Decision Making and Programming.
Title:
Decision Making and Programming.
Author:
Kolbin, V. V.
ISBN:
9789812775467
Personal Author:
Physical Description:
1 online resource (757 pages)
Contents:
CONTENTS -- INTRODUCTION -- Chapter 1 SOCIAL CHOICE PROBLEMS -- 1.1. INDIVIDUAL PREFERENCE AGGREGATION -- 1.1.1. Individual Preference Aggregation under Certainty -- 1.1.2. Individual Preference Aggregation under Uncertainty -- 1.1.3. Decision-making under Fuzzy Preference Relation on the Set of Alternatives -- 1.2. COLLECTIVE PREFERENCE AGGREGATION -- 1.2.1. The Procedures Using the Scale as the Auxiliary Collective Structure -- 1.2.2. The Procedures Taking into Account Individual Utility Alternatives -- 1.2.3. The Procedures with Exclusion of a Part of Alternatives -- 1.2.4. The Procedure with the Aggregating Rule Altered -- 1.2.5. Collective Preference Aggregation -- 1.3. MANIPULATION -- 1.3.1. Dictation policy -- 1.3.2. Methods of group manipulation -- 1.3.3. Manipulation theorems and proofs -- 1.4. EXAMPLES AND ALGORITHMS FOR PREFERENCE AGGREGATION -- 1.4.1. Examples and Algorithm for Preference Aggregation Subject to Criterion Convolution -- 1.4.2. Examples and Algorithm for Preference Aggregation in Terms of a Set of Attributes -- 1.4.3. The Examples Using the Aggregating Rules during Collective Decision Making (Voting Rules) -- Chapter 2 VECTOR OPTIMIZATION -- 2.1. DEFINITION OF UNIMPROVABLE POINTS -- 2.2. OPTIMIZATION OF THE HIERARCHICAL SEQUENCE OF QUALITY CRITERIA -- 2.3. TRADEOFFS -- I. Uniformity principles -- II. Fair concession principles -- III. Other optimality principles -- 2.4. THE LINEAR CONVOLUTION OF CRITERIA IN MULTICRITERIA OPTIMIZATION PROBLEMS -- 2.4.1. The linear convolution of criteria in multicriteria optimization problems -- 2.4.2. Properties of linear convolution -- 2.4.3. A geometric interpretation of linear convolution -- 2.4.4. Bicriterial problems -- 2.5. SOLVABILITY OF THE VECTOR PROBLEM BY THE LINEAR CRITERIA CONVOLUTION ALGORITHM -- 2.5.1. Test for solvability.
2.5.2. Solvability of trajectory problems -- 2.5.3. The reduction algorithm for the solvable problem -- 2.6. THE LOGICAL CRITERION VECTOR CONVOLUTION IN THE PARETO SET APPROXIMATION PROBLEM -- 2.6.1. The regular case -- 2.6.2. The convex case -- 2.6.3. The linear case -- 2.7. COMPUTATIONAL RESEARCH ON LINEAR CRITERIA CONVOLUTION IN MULTICRITERIA DISCRETE PROGRAMMING -- 2.7.1 Computational complexity of multicriteria discrete optimization problems -- 2.7.2. A computational experiment -- 2.7.3. A problem-solving algorithm -- 2.7.4. The results of computational experiment -- Chapter 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 -- 3.4.1. Existence conditions for solutions in separable infinite-valued problems -- 3.4.2. Some methods for solving separable infinite-dimensional problems -- Chapter 4 STOCHASTIC PROGRAMMING -- 4.1. STOCHASTIC PROGRAMMING MODELS -- 4.2. STOCHASTIC PROGRAMMING METHODS -- 4.3. SOLUTION ALGORITHMS FOR STOCHASTIC PROGRAMMING PROBLEMS -- 4.3.1. Solution of a two-stage linear stochastic programming problem -- 4.3.2. Solution of a stochastic programming problem by the stochastic quasigradient method with adaptive step regulation -- 4.4. EXISTENCE OF A DETERMINISTIC ANALOG -- 4.4.1. Common chance constraints -- 4.4.2. Uniqueness of a Deterministic Analog -- 4.4.3. Solution Stability -- 4.4.4. The Approximation Method and Its Convergence -- 4.5. RESULTS -- 4.5.1. Preliminary Results -- 4.5.2. Existence of a Semiinfinite Analog for the MSP - M Model -- 4.5.3. Existence of a Semiinfinite Analog for Model MSP - P -- 4.5.4. Uniqueness of a Semiinfinitie Analog to Model MSP - M.
