ON FUZZY LINEAR REPRESENTATIONS OF FINITE-GROUPS

A linear representation rho of a finite group G in a finite-dimensiona l vector space V induces, through Zadeh's extension principle, a funct ion, <(rho)over tilde>, from I-G into I-GL(V), where GL(V) is the grou p of all linear automorphisms of V. If W is a fuzzy subspace of V, the group of all fuzzy linear automorphisms of W, GL(W), is a subgroup of GL(V). W is said to be stable under the action of a fuzzy subgroup A of G if <(rho)over tilde>(A) is a subset of GL(W), i.e. <(rho)over til de>(A) is zero at every f inside GL(V) and outside GL(W). If W is stab le under the action of A, then its support subspace is stable under th e action of the support subgroup of A in the crisp sense. Finally, we show that; if there are two stable fuzzy subspaces one of them is cont ained in the other, then the smaller one has a fuzzy direct summand in the bigger which is also a stable fuzzy subspace.