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

Pratiksha Saxena and Ravi Jain
Additional contact information
Pratiksha Saxena: Department of Applied Mathematics, Gautam Buddha University, Greater Noida, India
Ravi Jain: Department of Mathematics, Maharaja Agrasen Institute of Management Studies, Delhi, India

International Journal of Fuzzy System Applications (IJFSA), 2019, vol. 8, issue 2, 68-88

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.

Date: 2019
References: Add references at CitEc
Citations:

Downloads: (external link)
http://services.igi-global.com/resolvedoi/resolve. ... 018/IJFSA.2019040104 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:igg:jfsa00:v:8:y:2019:i:2:p:68-88

Access Statistics for this article

International Journal of Fuzzy System Applications (IJFSA) is currently edited by Deng-Feng Li

More articles in International Journal of Fuzzy System Applications (IJFSA) from IGI Global
Bibliographic data for series maintained by Journal Editor ().