Aggregation of unbalanced fuzzy linguistic information in decision problems based on Type-1 OWA operator

Information aggregation is a key task in any group decision making problem. In the fuzzy linguistic context, when comparing two alternatives, it is usually assumed that assessments belong to linguistic term sets of symmetrically distributed labels with respect to a central label that stands for the indifference state. However, in practice there are many situations whose nature recommends their modelling using not symmetric linguistic term sets, and therefore formal approaches to deal with sets of unbalanced linguistic labels in decision making are necessary to be appropriately developed. In literature, the linguistic hierarchy methodology has proved successful when modelling unbalanced linguistic labels using an ordinal approach in their representation. However, linguistic labels can be modelled using a cardinal approach, i.e. as fuzzy subsets represented by membership functions. Obviously, the linguistic hierarchy methodology is not appropriate in these cases. In this contribution, a Type-1 OWA approach is proposed to deal with the aggregation step of the resolution process of a group decision making problem with unbalanced linguistic information modelled using a cardinal approach. The Type-1 OWA operator aggregates fuzzy sets and uses whole membership functions to compute the aggregated output fuzzy sets. The application of the Type-1 OWA approach to an example where the linguistic hierarchy approach was applied before will provide us an opportunity to compare the aggregated results obtained in both cases. Following the defuzzification of the Type-1 OWA aggregated values, it can be concluded that both methodologies are equivalent. The use of the Type-1 OWA approach in this decision making context does not require building linguistic hierarchies while at the same time allows a fully exploitation of the fuzzy nature of linguistic information.