MODEL LOGISTIK FUZZY DENGAN ADANYA PEMANENAN PROPORSIONAL

Fitri Nor Annisa; Muhammad Ahsar Karim; Yuni Yulida

doi:10.20527/epsilon.v16i1.5552

MODEL LOGISTIK FUZZY DENGAN ADANYA PEMANENAN PROPORSIONAL

Fitri Nor Annisa, Muhammad Ahsar Karim, Yuni Yulida

Abstract

The logistic growth model with proportional harvesting is a population growth model that takes into account harvesting factors. In real life, not all conditions can be known with certainty, such as different growth rates in each population and harvest rates depending on the needs of the harvester. To overcome these conditions, there is a concept that accommodates the problem of uncertainty, namely the fuzzy concept. This concept can be induced into a logistic model with proportional harvesting which assumes the intrinsic growth rate and the harvest rate is expressed by fuzzy numbers. The purpose of this research is to form a logistic model with fuzzy proportional harvesting, analyze the stability of the model, and form a numerical simulation. This study uses the alpha-cut method to generalize the intrinsic growth rate and harvest rate from crisp numbers to fuzzy numbers, then the Graded Mean Integration Representation (GMIR) method to defuzzify the model, and the linearization method to analyze the stability of the model. The results of this study obtained a logistic model with proportional harvesting. Then the model was developed into a logistic model with fuzzy proportional harvesting by assuming the intrinsic growth rate and the harvest rate expressed by fuzzy numbers. From the model obtained 2 equilibrium points, namely the first equilibrium point is unstable and the second equilibrium point is asymptotically stable under certain conditions. Model simulation is given to show illustration of stability analysis. From the simulation, it can also be shown that the higher the graded mean value, the lower the population.

Keywords

logistic model, fuzzy, growth rate, harvesting, equilibrium, stability

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DOI: https://doi.org/10.20527/epsilon.v16i1.5552