4.5.5. The Approximation Scheme for Model MSP - M. Convergence Theorems -- 4.6. AN EXAMPLE OF APPLIED PROBLEM -- 4.6.1. Natural Dynamics in Forest Stand Areas -- 4.6.2. Stock Dynamics -- 4.6.3. Area Dynamics under Forest Management -- 4.6.4. Problem Constraints -- Chapter 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 -- 5.2.1. -- 5.2.2. A group interpretation of the integer linear programming problem -- 5.2.3. The equivalent forms and the group structure of the mixed integer programming problem -- 5.3. AN ALGORITHM FOR SOLVING THE INTEGER LINEAR PROGRAMMING PROBLEM -- 5.3.1. Statement of the problem in terms of existing algorithms -- 5.3.3. Elements of algorithm -- 5.3.4. Block diagram of algorithm -- 5.3.5. The case of dual degeneracy -- 5.4. THE OPTIMALITY CONDITION AND THE SEARCH METHOD FOR DISCRETE OPTIMIZATION PROBLEMS -- 5.4.1. The basic theorem and corollaries -- 5.4.2. The search method for an optimal solution to large-dimension discrete problems -- 5.4.3. The proof of convergence for the search method -- 5.4.4. A direct application of the search method to discrete programming problems -- 5.5. AN ALGORITHM FOR SOLVING MIXED INTEGER LINEAR PROGRAMMING PROBLEMS -- 5.5.1. m-problem and algorithm for its solution -- 5.5.2. Methods for solving M-problem -- 5.5.3. An algorithm for solving a special class of problems -- 5.5.4. A general algorithm -- 5.6. SOLVING THE LARGE LINEAR PROGRAMMING PROBLEM BY THE DYNAMIC PROGRAMMING METHOD -- 5.6.1. -- 5.6.3. A dynamic programming algorithm -- Chapter 6 FUNDAMENTALS OF DECISION MAKING -- 6.1. DEFINITION OF THE DECISION PROBLEM -- 6.1.1. Definition of the Problem -- 6.1.2. Generation of Alternative Decisions -- 6.1.3. Selection of an Optimal Decision.
6.2. BASIC NOTIONS OF THEORY OF CHOICE -- 6.2.1. Binary Preference Relations. Methods of Specification -- 6.2.2. Basic Concepts of Choice Functions -- 6.2.3. General Properties of Binary relations on Em -- 6.2.4. General Properties of the Class of Coordinate Relations -- 6.2.5. Decomposition and Composition of Choice Functions -- 6.3. FUNDAMENTALS OF DECISION MAKING -- 6.3.1. Methods of Expert Evaluation and Data Processing -- 6.3.2. Algoritms for Solving the Problem of Selection -- 6.3.3. Optimization of the Utility Function in the Problems of Selection -- Chapter 7 MULTICRITERION OPTIMIZATION PROBLEMS -- 7.1. MULTICRITERION PROBLEMS OF SELECTION -- 7.1.1. Multicriterion Control Problems -- 7.2. NUMERICAL REPRESENTATION OF PREFERENCE RELATIONS -- 7.2.1. Utility Functions -- 7.2.2. Preference Intensity -- 7.2.3. Comparative Utility -- 7.3. PREFERENCE REPRESENTATION ON PROBABILITY MEASURES -- 7.3.1. Theory of Expected Utility -- 7.3.2. Expected Comparative Utility -- Chapter 8 DECISION MAKING UNDER INCOMPLETE INFORMATION -- 8.1. DECISION MAKING UNDER INCOMPLETE INFORMATION -- 8.1.1. Statistical Decision Models -- 8.1.2. Dynamic Models for Decision Processes -- 8.1.3. The Markovian Models for Decision Processes -- 8.2. DECISION MAKING UNDER MULTIPLE CRITERIA -- 8.2.1. Pareto Optimality -- 8.2.2. Comparability and Aggregation of Criteria -- 8.3. THE MULTILATERAL DECISION MODEL -- 8.3.1.1. Definition of the Game -- 8.3.2. Optimal Outcomes in the Game -- 8.3.3. Solution of the game -- Chapter 9 MULTICRITERION ELEMENTS OF OPTIMIZATION THEORY -- 9.1. LEXICOGRAPHIC OPTIMIZATION -- 9.1.1. Lexicographic Orders -- 9.1.2. Axioms of Lexicographic Preferences -- 9.1.3. Lexicographic Utility -- 9.1.4. Lexicographic Ordering of Stochastic Models -- 9.2. THE FACTOR ANALYSIS IN ORGANIZATIONAL SYSTEMS.
