Using fuzzy set theory to address the uncertainty of susceptibility to drought

This paper presents the technical aspects of a new methodology for assessing the susceptibility of society to drought. The methodology consists of a combination of inference modelling and fuzzy logic applications. Four steps are followed: (1) model input variables are selected—these variables reflect the main factors influencing susceptibility in a social group, population or region, (2) fuzzification—the uncertainties of the input variables are made explicit by representing them as ‘fuzzy membership functions’, (3) inference modelling—the input variables are used to construct a model made up of linguistic rules, and (4) defuzzification—results from the model in linguistic form are translated into numerical form, also through the use of fuzzy membership functions. The disadvantages and advantages of this methodology became apparent when it was applied to the assessment of susceptibility from three disciplinary perspectives: Disadvantages include the difficulty in validating results and the subjectivity involved with specifying fuzzy membership functions and the rules of the inference model. Advantages of the methodology are its transparency, because all model assumptions have to be made explicit in the form of inference rules; its flexibility, in that informal and expert knowledge can be incorporated through ‘fuzzy membership functions’ and through the rules in the inference model; and its versatility, since numerical data can be converted to linguistic statements and vice versa through the procedures of ‘fuzzification’ and ‘defuzzification’.     

Combined influence of food level and inoculation density on competition between <Emphasis Type="Italic">Anuraeopsis fissa</Emphasis> and <Emphasis Type="Italic">Brachionus patulus</Emphasis> or <Emphasis Type="Italic">Brachionus macracanthus</Emphasis> (Rotifera: Brachionidae)

We tested separately the effect of two taxonomically related rotifers (B. patulus and B. macracanthus) on the population dynamics of another species (A. fissa) at low (0.5 ×10 ⁶) and high food levels (1.5 × 10⁶ cells/ml of Chlorella vulgaris) using different inoculation densities (0–100%). We also quantified the impact of A. fissa on the two brachionid species. Regardless of the presence of the competing species, an increase in the availability of food led to increase in the abundances of the three rotifers. The population growth of B. patulus, B. macracanthus, or A. fissa was affected negatively when cultured together with another species. An increase in the initial density of any one of the competing species became advantageous to maintain a certain population size. At a low algal food level, B. patulus was able to suppress A. fissa more strongly than B. macracanthus. On the other hand, at a high food level, B. macracanthus suppressed the population of A. fissa more strongly than B. patulus. Peak population densities for A. fissa varied from about 150 to 1000 ind./ml, depending on food density and the presence of competitors. The rate of population increase (r) of A. fissa, B. patulus, and B. macracanthus increased with an increase in food availability but decreased with increasing initial density of the competitor. Both Brachionus spp. experienced negative growth rates in the presence of A. fissa, especially at a high initial density of the latter. Published in Russian in Ekologiya, 2007, Vol. 38, No. 5, pp. 381–390. The article was submitted by the authors in English.