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Abstract-This paper introduces a new approach for estimating the uncertainty in the forecast through the construction of Triangular Fuzzy Numbers (TFNs). The interval of the proposed TFN presentation is generated from a Fuzzy logic based Lower and Upper Bound Estimator (FLUBE). Here, instead of the representing the forecast with a crisp value with a Prediction Interval (PI), the level of uncertainty associated with the point forecasts will be quantified by defining TFNs (linguistic terms) within the uncertainty interval provided by the FLUBE. This will give the opportunity to handle the forecast as linguistic terms which will increase the interpretability. Moreover, the proposed approach will provide valuable information about the accuracy of the forecast by providing a relative membership degree. The demonstrated results indicate that the proposed FLUBE based TFN representation is an efficient and useful approach to represent the uncertainty and the quality of the forecast.

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This version is available at https://strathprints.strath.ac.uk/60316/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output.  Abstract-This paper introduces an enhancement to linguistic forecast representation using Triangular Fuzzy Numbers (TFNs) called Enhanced Linguistic Generation andRepresentation Approach (ElinGRA). Since there is always an error margin in the predictions, there is a need to define error bounds in the forecast. The interval of the proposed presentation is generated from a Fuzzy logic based Lower and Upper Bound Estimator (FLUBE) by getting the models of forecast errors. Thus, instead of a classical statistical approaches, the level of uncertainty associated with the point forecasts will be defined within the FLUBE bounds and these bound can be used for defining fuzzy linguistic terms for the forecasts. Here, ElinGRA is proposed to generate triangular fuzzy numbers (TFNs) for the predictions. In addition to opportunity to handle the forecast as linguistic terms which will increase the interpretability, ElinGRA improved forecast accuracy of constructed TFNs by adding an extra correction term. The results of the experiments, which are conducted on two data sets, show the benefit of using ElinGRA to represent the uncertainty and the quality of the forecast.