The Research On The Uniqueness And Strong Regularity Of Fuzzy Relation Equations With Max-av Composition

The problem of solving a fuzzy relational equation is very important in fuzzy system. In the past ten years, people have researched the uniqueness and strong regularity of the max-min composition. But there are not good results about other compositions. So, in this paper, we research on the uniqueness and strong regularity of fuzzy relation equations with max-av composition Through the relationship of minimal solutions and minimal coverage, our paper studies the only solution of fuzzy relational equations with max-av composition, and gives a sufficient and necessary condition for it and approaches for verifying the strong regularity of the given matrices.The main content could be list as follows:In the first section, we introduce the research background of Fuzzy mathematics and the development about uniqueness and strong regularity of fuzzy relational equations.In the second section, which is the prime part of this paper, we analyze the sole solution of fuzzy relational equations with max-av composition.In the third section, we get sufficient condition and necessary condition on the regu-larity of matrices.In the fourth section, to check the strong regularity of matrix, we give two algorithms. And two examples about the algorithms.