House Selection using Fuzzy Distance of Trapezoidal Fuzzy Numbers

Whether it is reasonable to define a crisp distance between fuzzy objects is a natural question to us. If the numbers themselves are not certain, how can the distance between them be certain? In this paper, we consider different approaches to compute the distance between fuzzy numbers, and introduce a fuzzy value distance by using graded mean integration representation of trapezoidal fuzzy numbers and the span of the fuzzy numbers. Then we also discuss the distance of the linguistic data "greater or less than x", or "about x". The result shows that it is more reasonable to say that "the fuzzy distance of about 3 and about 7 is about 4, not 4". Here, we apply the proposed fuzzy distance concept to make house buying decision. The idea is that the buyer is looking for a house that is the minimal distance to her/his ideal house comparing with other houses. Suppose the buyer considers m attributes (price, district, area, location... etc.) for buying a house, and assigns the weight and ideal value of each attribute. Then we use the sum of the m-weighted fuzzy distance of the attributes for the buyer and the corresponding attributes of the house. The graded mean integration representation of the sum is used to rank the order of the house in selling queue. The real estate sales person can introduce the suitable houses to the buyer in the ranking order of the houses. Through this process, the buyer can find a satisfactory house much quicker. However, the concept of fuzzy distance can be applied in solving many other decision problems.