Affiliations: [a] Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| [b] Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey
Correspondence:
[*]
Corresponding author. Tofigh Allahviranloo, Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey. E-mail: allahviranloo@yahoo.com.
Abstract: Transportation Problems (TP) have multiple applications in supply chain management to reduce costs. Efficient methods have been developed to address TP when all factors, including supply, demand, and unit transportation costs, are precisely known. However, due to uncertainty in practical applications, it is necessary to study TP in an uncertain environment. In this paper, we define the Trapezoidal Fermatean Fuzzy Number (TrFFN) and its arithmetic operations. Then we introduce a new approach to solve TP, where transportation cost, supply, and demand are treated as TrFFN, and we call it Fermatean Fuzzy TP (FFTP). We illustrate the feasibility and superiority of this method with two application examples, and compare the performance of this method with existing methods. Furthermore, the advantages of the proposed method over existing methods are described to address TP in uncertain environments.
Keywords: Trapezoidal Fermatean fuzzy sets, linear programming problem, transportation problem, supply and demand
