Enumeration Technique for Solving Linear Fractional Fuzzy Set Covering Problem

In this paper an enumeration technique for solving linear fractional fuzzy set covering problem is defined. Set covering problems belong to the class of 0-1 integer programming problems that are NP-complete. Many applications arises having the set covering problems, switching theory, testing of VLSI circuits and line balancing often take on a set covering structure. Linear fractional set covering problems involving coefficients in the objective function with some lack of precision are usual. To solve them several approaches have been proposed. In this paper a solution algorithm to fuzzy linear fractional set covering problem is suggested, in order to defuzzify the problem the concept of vector ranking function is presented further for obtaining efficient solution to the problem, a lexicographic approach is used. A linearization technique is used to obtain the optimal solution for crisp linear fractional set covering problem. An illustrative example is included to demonstrate the correctness of the proposed solution algorithm. AMS Subject Classification: 05C72