Intuitionistic Fuzzy Approach in Solving Travelling Salesman Problem

Anju Thomas¹ , Shiny Jose²

Section:Review Paper, Product Type: Isroset-Journal
Vol.6 , Issue.1 , pp.173-177, Feb-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.173177

Online published on Feb 28, 2019

Copyright © Anju Thomas, Shiny Jose . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The Travelling Salesman Problem is to find out the shortest route such that the salesman start from a particular place, visit all the places exactly once and return to the starting place with minimum cost. A Fuzzy version of Hungarian algorithm for the solution of Intuitionistic Fuzzy Travelling Salesman Problem using Triangular Intuitionistic Fuzzy numbers was studied earlier[1]. In this paper we introduce a new representation of Triangular Intuitionistic Fuzzy Number (TIFN) called Arithmetic F- Average using which an Intuitionistic Fuzzy Travelling Salesman Problem is solved. This Arithmetic F- Average is applied in Fuzzy Hungarian algorithm which will be more elegant and simpler than given in [1]. Also we defined some of the properties of this average and a ranking method for this average. The Fuzzy Hungarian algorithm of this average is illustrated with an example.

Key-Words / Index Term :
Arithmetic F- Average

References :
[1] Prabhakaran, K., Ganeshan, K. Fuzzy Hungarian Method for Solving Intuitionistic Fuzzy Travelling Salesman Problem, National Conference on Mathematical Techniques and its Applications, 2018.
[2] Mukherjee, S., Basu, K. Solving Intuitionistic Fuzzy Assignment Problem by using Similarity Measures and Score Functions, Int. J. Pure Appl.Sci.Technol, Vol. 2, 2011, No. 1, 1-18.
[3] Atanassov, K. T. Intuitionistic Fuzzy sets, Verlag, New York, 1999.
[4] Annie Varghese and Sunny Kuriakose. Centroid of an intuitionistic fuzzy number, Notes on Intuitionistic Fuzzy Sets , Vol. 18, 2012, No. 1, 19 -24.