Applied Mathematics, 2016, 7, 2149-2164 http://www.scirp.org/journal/am ISSN Online: 2152-7393 ISSN Print: 2152-7385 DOI: 10.4236/am.2016.717171 November 17, 2016 On Fuzzy Control of Soybean Aphid Magda S. Peixoto 1 , Laécio C. Barros 2 , Rodney C. Bassanezi 2 , Odair A. Fernandes 3 1 Universidade Federal de São Carlos (UFSCar), Sorocaba, Brazil 2 Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 3 Universidade EstadualPaulista (UNESP), Jaboticabal, Brazil Abstract This paper uses a methodology based in Fuzzy Sets Theory in order to describe the interaction between the prey, Aphis glycines (Hemiptera: Aphididae)—the soybean aphid, and its predator, Orius insidiosus (Hemiptera: Anthocoridae) and to propose a biological control to soybean aphid. Economic thresholds were already developed for this pest. The model includes biotic (predator) and abiotic (temperature) factors, which affect the soybean aphid population dynamics. The dynamic model results in a fuzzy model that preserves the biological meaning and nature of the predator-prey model. The paper also includes a comparison between the fuzzy model and real data reported in the literature. Subsequently, we propose a biological control to soybean aphid by another fuzzy rule-based system. This model has allowed to predict timing and releasing number of predators for soybean aphid biological control. On the one hand, the soybean aphid has still not found in Brazil. Therefore, before any eventual invasion, a predictive model to enhance biological control program is desirable. On the other hand, the soybean aphid has become the most devastating insect pest of soybeans in the United States. Brazil is the second largest exporter of soybean at present, after the USA and before Argentina. According to the Bureau of Agriculture of the USA, it has been estimated that Brazil will be the largest soybean exporter in 2023. Keywords Fuzzy Sets, Fuzzy Systems, Mamdani Inference Method, Prey, Predator, Control 1. Introduction The soybean aphid, Aphis glycines (Hemiptera: Aphididae), is an invasive herbivore new to North America. It was first discovered in North America in Wisconsin in late July 2000 infesting soybean crop. High soybean aphids densities damage soybean plants How to cite this paper: Peixoto, M.S., Barros, L.C., Bassanezi, R.C. and Fernandes, O.A. (2016) On Fuzzy Control of Soybean Aphid. Applied Mathematics, 7, 2149-2164. http://dx.doi.org/10.4236/am.2016.717171 Received: September 15, 2016 Accepted: November 14, 2016 Published: November 17, 2016 Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access