Intrinsic growth rate and evolution of the Premnotrypes Vorax population using fuzzy information.

The white potato worm (Premnotrypes Vorax (Hustache)) is one of the pests that causes the greatest damage to the potato crop and the greatest economic losses to the grower; therefore, knowing its life cycle and estimating its intrinsic growth rate is crucial for selecting an appropriate chemical control method, in order to reduce the environmental impact and ensure a profitable production suitable for consumption. In this article, we present a fuzzy Malthusian model describing the evolution of the white potato worm in the crop, considering that the intrinsic growth rate and the reported initial data on the problem are of fuzzy nature. The main contributions and novelty of this paper are summarized in the following two aspects: first, the estimation of the intrinsic growth rate of the white potato worm, in function of the temperature, by using a Takagi-Sugeno-Kang type fuzzy rule-based model; and second, since in practice the initial white potato worm population in a crop is subjective, imprecise and vague, knowing the intrinsic growth rate, we propose and solve a fuzzy initial value problem to determine the evolution in time of the white potato worm population. In conclusion, given a weekly average temperature, it is possible to know the white potato worm population per unit area oscillating in an interval whose length depends on the degree of inaccuracy of the initial population and the intrinsic growth rate. This study can be relevant for grower decision making in terms of the type and frequency of pest control on his crop.

Medidas difusas e integrales difusas / Fuzzy measures and fuzzy integrals

Se presenta un estudio de las medidas difusas y de las integrales difusas, y se muestran algunos fenómenos donde estas son utilizadas- Se expone cómo es introducido el concepto de medida difusa y cómo a partir de él se introduce la noción de integral difusa. Se establecen propiedades de las medidas difusas y se clasifican de acuerdo a la propiedad aditiva y las λ-medidas, se observa cómo las medidas de probabilidad, plausibilidad, credibilidad, posibilidad y necesidad son ejemplos clásicos en la clasificación realizada. Se hace un análisis de las dos principales integrales difusas: integral de Sugeno e integral de Choquet, dado que la aplicación de estas integrales se hace sobre conjuntos finitos, se realiza utilizando el concepto de función equiordenada una comparación de ellas para el caso finito. Se presentan dos ejemplos donde se utilizan las medidas difusas e integrales difusas en los procesos de clasificación de individuos y evaluación de calidad. También se describen algunos fenómenos donde ellas son aplicadas. Las medidas clásicas son usadas en ciertos casos especiales de incertidumbre basados en la aleatoriedad.La utilización en determinados contextos de medidas difusas (no aditivas) y de las integrales difusas ofrece un enfoque más flexible y realista para modelar la incertidumbre...

This is a study of fuzzy measures and fuzzy integrals; it presents some of the phenomena where they are used. It exposes how the concept of fuzzy measure is introduced and from it, the notion of fuzzy integral is presented. Properties of fuzzy measures are established and they are classified according to additive property and λ-measures, while the probability, plausibility, credibility, possibility and necessity measures are observed as classic examples of the classification completed.The two main fuzzy integrals were analyzed: the Sugeno integral and the Choquet integral, given the application of these integrals is made on finite sets, a comparison between them for the finite case is performed using the concept of equiordered functions. We present two examples in which fuzzy measures and fuzzy integrals are used in the classification of individuals and in quality assessment. It also describes some phenomena where they are applied. Classic measures are used in certain special cases of uncertainty based on randomness. The use in certain contexts of fuzzy measures (non-additive) and fuzzy integrals offer a more flexible and realistic focus in modeling uncertainty...

Apresentamos um estudo de medidas difusas e integráis difusas, e mostramos alguns fenómenos onde são utilizadas. Expõe-se como é introduzido o conceito de medida difusa e como a partir daí se introduz a noção de integral difusa. Estabelecem-se propriedades das medidas difusas e classÍficam-se de acordó com a propriedade aditiva e as λ-medidas, observa-se como as medidas de probabilidade, plausibílidade, credibilidade, possibílidade, e necessidade sao exemplos clássicos da classificacão feka. Faz-se urna análise das duas principáis integráis difusas: integral de Sugeno e integral de Choquet, urna vez que a aplicação destas integráis é feka sobre conjuntos finitos, realiza-se utilizando o conceito de funcao equiordenada comparando-as com o caso finito.Apresentam-se dois exemplos que usam medidas difusas e integráis difusas nos processos de classificação dos individuos e de avaliagao de qualidade. Também se descreve alguns fenómenos onde elas são aplicadas. As medidas clássicas são usadas em certos casos especiáis de incerteza baseados em aleatoriedade. O uso em determinados contextos das medidas difusas (não aditiva) e integráis difusas fornece urna incerteza de modelagem mais flexível e realista...