Simple Additive Weighting Method Equipped with Fuzzy Ranking of Evaluated Alternatives

Abstract

From the perspective of each evaluation criterion, any decision alternative is evaluated by means of trapezoidal ordered fuzzy numbers (TrOFN). This approach is justified in the way that some criteria are linguistically evaluated. In this paper, decision alternatives are evaluated using oriented fuzzy Simple Additive Weighting (OF-SAW) scoring function. The ranking of alternatives may be defined by means of a nonincreasing sequence of defuzzified values of a scoring function. Any defuzzification procedure distorts ordered fuzzy numbers in a way that information on imprecision and orientation is lost. This undermines the credibility of the determined alternatives' ranking. The main purpose of this paper is to avoid the defuzzification stage in the OF-SAW method. Thus, the OF-SAW method is equipped with fuzzy scoring order. This OF-SAW method is described as a negotiation scoring system. We study an empirical example of the OF-SAW application and rank some negotiation offers. Here, we focus on the effects of replacing the defuzzified scoring function by a fuzzy one. The obtained conclusions are generalized for the case of any decision alternatives.

Impact of the Orientation of the Ordered Fuzzy Assessment on the Simple Additive Weighted Method

“…Therefore, the number m(γ) will be used in comparing the individual g-SAW methods equipped with different scoring function γ ∈ F Tr A . In [15], the same approach was used for comparisons of individual OF-SAW methods with different initial preorder. along with the increase in the number ( ) of elements of the sequence ( ) ( ) ( ) , the amount of information described by the partially ordered set , ( ) grows.…”

“…Therefore, the number ( ) will be used in comparing the individual g-SAW methods equipped with different scoring function ∈ . In [15], the same approach was used for comparisons of individual OF-SAW methods with different initial preorder. The main goal of this chapter is to study the effects of replacing the OF-SAW method by the d-SAW method.…”

“…Any induced preorder may be used as order (42). An example of induced partial order is faithful order BE IND introduced in [15] for OF-SAW method.…”

“…In this way, we lose a lot of information about evaluated negotiation offers. Thus, in [15], considered negotiation offers are arranged by initial preorder obtained without a defuzzification procedure.…”

“…In [14], the OF-SAW method is modified in a way that is compatible with revised theory of OFNs [12]. In [15] it is justified that the OF-SAW method equipped with the fuzzy initial preorder is significantly better than the OF-SAW methods equipped with any crisp initial preorder outlined with the use of any defuzzification method. There it is shown that the use of defuzzification procedures can totally blur the true picture of a real order of decision alternatives.…”