Closed Form of Nearest Point of Linear Pentagonal Fuzzy Number and its Application to Course Assignment Problem with Fuzziness in Preference Level
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Abstract
This study focuses on optimizing course assignments for instructors based on their preferences, which are inherently uncertain due to personal conflicts affecting decision making. To address this, we model each preference level using two triangular fuzzy numbers, generated based on distinct instructor personality types. When instructors experience uncertainty in selecting a precise preference level, they can choose from these predefined triangular fuzzy numbers. The MIN aggregation of these triangular fuzzy numbers results in a linear pentagonal fuzzy number, whose nearest point in closed form is derived and utilized to represent fuzzy preference levels in our course assignment model. The assignment results obtained using this approach are comparable to those derived from optimal fuzzy weight assignments for specific preference levels. Our method is validated with data from the Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, demonstrating its effectiveness in handling uncertainty in course assignment decisions.
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