完备Brouwerian格上求Fuzzy关系方程的具有最大布尔度的解的算法注记

A Note on an Algorithm Finding the Solutions with Maximal Booleanity of Fuzzy Relational Equations on Complete Brouwerian Lattice

在A .Di.Nola等 (OnbooleanityofrelationalequationinBrouwerianlattices.BollUnMatItal,1984,6 (3) :871～882 .)给出了有限论域上Fuzzy关系方程A⊙R =B(⊙ :max min ,A、B为已知Fuzzy集 )在解集非空且无布尔解时如何找到它的一个具有最大布尔度的解的一种方法的基础上 ,给出了一种类似的算法 ,运用该算法能找到具有最大布尔度的所有解 ,并在最后讨论了方程的极小解 (若存在 )与具有最大布尔度的解的关系 .

On the basis of A. Di. Nola and A. Ventre's paper(On booleanity of relational equation in Brouwerian lattices. Boll Un Mat Ital,1984,6(3):871～882.) which gave a method finding a solution with maximal booleanity of fuzzy relational equations A⊙R=B when its solution set is unempty, but without boolean solutions. We give a similar algorithm. By this algorithm, we can find all of the solutions which have maximal booleanity. Moreover, the relation between the minimal solutions of the equation and the solutions with maximal booleanity is discussed.