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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 29 | Number 1 | Year 2016 | Article Id. IJMTT-V29P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V29P502

An Intuitionistic Fuzzy Approach for Solving Generalized Trapezoidal Travelling Salesman Problem


Dr.A.Sahaya sudha, G.Alice Angel, M.Elizabeth Priyanka, S.Emily jennifer
Abstract

In this paper the Generalized trapezoidal intuitionistic fuzzy numbers and ranking method has been adopted and for finding an optimal solutionfor travelling salesman problem (TSP) Hungarian method is used. This method requires least iteration to obtain the optimality.The method is illustrated by a numerical example.

Keywords
Travelling salesman problem, generalized trapezoidal intuitionistic fuzzy numbers, fuzzy Hungarian method, optimal solution.
References

[1] Atanassov, K., (1986), Intuitionistic fuzzy sets, Fuzzy Sets and Systems,Vol.20,pp.87-96.
[2] Atanassov, K., (1989), More on intuitionistic fuzzy sets, Fuzzy Sets and Systems,Vol.33,pp. 37-46
[3] Jat. R. N, Sharma. S. C., Sanjay Jain, Anchal Choudhary(2015),A Fuzzy approach for solving mixed intuitionistic fuzzy travelling salesman problem, International Journal of Mathematical Archive,vol.6(10), pp.99-104
[4] NagoorGani.A and Mohamed,V.N (2015), A Method of Ranking Generalized Trapezoidal Intuitionistic Fuzzy Numbers, International Journal of Applied Engineering Research, Vol.10(10) pp. 25465-25473
[5] NagoorGani, A., and Mohamed, V.N.,(2015), Generalized Trapezoidal Fuzzy Numbers in Intuitionistic Fuzzy Environment, Jamal Academic Research Journal(JARJ):An interdisciplinary, Special Issue, pp. 711-714.
[6] Ponnivalavan. K, and Pathinathan T.,(2015) Intuitionistic pentagonal fuzzy number, ARPN Journal of Engineering and Applied Sciences, vol. 10( 12)
[7] Rajarajeswari. P ,SahayaSudha. A,(2014) Solving a Fully Fuzzy Linear Programming Problem by Ranking, International Journal of Mathematical Trends and Technology (IJMTT). Vol.9,pp:159-164.
[8] Srinivas. B, Ganesan. G(2015),Optimal solution for Intuitionistic Fuzzy Transportation Problem via Revised Distribution Method, International Journal of Mathematics Trends and Technology (IJMTT). Vol.9(2),pp:150-161
[9] Thamaraiselvi. A, Santhi. R,(2015),Solving Fuzzy Transportation problem with Generalized Hexagonal Fuzzy Numbers, IOSR Journal of Mathematics, Vol. 11(5),pp: 08-13
[10] Thamaraiselvi. A, and Santhi .R,(2015),On Intuitionistic Fuzzy Transportation Problem Using Hexagonal Intuitionistic Fuzzy Numbers,, International Journal of Fuzzy Logic Systems (IJFLS) Vol.5(1).
[11] Zimmermann H.J.(1978), Fuzzy programming and linear programming with several objective functions, Fuzzy sets and systems,pp45-55.

Citation :

Dr.A.Sahaya sudha, G.Alice Angel, M.Elizabeth Priyanka, S.Emily jennifer, "An Intuitionistic Fuzzy Approach for Solving Generalized Trapezoidal Travelling Salesman Problem," International Journal of Mathematics Trends and Technology (IJMTT), vol. 29, no. 1, pp. 9-12, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V29P502

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