Abstract
In real world there are many problems which have linear programming models where all decision parameters are fuzzy numbers. There are some approaches which are using different ranking functions for solving these problems. Unfortunately all these methods when there exist alternative optimal solutions, usually with different fuzzy value of the objective function for these solutions, can not specify a clear approach for choosing a solution. In this paper using the concept of expectation and variance as ranking functions, we propose a method to remove the above shortcomings in solving fuzzy number linear programming problems.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bass S. M. and Kwakernaak H.: Rating and Ranking of Multiple Aspent Alternative Using Fuzzy Sets. Automatica, 13 (1977), 47–58.
Bellman R. E. and Zadeh L. A.:Decision Making in a Fuzzy Environment. Management Sci., 17 (1970), 141–164.
Bortolan G. and Degani R.: A Review Of Some Methods For Ranking Fuzzy Numbers. Fuzzy Sets and Systems, 15 (1985), 1–19.
Chen S. J. and Hwang C. L.: Fuzzy Multiple Attribute Decision Making, Methods and Applications. Springer, Berline, (1992).
Maleki H. R., Tata M. and Mashinchi M.: Linear Programming With Fuzzy Variables. Fuzzy Sets and Systems, 109 (2000), 21–33.
Modarres M. and Sadi-Nezhad S.: Ranking Fuzzy Numbers by Preference Ratio. Fuzzy Sets and Systems, 118 (2001), 429–436.
Yazdani Peraei E., Maleki H.R. and Mashinchi M.: A Method For Solving A Fuzzy Linear Programming. Korean J. Comput. & Appl. Math., 8 (2001), No. 2, 347–356.
Yoon K.P.: A Probabilistic Approach To Rank Complex Fuzzy Numbers. Fuzzy Sets and Systems, 80 (1996) 167–176.
Zimmermann H. J.: Applications of Fuzzy Sets Theory to Mathematical Programming. Inform. Sci. 36 (1985), 29–58.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maleki, H.R., Mishmast, N.H., Mashinchi, M. (2002). Fuzzy Number Linear Programming: A Probabilistic Approach. In: Pal, N.R., Sugeno, M. (eds) Advances in Soft Computing — AFSS 2002. AFSS 2002. Lecture Notes in Computer Science(), vol 2275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45631-7_67
Download citation
DOI: https://doi.org/10.1007/3-540-45631-7_67
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43150-3
Online ISBN: 978-3-540-45631-5
eBook Packages: Springer Book Archive