Currently the methods of Soft Computing are successfully used for risk analysis in: budgeting, e-commerce development, portfolio selection, Black-Scholes option pricing models, corporate acquisition systems, evaluating investments in advanced manufacturing technology, interactive fuzzy interval reasoning for smart web shopping, fuzzy scheduling and logistic.
An essential feature of economic and financial problems it that there are always at least two criteria to be taken into account: profit maximization and risk minimization. Therefore, the economic and financial problems are multiple criteria ones. In this book, a new systematization of the problems of multiple criteria decision making is proposed which allows the author to reveal unsolved problems. The solutions of them are presented as well and implemented to deal with some important real-world problems such as investment project's evaluation, tool steel material selection problem, stock screening and fuzzy logistic.
It is well known that the best results in real -world applications can be obtained using the synthesis of modern methods of soft computing. Therefore, the developed by the author new approach to building effective stock trading systems, based on the synthesis of fuzzy logic and the Dempster-Shafer theory, seems to be a considerable contribution to the application of soft computing method in economics and finance.
An important problem of capital budgeting is the fuzzy evaluation of the Internal Rate of Return. In this book, this problem is solved using a new method which makes it possible to solve linear and nonlinear interval and fuzzy equations and systems of them. The developed new method allows the author to obtain an effective solution of the Leontjev's input-output problem in the interval setting.

Inhalt

Introduction.- Convex Probabilistic Wavelet like Approximation.- Bidimensional Constrained Wavelet like Approximation.- Multidimensional Probabilistic Scale Approximation.- Multidimensional probabilistic approximation in wavelet like structure.- About L-Positive Approximations: About Shape Preserving Weighted Uniform Approximation.- Jackson-Type Nonpositive Approximations for Definite Integrals.- Discrete Best L1 Approximation using the Gauges Way.- Quantitative Uniform Convergence of Smooth Picard Singular Integral Operators.- Global Smoothness and Simultaneous Approximation by Smooth Picard Singular Operators.- Convergence Results.- Approximation with Rates by Fractional Smooth Picard.- Singular Operators.- Multivariate Generalized Picard Singular Integral Operators.- Approximation by q-Gauss-Weierstrass Singular Integral Operators.- Quantitative Approximation by Univariate Shift-Invariant.- Integral Operators.