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In this paper, bondage and non-bondage set of a fuzzy graph are discussed. The bondage number b(G) and non-bondage number b n (G) of a fuzzy graph G are defined. The upper bound for both b(G) and b n (G) are given. Also some results on b(G) and b n (G) are discussed. The exact values of b(G) and b n (G) are determined for several classes of fuzzy graphs.

programming models and there application in real world has been discussed. The reason behind that is the simplicity and In the process of finding the solutions of real life easy computation with the models. problems decision makers always remain in confusion that the data they are using to solve there problems are exact or not. InThe task of developing a general theory of decisionsolving a linear programming problem, optimize Z = C T making in a fuzzy environment is one of very considerable magnitude and complexity. First approach to decision making subject to (Ax)j . bi, Vi, x>2 0 there may be confusion about in a fuzzy environment was introduced by Bellman and Zadeh the values of cT, b and A and due to confusion for these [1]. Zimmermann [17] presented the application of fuzzy values the confusion may also exist for the value of objective linear programming approaches to the linear vector maximum function. Several researchers have used fuzzy set theory for problem which had shown that solutions obtained by fuzzy linear programming problems but this theory could not tackle linear programming are always efficient solutions. Chanas [3] the confusion part of the data. There is no method in the had proposed technique to solve fuzzy linear programming literature for solving linear programming problems in the using parametric programming which provides useful situation when decision makers are in confusion about the information to decision maker for taking decision. Delgado et exactness of the data. To incorporate this confusion concept of al. [8] gave a general model from which each particular fuzzy vague sets [9] have been used. linear programming model can be deduced. In this paper, we have extended the idea of fuzzy In real life, a person may consider that an object belongs linear programming by vague linear programming and to a set to a certain degree but it is possible that he is not sure proposed a new method to solve linear programming problems . t by~~~~~~ãsumn tha th deiso maer ar ofsdoloh about it. In other words there may be hesitation or uncertainty vyalsuesi thand therdecisono conusi areondfunerinty for the about the membership degree. In fuzzy set theory there is no means to incorporate that hesitation in the membership degree. values of cTand A. To incorporate that hesitation in the membership degree Gau To explain the advantage of proposed method, a and Buehrer [9] proposed the concept of vague set. Vague sets numerical example is solved. Obtained results are explained. can easily deal with this hesitation. Chen [4, 5, 6] presented the measures of similarity between vague sets and proposed a Keywords Vague sets; Fuzzy sets; Fuzzy Mathematical new method for analyzing fuzzy system reliability based on programming vague set theory [7]. Kumar et al. [10] extended the concept of triangular vague set [7] by idea of trapezoidal vague set and 1. Introductionproposed a new method for analyzing the fuzzy system reliability. Any linear programming model representing real-world situations involves a lot of param...