推理句(a(x)→b(y))真域的最大乘积型模糊关系方程

Max-Product Fuzzy Relation Equation of Inference Sentence (a(x)→b(y))

设"x是a"与"y是b"的真域分别是A∈F(X)与B∈F(Y).按照模糊推理的要求,希望求推理句"若x是a,则y是b"的真域R且满足:A R=B,BC RT=AC.针对X,Y为有限论域,通过解最大乘积模糊关系方程,给出方程A R=B,BC RT=AC相容的条件,并给出最大解.

Let fuzzy Sets A∈F(X),B∈F(Y) denote propositions 'x is a' and 'y is b' respectively. According to fuzzy inference rules,fuzzy relation R (denote proposition 'if x is a,then y is b') should satisfy:AR=B,BCRT=AC. By solving maxproduct fuzzy relation equation,a necessary and sufficient condition is given that fuzzy relation equation AR=B,BCRT=AC has a solution,and its maximum solution is obtained when X and Y ave finite sets.