Method for Measurement of Uncertainty Applied to the Formation of Interval Type-2 Fuzzy Sets Mauricio A. Sanchez, Oscar Castillo and Juan R. Castro Abstract This paper proposes a new method for directly discovering the uncer- tainty from a sample of discrete data, which is then used in the formation of an Interval Type-2 Fuzzy Inference System. A Coef ficient of Variation is used to measure the uncertainty on a finite sample of discrete data. Based on the maximum possible coverage area of the Footprint of Uncertainty of Gaussian membership functions, with uncertainty on the standard deviation, which then are modified according to the found index values, obtaining all antecedents in the process. Afterwards, the Cuckoo Search algorithm is used to optimize the Interval Sugeno consequents of the Fuzzy Inference System. Some sample datasets are used to measure the output interval coverage. 1 Introduction Uncertainty, as it is currently perceived, is still something of a mistified topic. Being defined as something that is doubtful or unknown, in which by nature cannot be directly measured, therefore showing a first problem in making use of it. Although by nature, uncertainty is an unknown, it has not stopped engineers, scientists, mathematicians, etc. from using it. That is, although directly not known, an approximate of it can be modeled and used, improving the models in which it is used. By using uncertainty in a model, that model will improve its resilience, thus obtaining a better model in the end. M.A. Sanchez  J.R. Castro Autonomous University of Baja California, Tijuana, Mexico e-mail: mauricio.sanchez@uabc.edu.mx J.R. Castro e-mail: jrcastror@uabc.edu.mx O. Castillo (&) Tijuana Institute of Technology, Tijuana, Mexico e-mail: ocastillo@hafsamx.org © Springer International Publishing Switzerland 2015 P. Melin et al. (eds.), Design of Intelligent Systems Based on Fuzzy Logic, Neural Networks and Nature-Inspired Optimization, Studies in Computational Intelligence 601, DOI 10.1007/978-3-319-17747-2_2 13