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.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

474 Views    221 Downloads    95 Downloads

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.