Elektronika 2009-11.pdf - Instytut SystemÃ³w Elektronicznych

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The block diagram of decision-making on realization of protective actions in conditions of the dangerous natural phenomenon threat Schemat blokowy procesu wyboru projektów przedsięwzięć ochronnych lub zapobiegawczych w warunkach zagrożenia niebezpiecznym zjawiskiem natury the help of a linguistic variable {β, T, C, G, M}, where: β - the name of fuzzy linguistic variable: for example, intensity of mudflow avalanche; T - set of values of a linguistic variable, each of which represents the name of a separate fuzzy variable: “small”, ”average”, “large”, “catastrophic”; X - range of definition of fuzzy variables which enter into definition of a linguistic variable β: X=[0, 5•10 6 ]; G - syntactic procedure of formation of new terms with the help of logic relations “AND”, “OR”, “NOT” etc., for example: “small or average intensity of an avalanche”, M - semantic procedure, tasks on X = [0, 5•10 6 ] fuzzy variables: α 1 - “low intensity”, α 2 - “average intensity”, α 3 - “the large intensity”, α 4 - “catastrophic intensity ”, and also the appropriate fuzzy sets A ~ = {x/µ A (x)} from terms G (T) according to rules of translation fuzzy relations and modifiers “AND”, “OR”, “NO” etc. Fuzzy models of an estimation of the damage connected to the dangerous hydrometeorological phenomenon As existing threat of the dangerous natural phenomenon (flooding, mudflow, … etc.) under its influence can be a territory with the economic objects . Among the models for an estimation of probable damage, there should be models, which allow determination of objects that find oneself under influence of the given natural phenomenon at its predicted intensity. The losses connected to influence of the dangerous phenomenon on each of objects depend on intensity of the phenomenon. We shall present sets of objects, which can appear under influence of the hydrometeorological phenomenon at different intensity, as fuzzy sets (tabl. 1). 20 ELEKTRONIKA 11/<strong>2009</strong>
Tabl. 1. Fuzzy sets of the objects, which are taking place in a dangerous zone of different intensity of the hydrometeorological phenomenon Tab. 1. Zbiory rozmyte zagrożonych obiektów w zależności od siły niebezpiecznego zjawiska natury spowodowanego czynnikami hydrometeorologicznymi Intensity of the hydrometeorological phenomenon Small Average Large Catastrophic Fuzzy set of objects in a dangerous zone It is possible to write down, that A ~ ⊂ B ~ ⊂ C ~ ⊂ D ~ , as m A (x i ) ≤ m B (x i ) ≤ m C (x i ) ≤ m D (x i ), as is shown in tabl. 2. Data in tabl. 2 are example of representation of a fuzziness of subjective experts estimation, where there is a concrete object under the dangerous phenomenon influence. Fuzzy logic for formalization of knowledge of intelligent systems of the decision support accepted in view of the hydrometeorological information For an estimation of a degree of the validity of any fuzzy statement concerning an opportunity of influence of the dangerous phenomenon we shall enter representation of the validity of fuzzy statements Т which operates from set of considered fuzzy statements concerning existence of threat of dangerous phenomenon U to an interval [0,1], i.e. T: U → [0,1]. In this case value of the validity of the fuzzy statement concerning threat of dangerous phenomenon A ∈ U we shall designate as T(A). Then, for example, for statements A ~ 1 , A~ 2 , A~ 3 , A~ 4 , concerning threat mudflow avalanches it is possible to present the validity of these statements as follows: A ~ 1 - strong long-term rains cause a mudflow avalanche: T(A~ 1 ) = 0.6, A ~ 2 - the growing temperature of air at the big stocks of snow in mountains causes a mudflow avalanche: T(A ~ 2 ) = 0.7, A ~ 3 - strong rains and growing temperature of air at the big stocks of snow in mountains cause a mudflow avalanche: T(A ~ 3 ) = 0.8, A ~ 4 - a high level of water in mountains lakes, the strong rains, growing temperature of air at the big stocks of snow in mountains cause a mudflow avalanche: T(A ~ 4 ) = 0.9. At fuzzy modeling of statements concerning of threat of mudflow avalanches should be take into account not only an illegibility of a linguistic variable “intensity of mudflow avalanches”, but also other statements used in a submitted example: a high level of water in mountains lakes; the big stocks of snow; strong rains; growing temperature of air. It is necessary to set those value areas of variables, which influence on the process of mudflow avalanches formation. On the basis of the analysis of decisions trees, using fuzzy statements, rules of conclusions are developing for base of knowledge of intelligent systems of decision’s support with taking into account of the hydrometeorological information. The received conclusions will help to make the final decision concerning a choice of strategy of reaction to dangerous natural phenomena. Summary The knowledge used in intelligent systems of decision’s support according to the hydrometeorological information, can have subjective character. This knowledge also can be incomplete and uncertain by virtue of feature of the hydrometeorological information, and also uncertainty of estimations of hydrometeorological factors influence on economic objects functioning. Development of fuzzy models for systems of this class will allow avoiding some difficulties in creation a component of their knowledge bases. In particular, creation of the fuzzy models supporting decision-making process on a choice of strategy of reaction in conditions of the dangerous hydrometeorological phenomenon threat seems to be necessary. These decisions can be accepted concerning accommodation of economic objects and their protection, and also in designing objects, in agriculture, transport, in power industry etc. In this paper the block diagram of this process at a choice of the decision on protective actions at a regional level is presented. In the article some methodological aspects of construction of models with use of fuzzy sets and fuzzy logic by Lotfi Zadeh are considered. Tabl. 2. Membership functions of objects in the area subject to danger of mudflow avalanche’s influence Tab. 2. Funkcja przynależności dla obiektów w strefie wpływu niebezpiecznego zjawiska natury NN Objects of the territory subject to danger of mudflow avalanche’s influence Membership funсtion µ: Χ → [0,1] at the appropriate intensity of mudflow avalanches: Small Average Large Catastrophic 1 2 10 50 n x 1 0.1 x 2 0.2 x 10 0.1 x 50 0.1 x n 0.2 0.2 0.4 0.3 0.3 0.4 0.5 0.6 0.4 0.5 0.7 0.6 0.8 0.6 0.7 0.8 ELEKTRONIKA 11/<strong>2009</strong> 21
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