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In conditions of fast development of space modelling systems and extension of firmwares of creation both simple and complex forms of constructions, the necessity in more full use of possibilities, that was submitted by this units, was defined.

Nowadays with simulation of machine-building constructions and equipment for their manufacture the application of solid-state modelling dominates. Сreation of machine-building constructions requires application of methods of operation above an exterior form of a product, where the tools of surface modelling. However, the surface modelling can be used with designing standard constructions. For example, it can be used for designing equipment for processing on machine tools with CNC and mold-forms for manufacture of constructions with complex space forms.

Modern systems of space modelling, for example CATIA, ensure operation both solid-state and surface methods. The methods of solid-state modelling are effective with creation of constructions of the rather simple form. For creation of a detail they not always require presence of a base frame. The surface modelling is effective with creation of surfaces aerodynamic, ergonomic, design forms. It requires less memory size for storage of a model in comparison with solid-state modelling.

Modern systems of space modelling ensure operation with libraries and creation of constructive units of a various type of representation. Presence of parametrization tools limited resources for storage of a model, feature of the consequent stages of operation in conditions of through designing, the methods of transition between solid-state and surface representation require reviewing possibility of application of surface simulation alternatively to solid-state simulation.

The Institute of Engineering Cybernetics in this time carries out researches in learning of possibilities and advantages of methods for surface modelling, that can be used in creation of libraries of constructive elements for various classes of constructions.




This paper is considered Analysis of Complex Systems. Steps of analysis were determined. A system may be called large-scale or complex, if its dimension (order) is so high and its model is nonlinear and interconnected with uncertain information. An objectives and tasks of each step of analysis were determined from view point of principle of uncertainty. New architecture of task solving system is suggested as Integration of Expert System and the Decision Making Support System. Soft computing , introduced by Zadeh L. A. , gives us possibility of integration. An effect of synergism is provided by using of neural networks, fuzzy inference systems and nonlinear aggregation of criteria’s in multicriteria choice. The result of this research is the architecture of Soft Expert System. The architecture was explored in area of economic analysis.

Keywords: Soft computing, Expert System, Complex System, Multicriteria Choice


Analysis of complex technical or social-economic real-world systems has two features: first, we should analyze qualitative and quantitative information; second, data base is imprecise, uncertain and fuzzy (Klir G.J., 1985). There is difficulty in tool’s support of Analysis of Complex System from the view point of different types of data integration. A most modern server of data has not facilities for time series or graphic processing. Expert systems and statistic programs are based on different principles. Development and implementation of tools for analysis of system behavior requires deep Integration Expert system, Decision Making Support System and the processing of uncertain information. One objective of this paper is to develop architecture based on Soft Computing. We will call such intelligent system Soft Expert System. An area of economic analysis was an example of using the suggested architecture. The exploring of real expert conclusions gives us a possibility to determine features of Complex System Analysis. An expert analyzes a value and dynamic of characteristic variables, express general estimate of object, determines of forecast and recommendation to enterprise managing. A principle of uncertainty by Zadeh provides us sequence of analysis steps. According to this principle, a precision and a meaning conflicts from some moment of analysis. An architecture of the Soft Expert System was developed on the basis of this principle.

Key concepts of Soft Expert System

First, let’s describe the problem using formal methods. An expert answers to important question on each step of analysis. The questions determines functions of expert tools. The architecture of Complex System Analysis was determined as an architecture of systems task solving (Klir G.J., 1985).

Real world data, acceptable for expert, is crisp, precise and are presented time series Z(t). An expert made resume contains imprecise and fuzzy conclusions, forecasts, suggestions. An analysis of real-world expert conclusions shows that up to 80 % of conclusions are either qualitative estimates or characteristics of trends in the dynamics of economic data and only 20 % are recommendation for control of objects.

Step of fuzzification is function F



where Oi is a fuzzy term for i=1,...n. Number n is a number of quality grade (“excellent”, “good”, ...). Time series Z(T) is a variable Z, depending from time T. Estimating trends in data dynamics reduces to relating diagrams Oi(T) to the concepts of “growth”, “fall”, “stabilization”, “fluctuation”, and “chaos”, which are broader than the classical mathematical notions for measuring changes of monotone functions. The solving task of trends estimating is function:



where Trj is called a trend; O(T) is fuzzy time series.

Complex System has large dimension. Thus, integral estimate is important. The computing of integral estimate is calculation of function E:

In=E(Tr1, Tr2, ... Trn).


Function E may be determined by different methods. Let’s describe a task of forecasting with two view points. First, we study a task of forecasting. Second, we will forecast general system state represented of many time series. From first view point forecasting is the obtaining of value o(tn+1) from fuzzy time series O(T), trend of variable Tr(T), where n is a number of last point of time series O(T):



The general forecasting is the obtaining of integral estimate i(tn+1) using of the row of previous integral estimates I(T) and sets of trends {Trk(T)}, where k is a dimension of the object:

i(tn+1)=PP(I(T), Tr1, Tr2, ... Trn).


Summary of any expert resume is a recommendation of achievement of objective S. It is necessary to develop a plan using objective S, row of integral estimates I(T), trends {Tr(T)}, where T is a period of analysis:

{Tr(TT)}=Plan(S,I(T),Tr1, Tr2, ..., Trn).


Period TT is a current planning period through tn to tn+m, where m is a length of planning period. It is necessary to draw sets of lines for each variables to state S.


  1. Klir, G. J. (1985), Architecture of Systems Problem Solving. Plenum press. New York.

  2. Yarushkina N. G. (1997), “Soft hierarchy analyzing method for economic expert system.” In : Processing 7-th World Congress IFSA’97. Prague, Chech Republic, Vol. 3, pp. 532-534.

  3. Yarushkina N.G. (1996) “An Analysis of Economical Data Diagrams Based on Fuzzy Intervals an Expert System of Economical Analysis.” J. Pattern Recognition and Image Analysis, Vol. 6, No. 2, pp. 329-330.

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