Literature for this section is for instance Sugiura [3, Ch. 1]. Let G be a group. Representations of G can be defined on any vector space (possibly infinite dimensional) over any field, but we will only consider representations on finite dimensional complex vector spaces. Let V be a finite dimensional complex vector space. Let GL(V ) be the set of all invertible linear transformations of V . Th...

Let G be a group. Representations of G can be defined on any vector space (possibly infinite dimensional) over any field, but we will only consider representations on finite dimensional complex vector spaces. Let V be a finite dimensional complex vector space. Let GL(V ) be the set of all invertible linear transformations of V . This is a group under composition. If V has dimension n and if we ...

The paper describes an approach to discover transparent fuzzy rules from data, which can be effectively used in fuzzy model-based medical diagnosis. The approach is based on three main stages. First, available symptoms measurements are clustered by our Crisp Double Clustering scheme, which identifies, in the first instance, informative prototypes in the original measurements space by a vector q...

Let T be a continuous linear operator on a Hausdorff topological vector space X over the field C. We show that if T is N -supercyclic, i.e., if X has an N dimensional subspace whose orbit under T is dense in X , then T ∗ has at most N eigenvalues (counting geometric multiplicity). We then show that N -supercyclicity cannot occur nontrivially in the finite dimensional setting: the orbit of an N ...

n-Dimensional fuzzy sets is a fuzzy set extension where the membership values are n-tuples of real numbers in the unit interval [0, 1] orderly increased, called n-dimensional intervals. The set of n-dimensional intervals is denoted by Ln([0, 1]). This paper aims to investigate a special extension from [0, 1] – n-representable fuzzy negations on Ln([0, 1]), summarizing the class of such function...

Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion (" acceleration equal force "), with linear and cubic forces, in N-dimensional space (N being an arbitrary positive integer, with special attention to N = 2, namely motions in a plane, and N = 3, namely motions in ordinary three-dimensional space). All the...

This paper proposes a compromise model, based on the technique for order preference through similarity ideal solution (TOPSIS) methodology, to solve the multi-objective large-scale linear programming (MOLSLP) problems with block angular structure involving fuzzy parameters. The problem involves fuzzy parameters in the objective functions and constraints. This compromise programming method is ba...

A measure of nonspecificity is proposed for fuzzy sets with continuous membership functions defined, in general, on the n-dimensional Euclidean space R". The proposed measure is restricted to fuzzy sets that are convex. The measure is justified in terms of the usual axiomatic requirements.