Book Chapter10.1007/978-81-322-2217-0_44
On Solving Multiobjective Quadratic Programming Problems in a Probabilistic Fuzzy Environment
Animesh Biswas,Arnab Kumar De +1 more
- 01 Jan 2015
- pp 543-557
2
TL;DR: A fuzzy goal programming (FGP) approach for solving fuzzy multiobjective quadratic chance-constrained programming (CCP) problem involving exponentially distributed fuzzy random variables (FRVs) is developed.
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Abstract: In this paper, a fuzzy goal programming (FGP) approach for solving fuzzy multiobjective quadratic chance-constrained programming (CCP) problem involving exponentially distributed fuzzy random variables (FRVs) is developed. In the proposed methodology, the problem is first converted into interval-valued quadratic programming problem using CCP technique and \( \alpha \)-cut of fuzzy numbers. Then, using fuzzy partial order relations, the problem is converted into its equivalent deterministic form. The individual optimal value of each objective is found in isolation to construct the quadratic fuzzy membership goals of each of the objective. The quadratic membership goals are transferred into linear goals by applying piecewise linear approximation technique. A minsum goal programming (GP) method is then applied to both the linearized and quadratic model to achieve the highest membership degree of each of the membership goals in the decision-making context. Finally, a comparison is made on the two different approaches with the help of distance function. An illustrative numerical example is provided to demonstrate the applicability of the proposed methodology.
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Citations
Introduction and Historical Background
M. A. C. Perryman
- 01 Jun 1989
Abstract: This chapter describes the evolution of different multi-objective decision-making (MODM) models with their historical backgrounds. Starting from MODM models in deterministic environments along with various solution techniques, the chapter presents how different kinds of uncertainties may be associated with such decision-making models. Among several types of uncertainties, it has been found that probabilistic and possibilistic uncertainties are of special interests. A brief literature survey on different existing methods to solve those types of uncertainties, independently, is discussed and focuses on the need of considering simultaneous occurrence of those types of uncertainties in MODM contexts. Finally, a bibliographic survey on several approaches for MODM under hybrid fuzzy environments has been presented. Through this chapter the readers can be able to get some concepts about the historical development of MODM models in hybrid fuzzy environments and their importance in solving various real-life problems in the current complex decision-making arena.
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Fuzzy random variables—I. definitions and theorems
TL;DR: Fuzziness is discussed in the context of multivalued logic, and a corresponding view of fuzzy sets is given.
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