FUZZY ALGEBRAIC-VARIETIES

The concept of a fuzzy algebraic variety is introduced in order to bring the current knowledge of fuzzy commutative ring theory to bear on the solution of nonlinear systems of equations of fuzzy singletons. It is shown for every finite-valued fuzzy ideal A of a polynomial ring in several indeterminates over a field with A(0) = 1 that the fuzzy algebraic variety of A can be expressed as a union of fuzzy irreducible algebraic varieties, no one of which is contained in the union of the others.