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’.     

Latest precambrian (Cadomian) zircon ages, Nd isotopic systematics and P-T evolution of granitoid orthogneisses of the Erzgebirge, Saxony and Czech Republic

Single zircons from two orthogneiss complexes, the Grey Gneiss and Red Gneiss, the lowermost tectonic units in the Erzgebirge, were dated. The grey Freiberg Gneiss is of igneous origin and has a ²⁰⁷Pb/²⁰⁶Pb emplacement age of 550±7 Ma. A quartz monzonite from Lauenstein contains idiomorphic zircons with a mean ²⁰⁷Pb/²⁰⁶Pb age of 555±7 Ma as well as xenocrysts ranging in age between 850 and 1910 Ma. Red gneisses from the central Erzgebirge contain complex zircon populations, including numerous xenocrysts up to 2464 Ma in age. The youngest, idiomorphic, zircons in all samples yielded uniform ²⁰⁷Pb/²⁰⁶Pb ages between 550±9 and 554±10 Ma. Nd isotopic data support the interpretation of crustal anatexis for the origin of both units. _Nd(t) values for the grey gneisses are –7.5 and –6.0 respectively, (mean crustal residence ages of 1.7–1.8 Ga). The red gneisses have a wider range in _Nd(t) values from –7.7 to –2.8 (T _DM ages of 1.4–1.8 Ga). The zircon ages document a distinct late Proterozoic phase of granitoid magmatism, similar in age to granitoids in the Lusatian block farther north-east. However, Palaeozoic deformation as well as medium pressure metamorphism ( 8 kbar/600–650° C) are identical in both gneiss units and distinguish these rocks from the Lusatian granitoids. The grey and red gneisses were overthrust by units with abundant high-pressure relicts and a contrasting P-T evolution. Zircon xenocryst and Nd model ages in the range 1000–1700 Ma are similar to those in granitoid rocks of Lusatia and the West-Sudetes, and document a pre-Cadomian basement in parts of east-central Europe that, chronologically, has similarities with the Sveconorwegian domain in the Baltic Shield.