Ebook: Stochastic Versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty

Operations Research is a field whose major contribution has been to propose a rigorous fonnulation of often ill-defmed problems pertaining to the organization or the design of large scale systems, such as resource allocation problems, scheduling and the like. While this effort did help a lot in understanding the nature of these problems, the mathematical models have proved only partially satisfactory due to the difficulty in gathering precise data, and in formulating objective functions that reflect the multi-faceted notion of optimal solution according to human experts. In this respect linear programming is a typical example of impressive achievement of Operations Research, that in its detenninistic fonn is not always adapted to real world decision-making : everything must be expressed in tenns of linear constraints ; yet the coefficients that appear in these constraints may not be so well-defined, either because their value depends upon other parameters (not accounted for in the model) or because they cannot be precisely assessed, and only qualitative estimates of these coefficients are available. Similarly the best solution to a linear programming problem may be more a matter of compromise between various criteria rather than just minimizing or maximizing a linear objective function. Lastly the constraints, expressed by equalities or inequalities between linear expressions, are often softer in reality that what their mathematical expression might let us believe, and infeasibility as detected by the linear programming techniques can often been coped with by making trade-offs with the real world.

---

---

Content:
Front Matter....Pages i-viii
Front Matter....Pages 1-1
Multiobjective Programming under Uncertainty : Scope and Goals of the Book....Pages 3-6
Multiobjective Programming: Basic Concepts and Approaches....Pages 7-22
Stochastic Programming: Numerical Solution Techniques by Semi-Stochastic Approximation Methods....Pages 23-43
Fuzzy Programming: A Survey of Recent Developments....Pages 45-68
Front Matter....Pages 69-69
Overview of Different Approaches for Solving Stochastic Programming Problems with Multiple Objective Functions....Pages 71-101
“Strange” : An Interactive Method for Multiobjective Stochastic Linear Programming, and “Strange-Momix” Its Extension to Integer Variables....Pages 103-115
Application of “Strange” to Energy Studies....Pages 117-130
Multiobjective Stochastic Linear Programming with Incomplete Information: A General Methodology....Pages 131-161
Computation of Efficient Solutions of Stochastic Optimization Problems with Applications to Regression and Scenario Analysis....Pages 163-188
Front Matter....Pages 189-189
Interactive Decision Making for Multiobjective Programming Problems with Fuzzy Parameters....Pages 191-228
A Possibilistic Approach for Multiobjective Programming Problems. Efficiency of Solutions....Pages 229-248
’FLIP’: An Interactive Method for Multiobjective Linear Programming with Fuzzy Coefficients....Pages 249-262
Application of the ’FLIP’ Method to Farm Structure Optimization under Uncertainty....Pages 263-278
Fulpal — An Interactive Method for Solving (Multiobjective) Fuzzy Linear Programming Problems....Pages 279-299
Multiple Objective Linear Programming Problems in the Presence of Fuzzy Coefficients....Pages 301-320
Inequality Constraints between Fuzzy Numbers and Their Use in Mathematical Programming....Pages 321-330
Using Fuzzy Logic with Linguistic Quantifiers in Multiobjective Decision Making and Optimization: A Step Towards More Human-Consistent Models....Pages 331-350
Front Matter....Pages 351-351
Stochastic Versus Possibilistic Multiobjective Programming....Pages 353-364
A Comparison Study of “Strange” and “Flip”....Pages 365-393
Multiobjective Mathematical Programming with Inexact Data....Pages 395-418
Back Matter....Pages 419-426

---

Content:
Front Matter....Pages i-viii
Front Matter....Pages 1-1
Multiobjective Programming under Uncertainty : Scope and Goals of the Book....Pages 3-6
Multiobjective Programming: Basic Concepts and Approaches....Pages 7-22
Stochastic Programming: Numerical Solution Techniques by Semi-Stochastic Approximation Methods....Pages 23-43
Fuzzy Programming: A Survey of Recent Developments....Pages 45-68
Front Matter....Pages 69-69
Overview of Different Approaches for Solving Stochastic Programming Problems with Multiple Objective Functions....Pages 71-101
“Strange” : An Interactive Method for Multiobjective Stochastic Linear Programming, and “Strange-Momix” Its Extension to Integer Variables....Pages 103-115
Application of “Strange” to Energy Studies....Pages 117-130
Multiobjective Stochastic Linear Programming with Incomplete Information: A General Methodology....Pages 131-161
Computation of Efficient Solutions of Stochastic Optimization Problems with Applications to Regression and Scenario Analysis....Pages 163-188
Front Matter....Pages 189-189
Interactive Decision Making for Multiobjective Programming Problems with Fuzzy Parameters....Pages 191-228
A Possibilistic Approach for Multiobjective Programming Problems. Efficiency of Solutions....Pages 229-248
’FLIP’: An Interactive Method for Multiobjective Linear Programming with Fuzzy Coefficients....Pages 249-262
Application of the ’FLIP’ Method to Farm Structure Optimization under Uncertainty....Pages 263-278
Fulpal — An Interactive Method for Solving (Multiobjective) Fuzzy Linear Programming Problems....Pages 279-299
Multiple Objective Linear Programming Problems in the Presence of Fuzzy Coefficients....Pages 301-320
Inequality Constraints between Fuzzy Numbers and Their Use in Mathematical Programming....Pages 321-330
Using Fuzzy Logic with Linguistic Quantifiers in Multiobjective Decision Making and Optimization: A Step Towards More Human-Consistent Models....Pages 331-350
Front Matter....Pages 351-351
Stochastic Versus Possibilistic Multiobjective Programming....Pages 353-364
A Comparison Study of “Strange” and “Flip”....Pages 365-393
Multiobjective Mathematical Programming with Inexact Data....Pages 395-418
Back Matter....Pages 419-426
....