I. Introduction
Type-2 fuzzy sets were initially proposed by Zadeh in 1975 [1]. Unlike type-1 fuzzy sets, whose membership values are precise numbers in [0, 1], membership grades of a type-2 fuzzy set are themselves type-1 fuzzy sets, and therefore, type-2 fuzzy sets offer an opportunity to model higher level uncertainty in the human decision-making process than type-1 fuzzy sets [2]–[5]. In a type-2 fuzzy inference system (T2FIS), some fuzzy sets used in the antecedent and/or consequent parts and each rule inference output are type-2 fuzzy sets. T2FISs have been used in many successful applications in various areas where uncertainties occur, such as in decision making [6]–[8], diagnostic medicine [9],[10], signal processing [11] [12], traffic forecasting [13], mobile robot control [14], pattern recognition [15]–[17], intelligent control [18] [19], and ambient intelligent environments[20].