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In this paper we report on the development of analytic methods which enable us to model and analyze physical systems by utilizing qualitative and quantitative fuzzy techniques. The main body of our research contains the development of a model for fuzzy statistics and its possible applications to evaluation of knowledge-base systems, modeling of social-economic systems, and the analysis of the policy decision.

The main thrust of this paper is to examine solutions to differential equations with fuzzy coefficients. Almost all problems in physics, engineering, biology, economics and other sciences to which mathematical methods are applicable are basically nondeterministic rather than deterministic. From the standpoint of applications, the modelling of such nondeterministic systems has been implemented via stochastic structures rather than fuzzy. It is thus the objective of this paper to give a careful presentation of the fuzzy approach to the solution of imprecise differential equations, by using the theory of fuzzy statistics, and to explore its applications to problems in science and engineering.

In this paper is shown that the probability-statistic methods application, especially at the early stage of the aviation gas turbine engine (GTE) technical condition diagnosing, when the flight information has property of the fuzzy, limitation and uncertainty is unfounded. Hence is considered the efficiency of application of new technology Soft Computing at these diagnosing stages with the using of the Fuzzy Logic and Neural Networks methods. Training with high accuracy of fuzzy multiple linear and non-linear models (fuzzy regression equations) which received on the statistical fuzzy data basis is made. Thus for GTE technical condition more adequate model making are analysed dynamics of skewness and kurtosis coefficients' changes. Researches of skewness and kurtosis coefficients values- changes show that, distributions of GTE work parameters have fuzzy character. Hence consideration of fuzzy skewness and kurtosis coefficients is expedient. Investigation of the basic characteristics changes- dynamics of GTE work parameters allows to draw conclusion on necessity of the Fuzzy Statistical Analysis at preliminary identification of the engines' technical condition. Researches of correlation coefficients values- changes shows also on their fuzzy character. Therefore for models choice the application of the Fuzzy Correlation Analysis results is offered. For checking of models adequacy is considered the Fuzzy Multiple Correlation Coefficient of Fuzzy Multiple Regression. At the information sufficiency is offered to use recurrent algorithm of aviation GTE technical condition identification (Hard Computing technology is used) on measurements of input and output parameters of the multiple linear and non-linear generalised models at presence of noise measured (the new recursive Least Squares Method (LSM)). The developed GTE condition monitoring system provides stage-bystage estimation of engine technical conditions. As application of the given technique the estimation of the new operating aviation engine temperature condition was made., {"references":["Pashayev A.M., Askerov D.D., Sadiqov R.A., Abdullayev\nP.S. \"Fuzzy-Neural Approach for Aircraft Gas Turbine Engines\nDiagnosing\", AIAA 1st Intelligent Systems Technical Conference\n(Chicago, Illinois, Sep. 20-22, 2004), AIAA-2004-6222, 2004.","Pashayev A.M., Sadiqov R.A., Abdullayev P.S., \"Complex\nidentification technique of aircraft gas turbine engine's health\", ASME\nTURBO EXPO 2003: Power for Land, Sea and Air Conference, June\n16-19, 2003, Atlanta, Georgia, USA, Paper GT2003-38704, 2003.","Abdullayev P.S., Pashayev A.M., Askerov D.D., Sadiqov R.A. \"Aicraft\nGas Turbine Engines- Technical Condition Identification system\",\nASME TURBO EXPO 2005: Power for Land, Sea and Air Conference,\nJune 6-9, 2005, Reno-Tahoe, Nevada, USA, Paper GT2005-69072, 2005","Ivanov L.A. and etc., \"The technique of civil aircraft GTE technical\ncondition diagnosing and forecasting on registered rotor vibrations\nparameters changes in service\", GosNII GA, Moscow, 1984, 88p.","Doroshko S.M., \"The control and diagnosing of GTE technical condition\non vibration parameters\", Transport, Moscow, 1984, 128 p.","Abasov M.T., Sadiqov A.H., Aliyarov R.Y., \"Fuzzy neural networks in\nthe system of oil and gas geology and geophysics\", Third International\nConference on Application of Fuzzy Systems and Soft Computing,\nWiesbaden, Germany, 1998, pp.108-117.","Yager R.R., Zadeh L.A. (Eds)., \"Fuzzy sets, neural networks and soft\ncomputing\", VAN Nostrand Reinhold, N.-Y. - Ôäû 4,1994.","Mohamad H. Hassoun., \"Fundamentals of artificial neutral networks\", A\nBradford Book, The MIT press Cambridge, Massachusetts, London,\nEngland, 1995","Pashayev A.M., Askerov D.D., Sadiqov R.A., Abdullayev P.S.,\n\"Aviation gas turbine engines technical condition diagnosing system\",\nAbstracts of XII All-Russian interinstitute science-technical conference\n\"Gaz turbine and combined installations and engines\" dedicated to 175-\nyear MSTU nam. N.E.BAUMAN and 55-year department E-3,\nN.E.BAUMAN MSTU, 24-26 november, Moscow, Russia, 2004,pp.209-\n210."]}