Cost minimization using triangular fuzzy numbers

In the thesis study, a fundamental cost problem was solved using fuzzy tools. Triangular fuzzy numbers were used as the fuzzy tool. The cost problem was expressed as follows: The goal is to lay an energy transmission line from a power plant located on a seaside to an offshore facility. The cost per kilometer of laying the energy line on land and the cost per kilometer of laying it underwater fluctuate due to various reasons. For example, seasonal labor cost variations and sudden changes in cable prices are among the primary factors affecting cost fluctuations. Considering that the costs of land and underwater lines are not fixed, these costs were represented using triangular fuzzy numbers, and the cost calculation was performed using fuzzy tools. The cost function, which aims to minimize the cost of laying the energy line between the power plant and the facility, was optimized. The thesis consists of four chapters. In the first chapter, a brief development of the fuzzy logic theory used to solve the problem is provided. A short introduction to cost problems related to energy and pipeline projects, as well as economic applications of fuzzy numbers, is included. Additionally, the study's contribution to filling a research gap is discussed. The second chapter presents the role of fuzzy number applications in economics and the literature on cost problems in energy and pipeline projects. In the third chapter, triangular fuzzy numbers, which were used as the fuzzification tool in this study, and their fundamental concepts are introduced. Additionally, defuzzification techniques such as centroid, signed distance, and weighted average methods are explained. The fourth chapter is examined in three sections. The first section provides the classical solution to the cost problem. The last two sections present original results introduced for the first time in this thesis. In the second section, the coefficients in the cost problem were fuzzified using triangular fuzzy numbers, and their minimum values were calculated using three different defuzzification methods. The calculated values were tabulated and compared. In the third section of the fourth chapter, another parameter in the cost function, distance, was also fuzzified using triangular fuzzy numbers. Similar to the second section, centroid, weighted average, and signed distance methods were used for defuzzification, and the obtained values were compared for each technique used. Finally, in the last chapter, the results obtained in the study were interpreted, and a discussion was conducted on the types of problems to which the applied methodology could be extended.