A Study on Subjectivities of Type 1 and 2 in Parameters of Differential Equations

This study presents the Verhulst's model for the analysis of population growth with the rate of reproductivity depending on the fertility rate and the country economic development. These linguistic variables are defined through Fuzzy Rule-Based Systems (FRBS). The analysis is made for FRBS types 1 and 2 where in the first case, the inference method used is Mamdani's and the defuzzification is the center of gravity. For type-2 FRBS is used as input variables interval type-2 fuzzy sets, and as output intervals. The output is defuzzificated by the Type Reducer method that use the algorithm of Karnik-Mendel (KM). The aim of this study is to compare the solutions of the Verhulst's model where the parameter, rate of reproductivity, is determined through the type-1 and type-2 FRBS. The comparison is made computing the region built from the solutions corresponding to the minimum and maximum rate. It has been noticed that the region corresponding to type-2 FRBS is contained in the region built similarly from type-1 FRBS, showing a higher accuracy in the response [1], [2], [4].

fuzzy sets; fuzzy rule-based systems; ordinary differential equations