Mamdani fuzzy inference system local tuning algorithm with the saving interpretation capability of inference rules

The article presents the Mamdani systems local tuning algorithm with saving interpretation capability of inference rules, which allows us to solve the problem of expert system configuration on the basis of statistical data or on the basis of information on the exact (crisp) value of the system output for certain input values. Restrictions were set on the conclusion rules for applying direct and inverse transformation of the Mamdani-type system to the Sugeno-type system. In this article a formula for local tuning of the Sugeno-type system is proposed. This formula calculates the values of the fuzzy logical rules consequences based on the construction of the perpendicular bisector between n-dimensional surfaces. Surfaces equations are based on the values of the conclusions of each rule before and after tuning. The Sugeno-type system is transformed back to the Mamdani-type system after local tuning. The saving of interpretation capability of inference rules is ensured by the introduction of a linguistic modifier. The modifier allows us to set the new language values to rules consequences by adding the degree of change based on reference linguistic values.