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A fuzzy linear programming model with fuzzy parameters and decision variables

A fuzzy linear programming model with fuzzy parameters and decision variables Linear programming (LP) is an optimisation technique most widely used for optimal allocation of limited resources amongst competing activities. Precise data are fundamentally indispensable in standard LP problems. However, the observed values of the data in real-world problems are often imprecise or vague. Fuzzy set theory has been extensively used to represent Copyright © 2015 Inderscience Enterprises Ltd. A fuzzy LP model with fuzzy parameters and decision variables ambiguous, uncertain or imprecise data in LP by formalising the inaccuracies inherent in human decision-making. We propose a new method for solving fuzzy LP (FLP) problems in which the right-hand side parameters and the decision variables are represented by fuzzy numbers. A new fuzzy ranking model and a new supplementary variable are utilised in the proposed FLP method to obtain the fuzzy and crisp optimal solutions by solving one LP model. Moreover, we introduce an alternative model with deterministic variables and parameters derived from the proposed FLP model. Interestingly, the result of the alternative model is identical to the crisp solution of the proposed FLP model. We use a numerical example from the FLP literature for comparison purposes and to demonstrate the applicability of the proposed method and exhibit the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Information and Decision Sciences Inderscience Publishers

A fuzzy linear programming model with fuzzy parameters and decision variables

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Publisher
Inderscience Publishers
Copyright
Copyright © 2015 Inderscience Enterprises Ltd.
ISSN
1756-7017
eISSN
1756-7025
DOI
10.1504/IJIDS.2015.074129
Publisher site
See Article on Publisher Site

Abstract

Linear programming (LP) is an optimisation technique most widely used for optimal allocation of limited resources amongst competing activities. Precise data are fundamentally indispensable in standard LP problems. However, the observed values of the data in real-world problems are often imprecise or vague. Fuzzy set theory has been extensively used to represent Copyright © 2015 Inderscience Enterprises Ltd. A fuzzy LP model with fuzzy parameters and decision variables ambiguous, uncertain or imprecise data in LP by formalising the inaccuracies inherent in human decision-making. We propose a new method for solving fuzzy LP (FLP) problems in which the right-hand side parameters and the decision variables are represented by fuzzy numbers. A new fuzzy ranking model and a new supplementary variable are utilised in the proposed FLP method to obtain the fuzzy and crisp optimal solutions by solving one LP model. Moreover, we introduce an alternative model with deterministic variables and parameters derived from the proposed FLP model. Interestingly, the result of the alternative model is identical to the crisp solution of the proposed FLP model. We use a numerical example from the FLP literature for comparison purposes and to demonstrate the applicability of the proposed method and exhibit the

Journal

International Journal of Information and Decision SciencesInderscience Publishers

Published: Jan 1, 2015

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