A PRIMER ON SOLVING FUZZY RELATIONAL EQUATIONS ON THE UNIT INTERVAL
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TL;DR
This overview starts with a thorough treatment of equations and systems of equations, with a continuous triangular norm, and shows that these are the basic problems: all other equations, image and composition equations, can be reduced to these problems.
Abstract
This paper has to be considered as a guide to solving fuzzy relational equations on the unit interval. Although the number of publications on this topic is quite impressive, there doesn't seem to exist a handy structured overview of all types of equations and their solution procedures. Our overview starts with a thorough treatment of [Formula: see text] equations and systems of [Formula: see text] equations, with [Formula: see text] a continuous triangular norm. It is shown that these are the basic problems: all other equations, image and composition equations, can be reduced to these problems. We do not only structure well-known results, we also present some new insights in the solution procedures of fuzzy relational equations.