Abductive reasoning with type 2 fuzzy sets

In fuzzy abduction, one needs to evaluate the membership distribution of the premise (antecedent clause), when the membership distribution of the consequent clause, and the fuzzy implication relations between the antecedent and the consequent clauses are provided. The paper formulates and solves the problem of fuzzy abduction by using type-2 fuzzy sets. It presumes background knowledge about the primary and the secondary antecedent to consequent implication relations to uniquely determine the type-2 fuzzy set corresponding to the antecedent clause, when the same for the consequent clause is provided. The proposed methodology of abduction would serve many interesting applications on predictions, forecasting, and diagnosis, where the environmental factor can be modeled with type-2 secondary distributions.