Novel Weighted Averages versus Normalized Sums in Computing with Words

In this paper, some properties of Novel Weighted Averages that are related to the concepts of possibility theory are examined. It is shown that Novel Weighted Averages have certain interpretations in terms of addition of interactive interval or fuzzy constraints. To do this, alternative forms of Novel Weighted Averages are provided. In particular, an alternative form of Novel Weighted Averages represented by the Extension Principle is determined. It is shown that, when fuzzy set models of words are obtained by collecting data from subjects in a Computing with Words setting, interactive addition of fuzzy sets is not a well-defined method, and the optimization problems related to it may have no solutions, although interactive addition is recommended in the literature for solving multicriteria decision making problems and for dealing with uncertain probabilities. On the other hand, Novel Weighted Averages perform a specific normalization that guarantees that they always exist.