Open AccessProperties of interval type-2 fuzzy sets in decision support systems
Author(s) -
Alexander Zakovorotnіy,
Артем Харченко
Publication year - 2021
Publication title -
vìsnik nacìonalʹnogo tehnìčnogo unìversitetu "hpì". novì rìšennâ v sučasnih tehnologìâh/vestnik nacionalʹnogo tehničeskogo universiteta "hpi". novye rešeniâ v sovremennyh tehnologiâh
Language(s) - English
Resource type - Journals
eISSN - 2413-4295
pISSN - 2079-5459
DOI - 10.20998/2413-4295.2021.04.10
Subject(s) - membership function , defuzzification , interval (graph theory) , fuzzy set , fuzzy number , data mining , mathematics , fuzzy classification , fuzzy logic , fuzzy set operations , computer science , mathematical optimization , artificial intelligence , combinatorics
Definitions and methods of designing interval type-2 fuzzy sets in fuzzy inference systems for control problems of complex technical objects in conditions of uncertainty are considered. The main types of uncertainties, that arise when designing fuzzy inference systems and depend on the number of expert assessments, are described. Methods for assessing intra-uncertainty and inter-uncertainty are proposed, taking into account the different number of expert assessments at the stage of determining the types and number of membership functions. Factors influencing the parameters and properties of interval type-2 fuzzy during experimental studies are determined. Such factors include the number of experiments performed, external factors, technical parameters of the control object, and the reliability of the components of the computer system decision support system. The properties of the lower and upper membership functions of interval type-2 fuzzy sets are investigated on the example of the Gaussian membership function, which is one of the most used in the problems of fuzzy inference systems design. The main features and differences in the methods of determining the lower and upper membership functions of interval type-2 fuzzy sets for different types of uncertainties are taken into account. Methods for determining the footprint of uncertainty, as well as the dependence of its size on the number of expert assessments, are considered. The footprint of uncertainty is characterized by the lower and upper membership functions, and its size directly affects the accuracy of the obtained solutions. Methods for determining interval type-2 fuzzy sets using regulation factors of membership function parameters for intra-uncertainty and weighting factors of membership functions for inter-uncertainties have been developed. The regulation factor of the function parameters can be used to describe the lower and upper membership functions while determining the size of the footprint of uncertainty. Complex interval type-2 sets are determined to take into account inter-uncertainties in the problems of fuzzy inference systems design.