Analyses the least cost using Travelling Salesman problem through Neutrosophic Fuzzy system
S. Ghousia Begum 1,*, N. Jose Parvin Praveena 2, A. Rajkumar 3, D. Nagarajan4*. Broumi Said5
1 Research Scholar, Department of Mathematics, Hindustan Institute of Technology and science, Padur, Chennai, India
2Department of Mathematics, St.Joseph’s College of Engineering, Chennai, India
3Department of Mathematics, Hindustan Institute of Technology and Science, Chennai, India
4*Department of Mathematics, Rajalakshmi Institute of Technology, Chennai, India
5Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco
Emails: ghousiabs@hindustanuniv.ac.in; jose30102003@gmail.com; arajkumar@hindustanuniv.ac.in; dnrmsu2002@yahoo.com; broumisaid78@gmail.com
Abstract
The following paper introduces a methodology to calculate the least cost for a directed network through Travelling salesman problem. Dynamic programming method is used to find the minimum Cost. The recursion formula is used. The edge weights of the networks are being taken in terms of Triangular, Trapezoidal and Pentagonal Neutrosophic set. Score function for the Triangular, Trapezoidal and Pentagonal Neutrosophic sets are being defined for deneutrosophication. The least cost is estimated using all the above said Neutrosophic sets and the result is compared.
Keywords: Triangular Neutrosophic Number (TNN); Trapezoidal Neutrosophic Number (TRNN); Pentagonal Neutrosophic number (PNN); Least Cost; Travelling salesman; Deneutrosophication; Recursion formula; Dynamic Programming