Rodney Carlos Bassanezi

Fuzzy modelling in population dynamics

The aim of this paper is to analyze the behavior of models which describe the population dynamics taking into account the subjectivity in the state variables or in the parameters. The models in this work have demographic and environmental fuzziness. The environmental fuzziness is presented using a life expectancy model where the fuzziness of parameters is considered. The demographic fuzziness is presented using the continuous Malthus and logistic discrete models. An outstanding result in this case is the emergence of new fixed points and bifurcation values to the discrete logistic model with subjective state variables in form of fuzzy sets. An interpretation is offered for this fact which differs from the deterministic one.

Fuzzy differential equations and the extension principle

We study the Cauchy problem for differential equations, considering its parameters and/or initial conditions given by fuzzy sets. These fuzzy differential equations are approached in two different ways: (a) by using a family of differential inclusions; and (b) the Zadeh extension principle for the solution of the model. We conclude that the solutions of the Cauchy problem obtained by both are the same. We also provide some illustrative examples.

A note on Zadeh's extensions☆

Let f:Rn→Rn and f:F(Rn)→F(R)n be Zadehs extension of f to the space of fuzzy compact sets F(Rn). The aim of this paper is to show that if f is continuous, then f:(F(Rn),D)→(F(Rn),D) is also continuous, D being the supremum over Hausdorff distances between their corresponding level sets.

Attractors and asymptotic stability for fuzzy dynamical systems

Abstract In this work we study the asymptotic properties of maps on fuzzy spaces which are extensions of maps on . The main results are in Section 4 (see Theorem 21) and we give an illustrative example in the last section.

Drug kinetics and drug resistance in optimal chemotherapy

A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. First-order drug kinetics and drug resistance are taken into account in a class of optimal control problems. The results show that the strategy corresponding to the maximum rate of drug injection is optimal for the Malthusian model of cell growth (which is a relatively good model for the initial phase of tumor growth). For more general models of cell growth, this strategy proved to be suboptimal under certain conditions.

The SI epidemiological models with a fuzzy transmission parameter

Abstract Fuzzy theory techniques are applied to susceptible-infectious SI epidemiological models. The transmission coefficient is considered as a fuzzy set and the mean number of infected individuals is compared with the trajectory of the mean virus charge I( v , t) . Also, the basic reproduction value Rf0f is discussed for this formulation and, using RF0f, a control policy of the disease is discussed.

A generalization of the Minkowski embedding theorem and applications

Abstract Puri and Ralescu (1985) gave, recently, an extension of the Minkowski Embedding Theorem for the class ELn of fuzzy sets u on Rn with the level application α → Lαu Lipschitzian on the C([0, 1] x Sn−1) space. In this work we extend the above result to the class ECn of level-continuous applications. Moreover, we prove that ECn is a complete metric space with E L n /nb E C n and E L n = E C n To prove the last result, we use the multivalued Bernstein polynomials and the Vitalis approximation theorem for multifunction. Also, we deduce some properties in the setting of fuzzy random variable (multivalued).

Chemotherapeutic treatments involving drug resistance and level of normal cells as a criterion of toxicity

A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Drug resistance and toxicity conveyed through the level of normal cells are taken into account in a class of optimal control problems. Alternative treatments for the exponential tumor growth are set forth for cases where optimal treatments are not available.

STABILITY OF FUZZY DYNAMIC SYSTEMS

In this work we are study the Fuzzy Initial Value Problem (FIVP) with parameters and/or initial conditions given by fuzzy sets. Starting from the flow equation of the deterministic Initial Value Problem (IVP) associates to FIVP, we obtain the FIVP flow, through the principle of Zadeh. Follow, we introduce the concept of fuzzy equilibrium stability of FIVP and some examples are given.

Theoretical approaches to forensic entomology: I. Mathematical model of postfeeding larval dispersal

Abstract: An overall theoretical approach to model phenomena of interest for forensic entomology is advanced. Efforts are concentrated in identifying biological attributes at the individual, population and community of the arthropod fauna associated with decomposing human corpses and then incorporating these attributes into mathematical models. In particular in this paper a diffusion model of dispersal of postfeeding larvae is described for blowflies, which are the most common insects associated with corpses.