Application of modified fuzzy TOPSIS method for multicriteria decisions in civil engineering

In this paper is presented and applied one fuzzy TOPSIS method for the multicriteria ranking of objects for reconstruction and maintenance. At the beginning is given short review on the genesis and development of this method and described a TOPSIS procedure with crisp input data that constitute a decision matrix and weights of criteria. This procedure is illustrated by one simple numerical example. The necessity of presentation of these parameters as triangular fuzzy numbers due to impossibility of their precise determination or assessment in the practice. The exact expressions for the determination of these products of the decision matrix and weights coefficients as triangular fuzzy numbers, that authors of this paper are derived earlier, are given in the paper. For every alternative (the object) these parameters are assumed as random fuzzy numbers for which are determined generalised expected values, variances and standard deviations. From the normalised matrix of the expected values are determined expected ideal positive and ideal negative values. For every alternative are determined generalized expected distances and relative closenesses to the ideal positive and ideal negative solution. The ranking of alternatives is performed according to these values. Mathematical expressions for coefficients of investments distribution on the alternatives (objects) are proposed in the work. One example of ranking of the bridge structures according to the risk is given at the end of the work and formulated corresponding conclusions.