Abstract
<span style="color: #000000;"> This study presents the </span><span style="color: #000000;">Verhulst's</span><span style="color: #000000;"> model for the analysis of population growth with the rate of </span><span style="color: #000000;">reproductivity</span><span style="color: #000000;"> depending on the fertility rate and the country economic development. These linguistic variables are defined through Fuzzy Rule-Based Systems (</span><span style="color: #000000;">FRBS</span><span style="color: #000000;">). The analysis is made for </span><span style="color: #000000;">FRBS</span><span style="color: #000000;"> types 1 and 2 where in the first case, the inference method used is </span><span style="color: #000000;">Mamdani's</span><span style="color: #000000;"> and the </span><span style="color: #000000;">defuzzification</span><span style="color: #000000;"> is the center of gravity. For type 2 </span><span style="color: #000000;">FRBS</span><span style="color: #000000;"> is used the inference method by </span><span style="color: #000000;">Karnik</span><span style="color: #000000;"> Mendel (KM) where the output is </span><span style="color: #000000;">defuzzificated</span><span style="color: #000000;"> by the </span><span style="color: #000000;"> Type Reducer method. A comparative study of the solutions of the </span><span style="color: #000000;">Verhulst's</span><span style="color: #000000;"> model for both techniques is performed. I has been noticed that the region determined by the solutions corresponding to the minimum and maximum rate resulting from </span><span style="color: #000000;">FRBS</span><span style="color: #000000;"> type 2 is contained in the region built similarly from type 1, showing a higher accuracy in the response.</span>
Highlights
[8] Zadeh proposed an extension of classical fuzzy sets for the concept of type-2 fuzzy sets, which would be especially useful in those situations where exact membership function for a fuzzy set is difficult to determine
This theory allows the modeling of the linguistic type, such as Fuzzy Rule-Based Systems (FRBS), minimizing the effects of uncertainties [4]
The classic fuzzy sets started to be known as type-1
Summary
In his pioneering work [8] Zadeh proposed an extension of classical fuzzy sets for the concept of type-2 fuzzy sets, which would be especially useful in those situations where exact membership function for a fuzzy set is difficult to determine. This theory allows the modeling of the linguistic type, such as FRBS, minimizing the effects of uncertainties [4]. [0, 1] that determines two functions, μ (x), A the lower membership, and μA(x) the upper membership, associated to the interval type-2 fuzzy set as follows: μA(x) = J x , and μ (x). As a model we use the population growth of a community, using as a technique the FRBS of both types
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