# FGP for Chance Constrained Fractional MODM Problem

Shyamal Sen (Brahmananda Keshab Chandra College, India) and Bijay Baran Pal (University of Kalyani, India)
DOI: 10.4018/978-1-4666-5202-6.ch086

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## Model Formulation

The general format of a chance constrained linear MOFPP can be stated as:

• Find X(x1, x2, …, xn) so as to:Maximize ,Minimize ,

subject to, (1) where Pr indicates the probabilistically defined constraints, A = (aij)m×n is a coefficient matrix and b is a resource vector, and are the coefficient vectors and where αk and βk are constants and p(0<p<1) is the vector of satisficing probability levels defined for randomness of parameters associated with the constraints set. It is assumed that the feasible region S is nonempty (S≠φ), and where

## Key Terms in this Chapter

Fractional Programming: A special field of study in the area of mathematical programming where certain objective(s) appear in the form of ratios for optimizing them in the decision environment.

Fuzzy Programming: Modeling aspects of optimization problems in which model parameters are defined imprecisely owing to inexactness of human judgments as well as inherent impressions in parameters themselves.

Chance Constrained Programming: In a programming environment, satisfying of certain probability levels as chance factors are imposed to objectives and / or system constraints for optimizing problems in a decision making context.

Fuzzy Goal Programming: It is an extension of conventional goal programming, where aspiration level of each objective is taken unity concerning achievement of the highest degree (unity) of fuzzy goals of a problem.

Goal Programming: In a certain programming environment, optimization of a set of objectives is involved there in the decision situation. Here, instead of optimizing them directly, achievement of the estimated / expected target values called aspiration levels of them are considered.

Stochastic Programming: In a certain programming environment, model parameters are random in nature and probabilities of occurrence of various events are considered there in modeling and solving problems.

Multiobjective Programming: A multiplicity of objectives is involved in a mathematical programming environment.

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