Vague Set Theory Essay

Introduction
Researchers in economics, environmental science, social science, medical science, business, and many other fields deal daily with the complexities of modelling uncertain data. Classical methods are not always successful because the uncertainties appearing in these domains may be of various types. Fuzzy set theory [14], Intuitionistic fuzzy set theory [2], Vague set theory [8], and other mathematical tools are well- known and often useful approaches to describing uncertainity. However, all of these theories have their own difficulties which have been pointed out in [10]. Molodtsov suggested that the one reason for these difficulties may be due to the inadequacy of the parameterization tools of these theories, To overcome these difficulties, Molodtsov introduced the

Definition 1.9[8]The intersection of two vague sets A and B is a vague set C, written as , whose truth -membership and false -membership functions are related to those of A and B by , .
2 Vague soft sets Let U be a universe, E a set of parameters, V(U) the power set of vague set on U, and . The concept of a vague soft set is given by the following definition.
Definition 2.1[15]A pair is called a vague soft set over U,where is a mapping given by . In other words, a vague soft set over U is a parametrized family of vague set of the universe U. For , is regarded as the set of - approximate elements of the vague soft sets.
Example 2.1:Consider a vague soft set , where U is a set of six cars under the six consideration of a decision maker to purchase , which is denoted by , and E is a parameter set, where E = = {expensive; comfort; good mileage; cheap; good power steering; colour}. Suppose that

The vague soft set is a parameterized family of vague on U, and = { expensive