Classification of Fuzzy Varieties

Abstract

In this thesis, we study the fuzzy algebraic varieties. The goal of discussing fuzzy algebraic varieties is to provide some significance to the fuzzy commutative ring theory that has been created thus far and to show the way forward for additional research. We apply fuzzy commutative ring theory to a natural application field, specifically the solution of nonlinear systems of fuzzy singleton intersection equations. It is demonstrated by Mordeson in 1993 that every fuzzy algebraic variety V with 0 ∈ Im(V ) could be represented uniquely as union of a finite number of irreducible algebraic varieties, none of which are contained in union of the others.