CFP last date
15 October 2024
Call for Paper
November Edition
IJAIS solicits high quality original research papers for the upcoming November edition of the journal. The last date of research paper submission is 15 October 2024

Submit your paper
Know more
Reseach Article

Multi-objective Assignment Problem with Generalized Trapezoidal Fuzzy Numbers

by Surapati Pramanik, Pranab Biswas
International Journal of Applied Information Systems
Foundation of Computer Science (FCS), NY, USA
Volume 2 - Number 6
Year of Publication: 2012
Authors: Surapati Pramanik, Pranab Biswas
10.5120/ijais12-450375

Surapati Pramanik, Pranab Biswas . Multi-objective Assignment Problem with Generalized Trapezoidal Fuzzy Numbers. International Journal of Applied Information Systems. 2, 6 ( May 2012), 13-20. DOI=10.5120/ijais12-450375

@article{ 10.5120/ijais12-450375,
author = { Surapati Pramanik, Pranab Biswas },
title = { Multi-objective Assignment Problem with Generalized Trapezoidal Fuzzy Numbers },
journal = { International Journal of Applied Information Systems },
issue_date = { May 2012 },
volume = { 2 },
number = { 6 },
month = { May },
year = { 2012 },
issn = { 2249-0868 },
pages = { 13-20 },
numpages = {9},
url = { https://www.ijais.org/archives/volume2/number6/167-0375/ },
doi = { 10.5120/ijais12-450375 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2023-07-05T10:44:05.231515+05:30
%A Surapati Pramanik
%A Pranab Biswas
%T Multi-objective Assignment Problem with Generalized Trapezoidal Fuzzy Numbers
%J International Journal of Applied Information Systems
%@ 2249-0868
%V 2
%N 6
%P 13-20
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The aim of this paper is to study multi-objective assignment problem with imprecise costs, time and ineffectiveness instead of its precise information. Here, elements of cost matrix, consumed time matrix and ineffectiveness level matrix have been represented by generalized trapezoidal fuzzy numbers as it is suitable way to represent the impreciseness of values provided by the decision makers due to time pressure or limited information and poor information processing capabilities. A priority based fuzzy goal programming method has been developed for generalized trapezoidal fuzzy numbers and it is applied for multi-objective assignment problem. Euclidean distance function is used to identify the most appropriate priority structure of fuzzy goals among the different priorities of the fuzzy goals. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.

References
  1. Kuhn, H. W. 1955. The Hungarian method for assignment problem, Naval Research Logistics Quarterly. 2, 83-97.
  2. Geetha, S. and Nair, K. P. K. 1993. A variation of the assignment problem, European Journal of Operation Research. 68(3), 422-426.
  3. Bao, C. P. , Tsai, M. C. and M. I. Tsai. 2007. A new approach to study the multi-objective assignment problem. WHAMPOA- An Interdisciplinary Journal. 53, 123-132
  4. Lin, C. J. , and Wen, U. P. 2004. A labeling algorithm for the fuzzy Assignment problem, Fuzzy Sets and Systems, 142, 373–391.
  5. Chen, M. S. 1985. On a fuzzy assignment problem. Tamkang J. 22, 407– 411.
  6. Tsai, C. H. , Wei, C. C. , and Cheng, C. L. 1999. Multi objective fuzzy deployment of manpower, International Journal of the Computer, the Internet and Management, 7(2), May-August.
  7. Belacela, N. and Boulasselb, M. R. 2001. Multi criteria fuzzy assignment problem: a useful tool to assist medical diagnosis. Artificial intelligence in Medicine 21, 201-207.
  8. Majumder, J. , and Bhunia, A. K. 2007. Elitist genetic algorithm for assignment problem with imprecise goal, European Journal of Operation Research. 177, 684-692.
  9. Kumar, A. , and Gupta, A. 2011. Methods for solving fuzzy assignment problems and fuzzy travelling salesman problems with different membership functions, Fuzzy Information and Engineering. 3(1), 3-21.
  10. Yager, R. R. 1981. A procedure for ordering fuzzy subsets of the unit interval, Information Sciences. 24, 143-161.
  11. Emrouznejad, A. , Angiz, M. Z. , and L, W. Ho. 2012. An alternative formulation for the fuzzy assignment problem. Journal of the Operational Research Society. 63, 59-63.
  12. Haddad, H. , Mohammadi, H. , and Pooladkhan, H. 2012. Two models for the generalized assignment problem in uncertain environment, Management Science Letters. 2, 623–630
  13. Biswas, P. and Pramanik, S. 2011. Multi-objective Assignment Problem with Fuzzy Costs for the Case Military Affairs, International Journal of Computer Applications. 30(10), 7-12.
  14. Pramanik, S. , and Roy, T. K. 2008, Multi-objective transportation model with fuzzy parameters: a priority based fuzzy goal programming approach, Journal of transportation System Engineering and Information Technology. 8(3), 40-48.
  15. Zadeh, L. A. 1965. Fuzzy sets, Information and Control. 8, 338–353.
  16. Kaufmann, A. , and Gupta, M. M. 1988. Fuzzy mathematical models in engineering and management science, Elsevier Science Publishers, B. V.
  17. Lee, E. S. And Li, R. J. 1993. Fuzzy multiple objective programming and compromise programming with Pareto optimum. Fuzzy Sets and Systems. 53(2), 275-288.
  18. Pramanik, S. , and Dey, P. 2011, A Priority based Fuzzy Goal Programming to Multi-Objective Linear Fractional Programming Problem, International Journal of Computer Applications. 30(10), 1-6.
  19. Yu, P. L. 1973. A class of solutions for group decision problems, Management Science. 19(8), 936-946.
Index Terms

Computer Science
Information Sciences

Keywords

Fuzzy Sets; Generalized Trapezoidal Fuzzy Numbers; Multi-objective Assignment Problem; Priority Based Fuzzy Goal Programming