A solution approach for a fully fuzzy assignment problem

We solve a fully fuzzy assignment problem (FAP) where the costs are triangular fuzzy numbers. The FAP has gained its importance in the recent years. We have represented the fuzzy numbers in their parametric form and then solved it through ones assignment method. To the best of our knowledge, several authors have acquired the solution for a FAP by converting the problem to its crisp form. We have proposed an algorithm where we have used our ranking method and arithmetic operations to obtain a desirable solution without converting to an equivalent crisp form. The solution we acquired is represented in terms of location index and fuzziness index functions which enables the decision maker to decide his/her preference of solution. An example is given to explain the proposed methodology.