# IJPAM: Volume 85, No. 4 (2013)

**ENUMERATION TECHNIQUE FOR SOLVING**

LINEAR FUZZY SET COVERING PROBLEM

LINEAR FUZZY SET COVERING PROBLEM

^{1}, Rashmi Gupta

^{2}

^{1}Department of Mathematics

Deen Dayal Upadhyaya College

University of Delhi

Delhi, 110015, INDIA

^{2}Department of Mathematics

University of Delhi

Delhi, 110007, INDIA

**Abstract. **In this paper a method for solving linear
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 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 set covering problem is suggested. In order to
defuzzify the problem the concept of vector ranking function is given and for obtaining efficient solution to the
problem, an algorithm is constructed with a weighted sum approach.An example is illustrated to demonstrate the correctness of the proposed solution algorithm.

**Received: **December 26, 2011

**AMS Subject Classification: **

**Key Words and Phrases: **set covering, fuzzy number, vector ranking function

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**DOI: 10.12732/ijpam.v85i4.2**

International Journal of Pure and Applied Mathematics

**How to cite this paper?****Source:****ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2013

**Volume:**85

**Issue:**4