A probabilistic linguistic-based deviation method for multi-expert qualitative decision making with aspirations

Abstract

Probabilistic linguistic term set (PLTS) is a popular tool for modeling complex linguistic perceptions of decision-makers (DMs) and has gained successful applications in the field of multi-expert multi-criteria decision making (MEMCDM). In many probabilistic linguistic decision-making situations DMs are usually aspiration oriented in which the utilities of DMs do not depend on the absolute level of criteria values, but on the degree to which the criteria values match their aspirations levels. However, the aspirations of DMs are not considered in existing probabilistic linguistic decision making methods. One contribution of this paper is to introduce five probabilistic linguistic-based aspiration utility functions to take DMs’ aspirations into account. These functions can well describe the utility variation of DMs under different preference structures with the aspiration levels. Afterwards, the probabilistic linguistic-based indicator is defined to take into account the criteria weights represented by PLTSs, which greatly facilitates DMs to provide the weights of criteria, comparing with the use of crisp numbers. As the second contribution, we build a probabilistic linguistic-based deviation model to identify the decision results in MEMCDM. This model can achieve the goal that the decision results for group opinions are consistent with that for the individual DM’s opinions to the greatest extent. On the other hand, we also show with some counterexamples that the existing probabilistic linguistic distance measures are unreasonable. We present an improving distance measure for PLTSs and show its desirable properties. The biggest advantage of the developed distance measure is that it not only considers the deviation between the proportion information of linguistic terms but also takes into account linguistic terms themselves in PLTS.