A compensatory model for computing with words under discrete labels and incomplete information

In this paper, we propose a compensatory model for computing with words under discrete linguistic labels and incomplete weight information. This particular model will be useful in the context of multi-attribute decision making problems characterized by discrete linguistic attribute evaluations and partially-known weight information. This group of multi-attribute decision making problems may be modeled as multi-objective programs by using the concept of satisfactory degree, defined for each decision alternative under study. We derive a compensatory program which can be substituted for such multi-objective models. Further, we prove that the optimal solution of this compensatory program is a Pareto solution to the original multi-objective model. To show the working principles of this approach, we illustrate the procedure on two numerical examples from the published literature. We then analyze a concrete example we developed for illustrating the real-life meanings of several model constructs and managerial connotations of the results obtained by using this new approach.