International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2358 2020 2020 Department of Mathematics, PSNA College of Engineering and Technology, Dindigul – 624622, Tamil Nadu, India S. Krishna Prabha Department of Mathematics, Mount Carmel College (Autonomous), Affiliated to Bengaluru City University, Bengaluru - 560052, Karnataka, India M. Clement Joe Anand Devision of Mathematics, Vellore Institute of Technology, Chennai - 600127, Tamil Nadu, India V. Vidhya Department of Mathematics, Panimalar Engineering College, Chennai - 600 123, Tamil Nadu, India G. Nagarajan Department of Mathematics, Silapathar College, Dhemaji, Assam – 787059, India Utpal Saikia Department of Mathematics, Arul Anandar College, Karumathur-625514, Tamil Nadu, India Nivetha Martin Department of Mathematics, Chaitanya Bharathi Institute of Technology, Gandipet, Hyderabad - 500075, India M. Santoshi Kumari Department of Computer Science and Engineering, Bharati Vidyapeeth’s College of Engineering, Delhi -110063, India Mohit Tiwari 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. 2024 2024 91 103 10.54216/IJNS.230208 https://www.americaspg.com/articleinfo/21/show/2358