《决策和优化》由会员分享，可在线阅读，更多相关《决策和优化（225页珍藏版）》请在金锄头文库上搜索。
1、Decision Making and OptimizationSpecial Matrices and Their Applications in Economics and ManagementContentsPart ISpecial Matrices in Decision Making1Preliminaries .3 1.1Triangular Norms and Conorms .3 1.2Properties of Triangular Norms and Triangular Conorms .6 1.3Representations of Triangular Norms
2、and Triangular Conorms.8 1.4Negations and De Morgan Triples .12 1.5Fuzzy Sets.13 1.6Operations with Fuzzy Sets .16 1.7Extension Principle .17 1.8Binary and Valued Relations .18 1.9Fuzzy Relations.20 1.10Fuzzy Quantities and Fuzzy Numbers.21 1.11Matrices with Fuzzy Elements .23 1.12Abelian Linearly O
3、rdered Groups .24 References .282Pairwise Comparison Matrices in Decision Making .29 2.1Introduction .29 2.2Problem Definition .31 2.3Multiplicative Pairwise Comparison Matrices .32 2.4Methods for Deriving Priorities from Multiplicative Pairwise Comparison Matrices.36 2.4.1Eigenvector Method (EVM).3
4、8 2.4.2Additive Normalization Method (ANM) .39 2.4.3Least Squares Method (LSM) .40 2.4.4Logarithmic Least Squares Method (LLSM)/Geometric Mean Method (GMM).42 2.4.5Fuzzy Programming Method (FPM) and Other Methods for Deriving Priorities .46ixxContents2.5Additive Pairwise Comparison Matrices .47 2.6M
5、ethods for Deriving Priorities from Additive Pairwise Comparison Matrices.49 2.7Fuzzy Pairwise Comparison Matrices .53 2.8Methods for Deriving Priorities from Fuzzy Pairwise Comparison Matrices.57 2.9Fuzzy Pairwise Comparison Matrices with Missing Elements .61 2.9.1Problem of Missing Elements in FPC
6、 Matrices Based on Optimization.63 2.9.2Particular Cases of FPC Matrices with Missing Elements Based on Optimization.64 2.9.3Case L D f.1;2/;.2;3/;:;.n ? 1;n/g .65 2.9.4Case L D f.1;2/;.1;3/;:;.1;n/g .68 2.9.5Problem of Missing Elements in FPC Matrices: Other Methods .71 2.10Unified Framework for Pa
7、irwise Comparison Matrices over ALO Groups.74 2.10.1Unified Framework .74 2.10.2Continuous Alo-Groups over a Real Interval .74 2.10.3Pairwise Comparison Matrices over a Divisible Alo-Group .79 2.10.4Consistency Index in Alo-Groups.81 2.11Conclusions .86 References .863Preference Matrices with Fuzzy
8、Elements in Decision Making.91 3.1Introduction .91 3.2PC Matrices with Elements Being Fuzzy Sets of Alo-Group over a Real Interval .93 3.3Methods for Deriving Priorities from PCFN Matrices.99 3.3.1PCFN Matrix on Additive Alo-Group . 102 3.3.2PCFN Matrix on Multiplicative Alo-Group . 104 3.3.3PCFN Ma
9、trix on Fuzzy Additive Alo-Group. 106 3.3.4PCFN Matrix on Fuzzy Multiplicative Alo-Group. 108 3.4Illustrative Numerical Examples. 112 3.5Conclusion . 114 References . 114Part IISpecial Matrices in Max-Min Algebra4Optimization Problems Under Max-Min Separable Equation and Inequality Constraints. 119 4.1Introduction . 119 4.2Systems of One-Sided Max-Separable Equationsand Inequalities: Unified Approach. 123Contentsxi4.3Optimization Problems with Feasible Set M.b/ . 125 4.4Duality Theory. 127 4.5Optimization Problems on Attainable
