Solution of Multi-Criteria Assignment Problem using Neutrosophic Set Theory

Abstract

Assignment Problem (AP) is a very well-known and also useful decision-making problem in real-life situations. It becomes more effective when different criteria are added. To solve Multi-Criteria Assignment Problem (MCAP), the different criteria have been considered as neutrosophic elements because Neutrosophic Set Theory (NST) is a generalization of the classical sets, conventional fuzzy sets, Intuitionistic Fuzzy Sets (IFS) and Interval Valued Fuzzy Sets (IVFS). In this paper, two different methods have been proposed for solving MCAP. In the first method, we have calculated the evaluation matrix, score function matrix, accuracy matrix and ranking matrix of the MCAP. The rows represent the alternatives and columns represent the projects of the MCAP. From the ranking matrix, the ranking order of the alternatives and the projects are determined separately. From the above two matrices, composite matrix is formed and it is solved by Hungarian Method to get the optimal assignment. In the second one, Cosine formula for Vector Similarity Measure [1] on neutrosophic set is used to calculate the degree of similarity between each alternative and the ideal alternative. From the similarity matrix, the ranking order of the alternatives and the projects are determined in the same way as above. Finally the problem is solved by Hungarian Method to obtain the optimal solution.