Fuzzy numbers

This paper evaluates and ranks the temporal dimensions, known as fourth dimension of urban design, of a number of places in a city by TOPSIS method. TOPSIS method is technique for order preference by similarity to ideal solution. TOPSIS is one of the renowned methods for classical multi-criteria decision-making (MCDM) problems that defines the positive ideal solution and negative ideal solution to maximize the benefit criteria and minimize the cost criteria. The best solution is a point that has the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution. Because of the vagueness of the input data, triangular fuzzy numbers are applied. In addition, Euclidian distance and a new positive and negative ideal solution are used in this paper. This technique is implemented in Marand, Iran to evaluate fifteen important places based on eight criteria of temporal dimensions. Closeness coefficient values verify the ranking order of fifteen important places, which is a vital decision for the urban managers.