The fuzzy saw and fuzzy TOPSIS procedures based on ordered fuzzy numbers

In this paper, two new techniques, linguistic fuzzy simple additive weighting (FSAW) and linguistic fuzzy technique for order of preference by similarity to the ideal solution (FTOPSIS) based on ordered fuzzy numbers (OFN) are presented. Although the linguistic fuzzy approach is discussed in the literature, there is no research on the applications of OFN to fuzzy multi-criteria decision making problems. The proposed methods extend the FSAW and FTOPSIS techniques. Since decision data are often vague and imprecise, linguistic variables represented by ordered fuzzy numbers are used to rate the alternatives with respect to each criterion. We have provided the theoretical foundations of this approach as well as numerical examples to illustrate its applications. The evaluations of alternatives are given by linguistic expressions, in which linguistic terms have to be quantified on the previously determined scale of values. In particular, we focus on the problem of extending the scale of values used in evaluating the criteria to take into account intermediate values, such as: “more than2” or “less than3”, together with “2” and “3”.