9.2.1. Factor Analysis and Decision Making in Organizational Systems -- 9.2.2. Methods of Deterministic Factor Analysis -- 9.2.3. Methods of statistical factor analysis -- 9.3. STABILITY OF PRINCIPLES OF OPTIMALITY -- 9.3.1. Problem Definition -- 9.3.2. Definitions of Stability of Principles of Optimality -- 9.3.3. Comparison of Principles of Optimality -- 9.4. GAME-THEORETIC DECISION MODELS -- 9.4.1. Basic Notions of Game Theory -- 9.4.2. Rational Methods of Choosing Strategies. The Generalized Principle of Guaranteed Result -- 9.4.3. Games With a Hierarchical Structure -- 9.4.4. Statistical Models of Hierarchical Systems -- 9.4.5. Dynamic Models of Hierarchical Systems -- Chapter 10 DECISION MODELS -- 10.1. CONCEPTUAL SETTING -- 10.1.1. The Essence of Decision Models -- 10.1.2. Versions of Multistage Decision Making -- 10.2. GENERALIZED MATHEMATICAL PROGRAMMING AS A DECISION MODEL -- 10.2.1. The Simplest Structure in the Space of Binary Relations -- 10.2.2. Maximal and Largest Elements with Respect to Binary Relations. The Optimal Choice Problem -- 10.2.3. Statement of the Generalized Mathematical Programming Problem -- 10.2.4. Multistage GMP Problem. Information Structure -- 10.2.5. Sufficient Conditions for Existence of Optimal Decisions in the Generalized Mathematical Programming Problem -- 10.2.6. Modeling of GMP Problems. The Notion of A Priori Investigation of GMP Problems -- 10.3. BINARY RELATIONS IN THE SPACE OF BINARY RELATIONS -- 10.3.1. Extension of Binary Relations from the Set of Feasible Alternatives to the Set of Pairs of Admissible alternatives -- 10.3.2. Principles of Ordering Binary Relations and Their Axiomatic Specification -- 10.3.3. The Notion of the Implementation Method for the Principle of Ordering Binary Relations -- 10.3.4. The Matching Principle (C). Implementation Methods and Their Hierarchical Structure.
10.3.5. The Extension Principle (P). Implementation Methods and Their Hierarchical Structure.
Abstract:
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 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: Social Choice Problems; Vector Optimization; Infinite-Valued Programming Problems; Stochastic Programming; Discrete Programming; Fundamentals of Decision Making; Multicriterion Optimization Problems; Decision Making Under Incomplete Information; Multicriterion Elements of Optimization Theory;
Decision Models; Decision Models Under Fuzzy Information; The Applied Mathematical Model for Conflict Management. Readership: Undergraduates, graduate students, professionals and researchers in applied mathematics.
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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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