Decision making and programming / V.V. Kolbin ; translated from Russian by V.M. Donets.
The problem of selection of alternatives or the problem of decision making in the modern world has become the most important class of problems constantly faced by business people, researchers, doctors and engineers. The fields that are almost entirely focused on conflicts, where applied mathematics...
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| Language: | English Russian |
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World Scientific,
©2003.
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Table of Contents:
- Ch. 1. Social choice problems. 1.1. Individual preference aggregation. 1.2. Collective preference aggregation. 1.3. Manipulation. 1.4. Examples and algorithms for preference aggregation
- ch. 2. Vector optimization. 2.1. Definition of unimprovable points. 2.2. Optimization of the hierarchical sequence of quality criteria. 2.3. Tradeoffs. 2.4. The linear convolution of criteria in multicriteria optimization problems. 2.5. Solvability of the vector problem by the linear criteria convolution algorithm. 2.6. The logical criterion vector convolution in the Pareto set approximation problem. 2.7. Computational research on linear criteria convolution in multicriteria discrete programming
- ch. 3. Infinite-valued programming problems. 3.1. Basic notions and propositions. 3.2. Justification of numerical methods for solving infinite-valued programming problems. 3.3. Numerical methods of solution. 3.4. Separable infinite-valued programming problems
- ch. 4. Stochastic programming. 4.1. Stochastic programming models. 4.2. Stochastic programming methods. 4.3. Solution algorithms for stochastic programming problem. 4.4. Existence of a deterministic analog. 4.5. Results. 4.6. An example of applied problem
- ch. 5. Discrete programming. 5.1. A geometric interpretation of integer linear programming methods. 5.2. Equivalent forms and group-theoretic interpretation of discrete programming problems. 5.3. An algorithm for solving the integer linear programming problem. 5.4. The optimality condition and the search method for discrete optimization problems. 5.5. An algorithm for solving mixed integer linear programming problems. 5.6. Solving the large linear programming problem by the dynamic programming method.
- Ch. 6. Fundamentals of decision making. 6.1. Definition of the decision problem. 6.2. Basic notions of theory of choice. 6.3. Fundamentals of decision making
- ch. 7. Multicriterion optimization problems. 7.1. Multicriterion problems of selection. 7.2. Numerical representation of preference relations. 7.3. Preference representation on probability measures
- ch. 8 Decision making under incomplete information. 8.1. Decision making under incomplete information. 8.2. Decision making under multiple criteria. 8.3. The multilateral decision model
- ch. 9. Multicriterion elements of optimization theory. 9.1. Lexicographic optimization. 9.2. The factor analysis in organizational systems. 9.3. Stability of principles of optimality. 9.4. Game-theoretic decision models
- ch. 10. Decision models. 10.1. Conceptual setting. 10.2. Generalized mathematical programming as a decision model. 10.3. Binary relations in the space of binary relations
- ch. 11. Decision models under fuzzy information. 11.1. Extension of the ordering aspects of well-defined binary relations to the fuzzy case. 11.2. Ordering of binary relations, as based on the notions of approximation and regularization of principles of optimality. 11.3. General methodology for a priori investigation of generalized mathematical programming problems
- ch. 12. The applied mathematical model for conflict management. 12.1. Mathematical control models for tariff policy in the regional fuel and energy complex. 12.2. Computational experiment and appraisal of results.