Intuitionistic Fuzzy Modeling to Travelling Salesman Problem

Authors

  • Arindam Garai Sonarpur Mahavidyalaya, West Bengal, India, Pin: 700149
  • Tapan Kumar Roy Bengal Engineering and Science University, Howrah, India, Pin: 711103

DOI:

https://doi.org/10.24297/ijct.v11i9.3414

Keywords:

Travelling salesman problem, intuitionistic fuzzy, degree of hesitation, fuzzy optimization, intuitionistic fuzzy decision making.

Abstract

This paper presents solution technique for travelling salesman problem (TSP) under intuitionistic fuzzy environment. Travelling salesman problem is a non-deterministic polynomial-time (NP) hard problem in combinatorial optimization, studied in graph theory, operations research and theoretical computer science. It must be noted that a traveling sales man even face a situation in which he is not able to achieve his objectives completely. There must be a set of alternatives from which he can select one that best meets his aspiration level. For Multi-Objective Symmetric TSP, in fuzzy environment, it is converted into a Linear Program using Fuzzy Multi-Objective Linear Programming technique. A route cannot be simply chosen just as it will most minimize time or it will cover the least possible distance. Examples with requirements to consider the degree of rejection or hesitation (or both) are overflowing in our materialistic world. Here comes the need to consider TSP under intuitionistic fuzzy environment. The degree of rejection as well as the degree of hesitancy must be studied to find the solution in a truly optimum sense! Proposed technique is an extension as well as collaboration of ideas of fuzzy traveling salesperson problem and intuitionistic fuzzy (IF) optimization technique.

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Author Biographies

Arindam Garai, Sonarpur Mahavidyalaya, West Bengal, India, Pin: 700149

Assistant Professor and Head, Dept. of Mathematics

Tapan Kumar Roy, Bengal Engineering and Science University, Howrah, India, Pin: 711103

Professor, Dept. of Mathematics

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Published

2013-12-05

How to Cite

Garai, A., & Roy, T. K. (2013). Intuitionistic Fuzzy Modeling to Travelling Salesman Problem. INTERNATIONAL JOURNAL OF COMPUTERS &Amp; TECHNOLOGY, 11(9), 3015–3024. https://doi.org/10.24297/ijct.v11i9.3414

Issue

Section

Research Articles