TODIM and TOPSIS with Z-numbers
  In this paper, we present an approach that is able to handle with Z-numbers in the context of Multi-Criteria Decision Making (MCDM) problems. Z-numbers are composed of two parts, the first one is a restriction on the values that can be assumed, and the second part is the reliability of the information. As human beings we communicate with other people by means of natural language using sentences like: the journey time from home to university takes about half hour, very likely. Firstly, Z-numbers are converted to fuzzy numbers using a standard procedure. Next, the Z-TODIM and Z-TOPSIS are presented as a direct extension of the fuzzy TODIM and fuzzy TOPSIS, respectively. The proposed methods are applied to two case studies and compared with the standard approach using crisp values. Results obtained show the feasibility of the approach. In addition, a graphical interface was built to handle with both methods Z- TODIM and Z-TOPSIS allowing ease of use for user in other areas of knowledge. 
R.A. Krohling, Artem dos Santos, A.G.C. Pacheco
cs.AI