Executive summaries of uncertain values close to the gain/loss threshold - a linguistic modelling perspective

Abstract In this paper we propose a novel method for the assessment of linguistic approximation of fuzzy outputs of decision-support and evaluation models in the presence of thresholds. The method provides graphical and numerical summaries of performance of different distance/similarity measures in combination with various linguistic scales in the process of assigning linguistic labels to the outputs of expert systems and decision-support models. We assume the existence of a specific threshold on the output scale that splits the outputs in two categories, i.e. gains/losses, acceptable/unacceptable values, better/worse than average values etc. This way a framing of the outputs can be obtained by labelling them linguistically. We consider numerical outputs in monetary units and assume zero to be the threshold value, splitting the universe into gains and losses. Based on a numerical analysis and yet without the knowledge of the most fitting linguistic label, the proposed analytical method is able to identify the cases where a clearly incorrect label is assigned (a loss label for a gain an/or vice versa) and hence the combinations of linguistic scales and distance/similarity measures of fuzzy numbers not to be used for the given purpose. We can also analyze specific features of some similarity/distance and linguistic scale combinations. The proposed method and its outputs is intended for the design of such expert systems and decision-support models, where a linguistic level of communicating the results to the users of these models is of importance, e.g. for the creation of executive summaries of outputs of mathematical models and results of financial data analyses. The method brings together the mathematical analysis of the linguistic approximation tools and the behavioral aspect of framing of the outputs e.g. as gains or losses prior to the final decision-making step. This way it provides much need guidance for the selection of reasonable distance/similarity measures of fuzzy numbers and reasonable linguistic scale for linguistic approximation. As such it is a useful tool for the design of system-user interfaces including a linguistic level of description.