Travelling salesman model in fuzzy environment

Downloads

DOI:

https://doi.org/10.26637/MJM0704/0032

Abstract

In classical travelling salesman model, the objective is to visit n cities, starting from his home city and returning to home city, with minimum cost. In this paper, travelling cost is represented by trapezoidal fuzzy number. TrFN is defuzzified by using linear ranking function proposed by Maleki [22]. Classical travelling salesman model is extended to solve FNTSP.

Keywords:

Trapezoidal fuzzy number, Linear Ranking function

Mathematics Subject Classification:

Mathematics
  • Pages: 826-831
  • Date Published: 01-10-2019
  • Vol. 7 No. 04 (2019): Malaya Journal of Matematik (MJM)

D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Application, Academic, New York, 1980.

A. Jones, A. Kaufmann and H.-J. Zimmermann, Fuzzy Sets Theory and Applications, Reidel, Dordrecht, 1985.

A. Kaufmann and M.M. Gupta, Introduction to Fuzzy Arithmetic: Theory and Applications, Van Nostrand Reinhold, New York, 1985.

H.-J. Zimmermann, Fuzzy Set Theory and Its Applications, Kluwer, Hinghum, 1985.

T. J. Ross, Fuzzy Logic with Engineering Applications, John Wiley and Sons, 2004.

R.E. Bellman and L.A. Zadeh, Decision making in a fuzzy environment, Management Sciences, 17(1970), 141-164.

E.L. Hannan, Linear programming with multiple fuzzy goals, Fuzzy Sets Syst., 6(1981), 235-248.

M.P. Hansen, Use of substitute scalarizing functions to guide local search based Heuristics: The case of MOTSP, J. Heuristics, 6(2001), 419-431.

A. Jaszkiewicz, Genetic local search for multiple objectives combinatorial optimization, Eur. J. Oper. Res., $137(1)(2002), 50-71$.

E. Angel, E. Bampis and L. Gourves, Approximating the pareto curve with local search for bi-criteria TSP $(1,2)$ problem, Theoretical Computer Science, $310(1-3)(2004)$, $135-146$

T.F. Liang, Distribution planning decisions using interactive fuzzy multi-objective linear programming, Fuzzy Sets Syst., 157(2006), 1303-1316.

A. Rehmat, H. Saeed and M.S. Cheema, Fuzzy multiobjective linear programming approach for traveling salesman problem, Pak. J. Stat. Oper. Res., 3(2)(2007), 87-98.

B. Javadia, M. Saidi-Mehrabad, A. Haji, I. Mahdavi, F. Olai and N. Mahdavi-Amiri, No-wait flow shop scheduling using fuzzy multi-objective linear programming, $J$. Franklin Inst., 345(2008), 452-467.

S. Mukherjee and K. Basu, Application of fuzzy ranking method for solving assignment problems with fuzzy costs, International Journal of Computational and Applied Mathematics, $5(2010), 359-368$.

A. Chaudhuri and K. De, Fuzzy multi-objective linear programming for traveling sales man problem, Afr. $J$. Math. Comp. Sci. Res., 4(2)(2011), 64-70.

J. Majumdar and A.K. Bhunia, Genetic algorithm for asymmetric traveling salesman problem with imprecise travel times, J. Comp. Appl. Math., 235(2011), 30633078.

Sepideh Fereidouni, Travelling salesman problem by using a fuzzy multi-objective linear programming, African Journal of Mathematics and Computer Science Research, $4(11)(2011), 339-349$.

Amit Kumar and Anil Gupta, Assignment and travelling salesman problems with co-efficient as LR fuzzy parameter, International Journal of Applied Science and Engineering, 10(3)(2012), 155-170.

R.R. Yager, A procedure for ordering fuzzy subsets of the unit interval, Information Sciences, 24(1981), 143-161.

L.A. Zadeh, Fuzzy Logic and Its Applications, Academic Press, New York, 1965.

L.A.Zadeh, Fuzzy sets, Information and Control, $8(3)(1965), 338-353$

H.R. Maleki, Ranking functions and their applications to fuzzy linear programming, Far East J. Math. Sci., $4(2002), 283-301$

  • NA

Similar Articles

1 2 3 4 5 > >> 

You may also start an advanced similarity search for this article.

Metrics

Metrics Loading ...

Published

01-10-2019

How to Cite

K.K. Mishra. “Travelling Salesman Model in Fuzzy Environment”. Malaya Journal of Matematik, vol. 7, no. 04, Oct. 2019, pp. 826-31, doi:10.26637/MJM0704/0032.