1. Introduction.- 1.1 Decision Making in Hierarchy Systems: Multi-ploy versus Interactive Decisions.- 1.2 Bi-Level and Multi-level Programming.- 1.3 Characteristics of Duo-ploy Systems.- 1.4 Characteristics of Duo-ploy Systems with Multi-followers.- 1.5 Fuzzy Interactive Decision Making.- 2. Linear Bi-level Programming.- 2.1 Linear Bi-level Programming.- 2.2 Extreme-point Search.- 2.2.1 kth-best Algorithm.- 2.2.2 Grid-search Algorithm.- 2.3 Transformation Approach.- 2.3.1 Mixed-integer Approach.- 2.3.2 Complementary-pivot algorithm.- 18.104.22.168 Parametric Complementary-pivot Algorithm.- 22.214.171.124 Sequential Linear Complementary Algorithm with Branch-and-bound.- 2.3.3 Branch-and-bound Algorithm.- 126.96.36.199 Algorithm of Bard and Moore.- 188.8.131.52 Algorithm of Hansen et al.- 2.3.4 Penalty-function Approach.- 2.4 Discussions.- 3. Other Multi-level Programming Algorithms.- 3.1 Linear Bi-level Distributed Programming.- 3.1.1 Mixed-integer Problem with Complementary Slackness.- 3.1.2 Penalty-function Approach.- 3.2 Linear Three-level Programming Problem.- 3.2.1 Hybrid Extreme-point Search Algorithm.- 3.2.2 Mixed-integer Problem with Complementary Slackness.- 3.2.3 Simplex-cutting-plane Algorithm.- 3.2.4 Penalty-function Approach.- 3.3 Non-linear Multi-level Programming.- 3.3.1 Sequential Linear-quadratic Complementary Algorithm with Branch-and-bound.- 3.3.2 Steepest-descent Approach.- 3.3.3 Evolutionary Approach: Genetic Algorithms.- 3.4 Discrete Bi-level Programming.- 3.5 Discussions.- 4. Possibility Theory and Knowledge Representation.- 4.1 Possibility Theory.- 4.1.1 Possibility Distribution.- 4.1.2 Possibility Measure.- 4.1.3 Possibility Measure Based on Fuzzy Set with Fuzzy Subset.- 4.1.4 Possibility versus Probability.- 4.2 Knowledge Representation.- 4.2.1 Linguistic Variable.- 4.2.2 The Syntactic Rule.- 4.2.3 The Semantic Rule.- 4.2.4 Test-score Semantics.- 5. Fuzzy Decision Making.- 5.1 Fuzzy Linear Programming.- 5.2 Multiple-objective Programming.- 5.2.1 Compromise Programming.- 5.2.2 Goal Programming.- 5.3 Fuzzy Approach to Multiple-objective Programming.- 5.4 Fuzzy Multiple-objective Programming with Fuzzy Parameters.- 5.5 Possibility Programming.- 5.5.1 Possibility Linear Programming.- 5.5.2 Multiple-objective Possibility Programming.- 6. Fuzzy Interactive Multi-level Decision Making.- 6.1 Fuzzy Bi-level Interactive Decision Making.- 6.2 Fuzzy Bi-level Interactive Decision Making with Multi-followers.- 6.3 Fuzzy Multi-level Interactive Decision Making.- 6.4 Fuzzy Multi-level Interactive Decision Making with Multi-followers.- 6.5 Discussions.- 7. Aggregation of Fuzzy Systems in Multi-level Decisions.- 7.1 Compensation in Bi-level Decisions.- 7.2Compensation in Multiple-level Problems.- 7.3 Bi-level Decentralized Problem with Equally Important Objectives.- 7.4 Bi-level Decentralized Problem with Unequally Important Objectives.- 7.5 Multiple-level Decentralized Problem.- 7.6 Fuzzy Multi-level Problem.- 7.7 Discussions.- 8. Possibilistic Minimum-cost Flow Problem.- 8.1 Minimum-cost Flow Problem.- 8.2 Possibility Approach to Minimum-cost Flow Problem.- 8.2.1 Capacity Constraint Modification.- 8.2.2 Possibility Programming.- 8.3 Possibility Approach to Multi-objective Minimum-cost Flow Problem.- 8.4 Possibility Approach to Multi-level Minimum-cost Flow Problem.- 8.5 Discussions.- References.
Managerial Decisions in hierarchy organizations, such as the various manufacturing and service companies, are difficult to formalize and even more difficult to optimize. By exploring the typical fuzziness, vagueness, or the "not-well-defined" nature of such organizations, this book presents the first comprehensive treatment of this difficult and practically important problem. The advantages of the proposed fuzzy interactive approach are that it significantly reduces computational requirements. Equally, the representation of the system is made more realistic through the recognition of the inherent fuzziness of such large organizations. Both the multi-ploy and the game-like decision making processes, also known as multi-level programming and the fuzzy interactive approach, are discussed in detail. The emphasis is on numerical algorithms and numerous examples are solved and compared. The concepts of fuzzy set and fuzzy linguistic representation, which form an integral part of any managerial decision, are also discussed.