Interval Type II Fuzzy Number Generation From Data Set Applied to Sedation Stage Classification

Introduction

The one of the way of the representing the uncertain, incomplete information in decision-making, data mining, pattern recognition is using fuzzy numbers and several fuzzy sets theories have been introduced to handle imprecise and uncertain or incomplete information (Ban and Coroianu, 2012; Torres-Blanc et al., 2018, Cheng et al., 2008).

There are various studies where classification, pattern recognition, fuzzy modelling based on the data sets are considered. For example, Shahmoradi and Shouraki (2018) introduced a novel fuzzy sequential pattern recognition tool and they applied this method in speech and handwriting recognition. Solanki and Pandey (2019) focused on predominant instrument recognition and proposed a deep convolution neural network framework where an arbitrary number of instruments from an audio signal with variable length is estimated. Sousa et al. (2019) worked on classification of potential fire outbreaks and offered a fuzzy modeling approach based on thermal images. The evaluations of membership functions from the data set is one of the topics in the classification problems, pattern recognition, fuzzy modeling (Kaufmann et al. 2015, Choi and Rhee, 2009, Bouhentala et al., 2018). For example, Kaufmann et al. (2015) proposed a method for the membership function generation from the data for inductive fuzzy classification. Choi and Rhee (2009) introduced three novel interval type-2 fuzzy membership function generation methods, focusing on heuristics, histograms, and interval type 2 fuzzy C-means. Yang and Bose (2006) mentioned about the importance of the automatic fuzzy membership generation for the pattern recognition and introduced a scheme for the generation of fuzzy membership function by using self-organizing future map. Nasibov and Peker (2011) focused on the generation of the membership function of exponential fuzzy number and evaluated the formulas of unknown parameters based on a minimization problem where the frequencies were used. The offered method was applied on a classification problem dealing with the bispectral index scores (BIS).

There are other various methods focused on the membership function generation. For example, Muhuri and Shukla (2017), underlined the advantages of semi elliptic membership function and introduced a technique for Type-2 semi elliptic membership function. Liao (2017) proposed an extended interval type-2 membership function and a procedure of the generation of a set of them. Chen et al. (2009) introduced an approach that processes the items in a divide-and-conquer strategy to find the minimum supports, membership functions, and fuzzy association rules. Medasani et al. (1998) focused on an overview of membership function techniques for the pattern recognition and mentioned about the membership function based on the perception, heuristic methods, histogram-based methods, transformation of the probability distributions to the possibility distributions, and so on.

Although the Type I fuzzy sets are often used in the works for mapping the uncertainty in mathematical form, sometimes Type II fuzzy numbers are needed in order to be handle the uncertainty originated from many sources (Shukla and Muhuri, 2019).