Implementing fuzzy reasoning with closeness and negligibility relations

The article presents a set of inference rules describing the properties of fuzzy relations for modeling orders of magnitude in terms of closeness and negligibility relations, and their behaviors with respect to arithmetic operations. This inference machinery can be automated for simplifying complex equations with a view to solving them approximately. The paper presents a proposal for the efficient implementation of this machinery which mainly takes advantage of the equivalence between closeness and negligibility. Implementation issues, especially, the encoding of pieces of information and the inference method are discussed. The inference strategy is both goal-driven and data-driven. An example is introduced to illustrate the basic steps of the reasoning