Fuzzy Sets Theory and its Application to Structural Elements Analysis

abstrakt

angličtina

The fuzzy logic intervenes in many fields of human activities, and the possibilities of its application are observed to occur more and more frequently. The major success lies in the capability of the fuzzy logic to include the inaccuracy and of working, in a relatively simple manner, with significations of words of a natural language which belongs among the most important constituents of human life and which distinguishes us, among others, from animals. The vagueness of the semantics of a natural language is its typical characteristic feature which cannot be omitted in any case. Therefore the description in a natural language cannot be converted into mathematical formulae. To be able to apply the classical mathematics a simplified system description is necessary to be at the disposal on behalf of precise digits. When describing the complex systems, a simplified system description must be formulated, abstracting from all unimportant facts regarding the aim and purpose of the model. When formulating the mathematical model, a more general phenomenon can be met which can be named uncertainty. The uncertainty has two complementary components at least - vagueness and indefiniteness. The vagueness of mathematical modelling lies in the function of the object examined imitation by another object called the model. The uncertainties can be modelled, in a mathematical model, on behalf of the probability theory. The aim was always the application of the calculation models as precise as possible but, at the same time, as well as the endeavour to understand the uncertainties in input data. The effort to reach the greater and greater precision leads to disproportionate growth of definitions and extent of treatises on practically simple things, until the limit has been reached which, behind which the precision and relevance are practically mutually excluding characteristics. The limit precision is the capability of describing each phenomenon in reality. For simpler systems, precise and significant judgements on behaviour can be formulated better. A real contradiction is met with the solution of which does not exist. Due to this, the science comes into the situation where it is telling more and more about smaller and smaller reality segment. An example of fuzzy sets application in the analysis of a structural element in the designing process is demonstrated in the paper presented.

fuzzy sets, membership function, structures, load-carrying capacity

KALA, Z.

24. 7. 2004

Jyväskylä (Finland)

329

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