Leontief Model Analysis with Fuzzy Parameters by Basic Matrixes Method

The basic matrixes method is suggested for the Leontief model analysis (LM) with some of its components indistinctly given. LM can be construed as a forecast task of product’s expenses-output on the basis of the known statistic information at indistinctly given several elements’ meanings of technological matrix, restriction vector and variables’ limits. Elements of technological matrix, right parts of restriction vector LM can occur as functions of some arguments. In this case the task’s dynamic analog occurs. LM essential complication lies in inclusion of variables restriction and criterion function in it.

An Interactive Method of Linear Mixed Integer Multicriteria Optimization

The paper describes a learning-oriented interactive method for solving linear mixed integer problems of multicriteria optimization. The method increases the possibilities of the decision maker (DM) to describe his/her local preferences and at the same time it overcomes some computational difficulties, especially in problems of large dimension. The method is realized in an experimental decision support system for finding the solution of linear mixed integer multicriteria optimization problems.

Uncertainty and Fuzzy Sets: Classifying the Situation

The so called “Plural Uncertainty Model” is considered, in which statistical, maxmin, interval and Fuzzy model of uncertainty are embedded. For the last case external and internal contradictions of the theory are investigated and the modified definition of the Fuzzy Sets is proposed to overcome the troubles of the classical variant of Fuzzy Subsets by L. Zadeh. The general variants of logit- and probit- regression are the model of the modified Fuzzy Sets. It is possible to say about observations within the modification of the theory. The conception of the “situation” is proposed within modified Fuzzy Theory and the classifying problem is considered. The algorithm of the classification for the situation is proposed being the analogue of the statistical MLM(maximum likelihood method). The example related possible observing the distribution from the collection of distribution is considered.

The System of Quality Prediction on the Basis of a Fuzzy Data and Psychography of the Experts

The system of development unstable processes prediction is given. It is based on a decision-tree method. The processing technique of the expert information is offered. It is indispensable for constructing and processing by a decision-tree method. In particular data is set in the fuzzy form. The original search algorithms of optimal paths of development of the forecast process are described. This one is oriented to processing of trees of large dimension with vector estimations of arcs.

Classification-Based Method of Linear Multicriteria Optimization

The paper describes a classification-based learning-oriented interactive method for solving linear multicriteria optimization problems. The method allows the decision makers describe their preferences with greater flexibility, accuracy and reliability. The method is realized in an experimental software system supporting the solution of multicriteria optimization problems.

About the Multi Criteria Ranging Problem in the Fuzzy Environment

Decision making and technical decision analysis demand computer-aided techniques and therefore more and more support by formal techniques. In recent years fuzzy decision analysis and related techniques gained importance as an efficient method for planning and optimization applications in fields like production planning, financial and economical modeling and forecasting or classification. It is also known, that the hierarchical modeling of the situation is one of the most popular modeling method. It is shown, how to use the fuzzy hierarchical model in complex with other methods of Multiple Criteria Decision Making. We propose a novel approach to overcome the inherent limitations of Hierarchical Methods by exploiting multiple criteria decision making.

Reduction Measurements for Calculation in Fuzzy Experiment Scheme

The papers is dedicated to the questions of modeling and basing super-resolution measuring- calculating systems in the context of the conception “device + PC = new possibilities”. By the authors of the article the new mathematical method of solution of the multi-criteria optimization problems was developed. The method is based on physic-mathematical formalism of reduction of fuzzy disfigured measurements. It is shown, that determinative part is played by mathematical properties of physical models of the object, which is measured, surroundings, measuring components of measuring-calculating systems and theirs cooperation as well as the developed mathematical method of processing and interpretation of measurements problem solution.

Application of Fuzzy Logic on Image Edge Detection

In this paper a novel method for an application of digital image processing, Edge Detection is developed. The contemporary Fuzzy logic, a key concept of artificial intelligence helps to implement the fuzzy relative pixel value algorithms and helps to find and highlight all the edges associated with an image by checking the relative pixel values and thus provides an algorithm to abridge the concepts of digital image processing and artificial intelligence. Exhaustive scanning of an image using the windowing technique takes place which is subjected to a set of fuzzy conditions for the comparison of pixel values with adjacent pixels to check the pixel magnitude gradient in the window. After the testing of fuzzy conditions the appropriate values are allocated to the pixels in the window under testing to provide an image highlighted with all the associated edges.

Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

2000 Mathematics Subject Classification: 47H04, 65K10.

A Method for Solving a Class of Multiple-Criteria Analysis Problems

AMS subject classification: 90C29.