TODIM and TOPSIS with Z-numbers

In this paper, we present an approach that can handle Z -numbers in the context of multi-criteria decision-making problems. The concept of Z -number as an ordered pair Z =( A , B ) of fuzzy numbers A and B is used, where A is a linguistic value of a variable of interest and B is a linguistic value of the probability measure of A . As human beings, we communicate with each other by means of natural language using sentences like “the journey from home to university most likely takes about half an hour.” The Z -numbers are converted to fuzzy numbers. Then 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. The results obtained show the feasibility of the approach.