Decision Making and ProgrammingThe 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 is successfully used, are law, military science, many branches of economics, sociology, political science, and psychology. There are good grounds to believe that medicine and some branches of biology and ethics can also be included in this list. Modern applied mathematics can produce solutions to many tens of classes of conflicts differing by the composition and structure of the participants, specific features of the set of their objectives or interests, and various characteristics of the set of their actions, strategies, behaviors, controls, and decisions as applied to various principles of selection or notions of decision optimization.The current issues of social and economic systems involve the necessity to coordinate and jointly optimize various lines of development and activities of modern society. For this reason, the decision problems arising in investigation of such systems are versatile, which shows up not only in the multiplicity of participants, their interests and complexity of reciprocal effects, but also in the laborious development of social utility criteria for a variety of indices and versatile objectives. The efficient decision methods for such complex systems can be developed only the basis of specially developed mathematical tools. |
Contents
INTRODUCTION | 1 |
Chapter 1 SOCIAL CHOICE PROBLEMS | 11 |
Chapter 2 VECTOR OPTIMIZATION | 85 |
Chapter 3 INFINITEVALUED PROGRAMMING PROBLEMS | 169 |
Chapter 4 STOCHASTIC PROGRAMMING | 211 |
Chapter 5 DISCRETE PROGRAMMING | 299 |
Chapter 6 FUNDAMENTALS OF DECISION MAKING | 345 |
Chapter 7 MULTICRITERION OPTIMIZATION PROBLEMS | 427 |
Chapter 10 DECISION MODELS | 583 |
Chapter 11 DECISION MODELS UNDER FUZZY INFORMATION | 651 |
Chapter 12 THE APPLIED MATHEMATICAL MODEL FOR CONFLICT MANAGEMENT | 691 |
APPENDIX 1 | 720 |
APPENDIX 2 | 724 |
APPENDIX 3 | 725 |
CONCLUSION | 729 |
733 | |
Chapter 8 DECISION MAKING UNDER INCOMPLETE INFORMATION | 469 |
Chapter 9 MULTICRITERION ELEMENTS OF OPTIMIZATION THEORY | 529 |
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Common terms and phrases
admissible alternatives affine function aggregating rule algorithm axioms Bayesian binary relations called candidate choice function coalition components consider constraints construct convex convex set criteria criterion decision problems defined Definition denote elements equivalent factors feasible solution finite fuzzy set given go to Step heat energy hence implementation integer integer linear programming Lemma lexicographic lexicographic ordering mathematical matrix maximal method multicriterion nondominated notion objective function optimal solution optimization problems ordering binary relations outcomes pairs parameters Pareto optimal players preference relation principle of optimality procedure proof properties relationship Saint-Petersburg satisfied sequence set of admissible set of alternatives set Q situation solution of problem solve space specified stochastic programming strategy subset sup v(z Suppose Theorem transitive utility function values variables vector voters voting