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Bector-Chandra Type Duality in Linear Programming Under Fuzzy Environment Using Hyperbolic Tangent Membership Functions

Bector-Chandra Type Duality in Linear Programming Under Fuzzy Environment Using Hyperbolic Tangent Membership Functions

Pratiksha Saxena, Ravi Jain
Copyright: © 2019 |Volume: 8 |Issue: 2 |Pages: 21
ISSN: 2156-177X|EISSN: 2156-1761|EISBN13: 9781522567691|DOI: 10.4018/IJFSA.2019040104
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MLA

Saxena, Pratiksha, and Ravi Jain. "Bector-Chandra Type Duality in Linear Programming Under Fuzzy Environment Using Hyperbolic Tangent Membership Functions." IJFSA vol.8, no.2 2019: pp.68-88. http://doi.org/10.4018/IJFSA.2019040104

APA

Saxena, P. & Jain, R. (2019). Bector-Chandra Type Duality in Linear Programming Under Fuzzy Environment Using Hyperbolic Tangent Membership Functions. International Journal of Fuzzy System Applications (IJFSA), 8(2), 68-88. http://doi.org/10.4018/IJFSA.2019040104

Chicago

Saxena, Pratiksha, and Ravi Jain. "Bector-Chandra Type Duality in Linear Programming Under Fuzzy Environment Using Hyperbolic Tangent Membership Functions," International Journal of Fuzzy System Applications (IJFSA) 8, no.2: 68-88. http://doi.org/10.4018/IJFSA.2019040104

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Abstract

Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. One approach to optimize a multi-objective mathematical model is to employ utility functions for the objectives. Recent studies on utility-based multi-objective optimization concentrates on considering just one utility function for each objective. But, in reality, it is not reasonable to have a unique utility function corresponding to each objective function. Here, a constrained multi-objective mathematical model is considered in which several utility functions are associated for each objective. All of these utility functions are uncertain and in fuzzy form, so a fuzzy probabilistic approach is incorporated to investigate the uncertainty of the utility functions for each objective. Meanwhile, the total utility function of the problem will be a fuzzy nonlinear mathematical model. Since there are not any conventional approaches to solve such a model, a defuzzification method to change the total utility function to a crisp nonlinear model is employed. Also, a maximum technique is applied to defuzzify the conditional utility functions. This action results in changing the total utility function to a crisp single objective nonlinear model and will simplify the optimization process of the total utility function. The effectiveness of the proposed approach is shown by solving a test problem.

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