• INCLINE RELATIONAL EQUATIONS

Abstract

Inclines are additively idempotent semirings in which products are less than (or) equal to either factor. In this paper, we discuss the consistency of incline relational equations, that is, equations of the form xA=b where A is a matrix and b is a vector over an incline. We apply our results for incline relational equations involving matrices over special types of inclines such as incline whose elements are all linearly ordered, incline whose idempotent elements are all linearly ordered, a regular incline whose elements are all linearly ordered and a distributive lattice whose elements are all linearly ordered. We deduce the solution set of a fuzzy relational equation as a special case.