A fuzzy approach for unequal workers-task assignment with heptagonal fuzzy numbers

Abstract

The problem of assigning n tasks to n workers with minimum assignment cost often arises in many practical applications. In real life, the cost of assignment may not be certain and also the number of tasks may not be always equal to the number of workers and an unbalanced situation may arise often. In this paper, the representation of the Heptagonal fuzzy number(HFN) and its arithmetic operations are reviewed and a fuzzy approach called as fuzzy row penalty method is extended within the context of Heptagonal fuzzy numbers to deal with the unbalanced Fuzzy Assignment Problems. The cost of assignment is represented by Heptagonal fuzzy numbers which are capable of incorporating the degree of satisfaction about the assignment cost. So the use of HFN is more suitable. The proposed method overcomes the limitations of existing methods and it is illustrated through numerical example.