Incoherence detection and approximate solving of equations using fuzzy qualitative reasoning

Deals with relative orders of magnitude reasoning that handles notions such as closeness (Cl) and negligibility (Ne), by means of fuzzy relations. A set of inference rules describes how these relations can be composed and how they behave with respect to addition and product. Fuzzy numbers play the role of parameters underlying the semantics of Cl and Ne. Some of rules lead to conclusions involving closeness relations which are no longer symmetric. We propose symmetric variants of these rules. The results provided by these variants are sound but not complete; although the symbolic reasoning is made easier. We show that this type of reasoning can be used for proving the incoherence of set of equations or finding approximate solutions thereof