Theoretical Informatics and Applications

A decomposition of a set X of words over a d-letter alphabet A = {a1,...,ad} is any sequence X1,...,Xd,Y1,...,Yd of subsets of A* such that the sets Xi, i = 1,...,d, are pairwise disjoint, their union is X, and for all i, 1 ≤ i ≤ d, Xi ~ aiYi, where ~ denotes the commutative equivalence relation. We introduce some suitable decompositions that we call good, admissible, and normal. A normal decomposition is admissible and an admissible decomposition is good. We prove that a set is commutatively prefix...

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