Aplicação da extensão de Zadeh para conjuntos Fuzzy tipo 2 intervalar

Abstract

The objective of this study is to present the classical Montroll s model and with type-1 and type-2 fuzzy parameter for the population of Peru, of 1961-2013. To model the population dynamics with type-1 fuzzy parameter, we use two techniques: the first through a Fuzzy Rule- Based System (FRBS), where the input variables are the fertility rate and the rate of economic growth of the country, and the output variable is the rate of population growth. The second technique is performed considering the rate of increase as a triangular fuzzy number and using the Zadeh s Extension Principle, to obtain the type-1 fuzzy solution of Montroll s model in function of time. Subsequently, we compare the approaches of Montroll classic model and the models obtained by the two techniques studied with population data, using as comparison method, the maximum relative error. To model the population dynamics with type-2 fuzzy parameter, we also used two techniques: the first through a type-2 Fuzzy Rule Based System (FRBS2), where the input variables are the fertility rate and the rate of economic growth of the country, and the output variable is the rate of population growth. The second technique is performed by considering the rate of population growth as an interval type-2 triangular fuzzy set and we using the Zadeh s Extension Principle for upper and lower membership functions of this set in each instant. Thus, we obtain the solution type-2 fuzzy of Montroll s model in function of time, subsequently, compare the approaches of these models with population data, using the maximum relative error. Finally, we compare the results obtained from the type-1 and type-2 fuzzy sets.