IDR - IIT Kharagpur

Deterministic Equivalent of Fuzzy Chance Constrained Programming Problems

Deterministic Equivalent of Fuzzy Chance Constrained Programming Problems

 

In this thesis we have tried to develop methodologies to convert different types of Chance Constrained Programming models under fuzzy environment into deterministic forms. Fuzziness is present in the Chance Constrained Programming problem in one or more of the forms: fuzzy random variables, fuzzy numbers and fuzzy partial order relations either in the constraint or in the objective function or in both of these. We have considered the linear Fuzzy Chance Constrained Programming problems from Chapters 2 to Chapter 6 and explored a new concept for nonlinear Fuzzy Chance Constrained Programming problem in Chapter 7. All the methodologies are developed using Buckley’s fuzzy probability theory. The deterministic equivalent of all the models in the thesis are linear or nonlinear optimization problems which can be solved using an optimization software package or by writing a proper program. Our objective is to convert the uncertainties in our models, to corresponding deterministic equivalent forms. So we have deviated ourselves from writing programs for the solution of the deterministic forms. However, in all models we have verified the methodologies using numerical examples.

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