Application of Type-2 Membership Functions in Fuzzy Logic Systems

Наталія Романівна Кондратенко


Background. Developing decision making models for problems, that are not easily formalized, and which operate the expert information, became possible by utilizing the capabilities of fuzzy sets theory and building fuzzy logic systems. Use of fuzzy sets theory techniques for knowledge formalization automatically results in the researcher having to select the type of fuzzy sets used for constructing membership functions, as well as the fuzzy model, that would fit the selected fuzzy set type. Therefore, the task of investigating the capabilities of type-2 membership functions in fuzzy logic systems is one of great interest.

Objective. Expanding the capabilities of fuzzy logic systems by using type-2 membership functions.

Methods. Research methods are directed towards utilizing interval and three-dimensional type-2 fuzzy sets in forecasting problems and medical diagnostics. The matter of investigating the capabilities of interval membership functions built on experimental data will be considered in two aspects: the first one – of how well interval membership functions reflect the uncertainties present in the source data, and the second one – of the advantages and disadvantages of an interval output of a fuzzy model with interval membership functions.

Results. A research of interval type-2 membership functions in fuzzy logic systems was conducted in the areas of forecasting problem and medical diagnostics. Applicability of three-dimensional type-2 membership functions built from experimental data was shown.

Conclusions. This paper shows the advantages of using interval membership functions in fuzzy logic systems, when developing fuzzy models using the multiple models principle. A research of three-dimensional type-2 membership functions’ applicability when modeling existing uncertainties is given. A technique for generating three-dimensional membership functions in fuzzy logic systems generated from experimental data is proposed.


Experimental data; Type-2 membership functions; Interval fuzzy model; Three-dimensional membership function


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