Sorting Out Interval Valued Neutrosophic Fuzzy Shortest Cycle Route Problem by Reduced Matrix Method
S. Krishna Prabha1*, M. Clement Joe Anand2, V. Vidhya3, G. Nagarajan4, Utpal Saikia5, Nivetha Martin6, M. Santoshi Kumary7, Mohit Tiwari8
1* Department of Mathematics, PSNA College of Engineering and Technology, Dindigul – 624622, Tamil Nadu, India.
2Department of Mathematics, Mount Carmel College (Autonomous), Affiliated to Bengaluru City University, Bengaluru - 560052, Karnataka, India.
3Devision of Mathematics, Vellore Institute of Technology, Chennai - 600127, Tamil Nadu, India.
4Department of Mathematics, Panimalar Engineering College, Chennai - 600 123, Tamil Nadu, India.
5Department of Mathematics, Silapathar College, Dhemaji, Assam – 787059, India.
6Department of Mathematics, Arul Anandar College, Karumathur-625514, Tamil Nadu, India.
7Department of Mathematics, Chaitanya Bharathi Institute of Technology, Gandipet, Hyderabad - 500075, India.
8Department of Computer Science and Engineering, Bharati Vidyapeeth’s College of Engineering, Delhi -110063, India.
Emails: jvprbh1@gmail.com; arjoemi@gmail.com; vidhya.v@vit.ac.in; sridinnaga@gmail.com; utpalsaikiajorhat@gmail.com; nivetha.martin710@gmail.com; santoshinagaram@gmail.com; mohit.tiwari@bharatividyapeeth.edu .
Abstract
The assertiveness theory next addresses the difficulties of the travelling salesman after discussing the problem with transportation and assignment. The Shortest Cycling Route Problem (SCRP) finds the shortest route that stops in each city exactly once using a preset set of cities and their bilateral distances. The arc lengths in TSO are typically seen as representing travel time or travel expenses rather than actual distance. The precise arc length cannot be predicted because cargo, climate, road conditions, and other factors also can affect the journey time or cost. For handling the unpredictability in SCRP, fuzzy set theory provides a new tool. The shortest cyclic route problem with interval-valued neutrosophic fuzzy numbers as cost coefficients is solved using the simplified matrix techniques in this study. Reduced Matrix Method is used to solve a numerical problem and its efficacy is demonstrated.
Keywords: Interval-valued neutrosophic fuzzy; shortest cyclic route problem; reduced matrix.