ON FUNCTIONALS REPRESENTABLE BY FUZZY MEASURES

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On multivalued fuzzy entropies

We analyze an axiomatic system that justifies the introduction of the concept of multivalued fuzzy entropy. This is a natural extension of the concept of fuzzy entropy given by De Luca and Termini. We also extend the results of Trillas-Riera and Knopfmacher to the class of finite measure spaces. (C) 1997 Elsevier Science B.V.86216917

ON THE CONTINUITY OF FUZZY INTEGRALS

We establish minimal conditions on a fuzzy measure to make the measure convergence a sufficient condition for continuity of the fuzzy integral. In particular, we give conditions such that measure convergence of fuzzy sets, with respect to a fuzzy measure, implies the convergence of the fuzzy integral with respect to another fuzzy measure.531879

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.125219120

A cybernetical strategy for optimal farming: On the growth of Caiman Crocodilus Yacare

Presents an optimal strategy for managing crocodile farms. The strategy is illustrated with the case study of Caiman Crocodilus Yacare of the farm Coocrijapan. However, the strategy can be easily transferred to other farms, once sufficient data on their own crocodile stock is gathered. The main advantage of the ideas developed is that they deal with just one parameter: the break-even point of the process. The underlying assumption of having a single parameter is that there is no seasonal change in prices; that is, the unitary price of food (say, per kilogram) and the unitary price of crocodile hide (say, per square centimetre) remain approximately constant in some currency. This may or may not be true in the local currency of the country that hosts the farm. With this assumption, dimensionless quantities for profit and return are found.2641700306

The basic reproduction ratio for a model of directly transmitted infections considering the virus charge and the immunological response

in order to describe mathematically the transmission of microparasites, especially directly transmitted infections, it is usual to set up differential equations assuming the mass action law and a homogeneously mixed population. In this paper we analyze such a model taking into account heterogeneity with respect to the infectivity, that is, the variability in the evolution of the interaction between parasite and the human host during the infectious period. The well established biological phenomenon of initial increase in parasite abundance followed by its decrease, due to the interaction between the host's immunological response and the parasite, has thus been taken into account. The variable amount of microparasites eliminated by an infectious individual, and the different (heterogeneous) immunological response build up by the host when in interaction with parasite are present in the model. The analytical expression for the basic reproduction ratio is derived through stability analysis.171153

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.125221122

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.171698

Study of the dynamics of HIV under treatment considering fuzzy delay

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)This article describes a study of the decay dynamics of the HIV (human immunodeficiency virus) population in blood plasma in response to antiretroviral therapy of HIV-positive individuals by means of a system of delay differential equations. This delay is defined as the time elapsed between the infection of a cell by the CD4+ type T lymphocyte and the production of new virus particles. The delay is considered uncertain due the differences in the cell activation state. To study the relationship between the rate of decline in the plasma virus concentration () and the intracellular delay (), we used a fuzzy rule-based system in Jafelice et al. (Bull Math Biol 66:1463-1942, 2004). Two inference methods were adopted: Mamdani and Takagi-Sugeno. The HIV decay curve, which is the solution of a system of differential equations with fuzzy distributed delay, is determined by means of Zadeh's extension principle. Finally, centroid defuzzification is used to determine a fuzzy expected HIV decay curve. The defuzzified curve that was obtained using Takagi-Sugeno method is closer to the deterministic solution than the one obtained using Mamdani method.3314561Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Brazilian National Research Council [306872/2009-9]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq [477918/2010-7]Brazilian National Research Council [306872/2009-9