Solving Intuitionistic Fuzzy Assignment Problem by using Similarity Measures and Score Functions

Classical Assignment Problem (AP) is a well-known topic world-wide. In this problem ij c denotes the cost for assigning the th j job to the th i person. This cost is usually deterministic in nature. But in realistic situations, it may not be practicable to know the precise values of these costs. In such uncertain situations, instead of exact values of costs, if we can evaluate the preferences for assigning the th j job to the th i person in the form of composite relative degree ( ij d ) of similarity to ideal solution (maximum degree indicates most preferable combination), we can replace ij c by ij d in the classical AP in the maximization form and can solve it by any standard procedure to get the optimal assignment. In this paper the cost ij c has been considered to be intuitionistic fuzzy numbers (IFN) denoted by ij c ~ which involves the positive and the negative evidence for the membership of an element in a set. It is a more realistic description than using the crisp and fuzzy concept. The similarity measures of intuitionistic fuzzy sets have been used in this paper for determining the composite relative degree of similarity ij d . The notion of score function has also been used for validating the solution obtained by the composite relative similarity degree method. Numerical examples show the effectiveness of the proposed method for handling the Intuitionistic Fuzzy Assignment Problem (IFAP). Mathematical formulation of IFAP has been presented in this paper. Int. J. Pure Appl. Sci. Technol., 2(1) (2011), 1-18. 2