Crisp-linear-and Models in Fuzzy Multiple Objective Linear Fractional Programming
Keywords:
fuzzy linear fractional programming, fuzzy multiple objective programming, fuzzy decision, aggregation operator.Abstract
The aim of this paper is to introduce two crisp linear models to solve fuzzy multiple objective linear fractional programming problems. In a novel manner we construct two piece-wise linear membership functions to describe the fuzzy goal linked to a linear fractional objective. They are related to the numerator and denominator of the fractional objective function; and we show that using the fuzzy-and operator to aggregate them a convenient description of the original fractional fuzzy goal is obtained. Further on, with the help of the fuzzy-and operator we aggregate all fuzzy goals and constraints, formulate a crisp linear model, and use it to provide a solution to the initial fuzzy multiple objective linear fractional programming problem. The second model embeds in distinct ways the positive and negative information, the desires and restrictions respectively; and aggregates in a bipolar manner the goals and constraints. The main advantage of using the new models lies in the fact that they are linear, and can generate distinct solutions to the multiple objective problem by varying the thresholds and tolerance limits imposed on the fuzzy goals.References
Bellman, R.E.; Zadeh, L.A. (1970). Decision-making in a fuzzy environment. Management Science, 17(4), B-141-B-164. https://doi.org/10.1287/mnsc.17.4.B141
Chang, C.-T. (2017). Fuzzy linearization strategy for multiple objective linear fractional programming with binary utility functions. Computers & Industrial Engineering, 112, 437 - 446. https://doi.org/10.1016/j.cie.2017.07.026
Dubey, D.; Chandra, S.; Mehra, A. (2015). Computing a Pareto-optimal solution for multiobjective flexible linear programming in a bipolar framework. International Journal of General Systems, 44(4), 457-470. https://doi.org/10.1080/03081079.2014.969253
Dubey, D.; Mehra, A. (2014). A bipolar approach in fuzzy multi-objective linear programming. Fuzzy Sets and Systems, 246, 127 - 141. Theme: Preference Modeling and Optimization. https://doi.org/10.1016/j.fss.2013.07.017
Dutta, D.; Tiwari, R.N.; Rao, J.R.(1992). Multiple objective linear fractional programming - A fuzzy set theoretic approach. Fuzzy Sets and Systems, 52(1), 39 - 45. https://doi.org/10.1016/0165-0114(92)90034-2
Lachhwani, K. (2015). Modified FGP approach for multi-level multi objective linear fractional programming problems. Applied Mathematics and Computation, 266, 1038 - 1049. https://doi.org/10.1016/j.amc.2015.06.027
Li, D.; Leung, Y.; Wu, W. (2019). Multiobjective interval linear programming in admissible-order vector space. Information Sciences, 486, 1 - 19. https://doi.org/10.1016/j.ins.2019.02.012
Pop, B. (2004). Fuzzy approach for multiple criteria fractional optimisation - comments and quadratic constraint generalization. Fuzzy Systems and A.I., 10(1-2), 57 - 65.
Stanojevic, B.; Stanojevic, M. (2013). On the efficiency test in multi-objective linear fractional programming problems by Lotfi et al. 2010. Applied Mathematical Modelling, 37(10), 7086 - 7093. https://doi.org/10.1016/j.apm.2013.01.041
Stanojevic, B.; Stanojevic, M. (2014). Comment on 'Fuzzy mathematical programming for multi objective linear fractional programming problem'. Fuzzy Sets and Systems, 246, 156 - 159. https://doi.org/10.1016/j.fss.2014.02.007
Toksari, M.D.; Bilim, Y. (2015). Interactive fuzzy goal programming based on jacobian matrix to solve decentralized bi-level multi-objective fractional programming problems. International Journal of Fuzzy Systems, 17(4), 499-508. https://doi.org/10.1007/s40815-015-0036-1
Zimmermann, H.-J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45 - 55. https://doi.org/10.1016/0165-0114(78)90031-3
Zimmermann, H.-J. (1985). Applications of fuzzy set theory to mathematical programming. Information Sciences, 36(1), 29 - 58. https://doi.org/10.1016/0020-0255(85)90025-8
Published
Issue
Section
License
ONLINE OPEN ACCES: Acces to full text of each article and each issue are allowed for free in respect of Attribution-NonCommercial 4.0 International (CC BY-NC 4.0.
You are free to:
-Share: copy and redistribute the material in any medium or format;
-Adapt: remix, transform, and build upon the material.
The licensor cannot revoke these freedoms as long as you follow the license terms.
DISCLAIMER: The author(s) of each article appearing in International Journal of Computers Communications & Control is/are solely responsible for the content thereof; the publication of an article shall not constitute or be deemed to constitute any representation by the Editors or Agora University Press that the data presented therein are original, correct or sufficient to support the conclusions reached or that the experiment design or methodology is adequate.
