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Interval type-2 fuzzy logic systems (IT2 FLSs) have demonstrated better abilities to handle uncertainties than their type-1 (T1) counterparts in many applications; however, the high computational cost of the iterative Karnik-Mendel (KM) algorithms in type-reduction means that it is more expensive to deploy IT2 FLSs, which may hinder them from certain cost-sensitive real-world applications. This paper provides a comprehensive overview and comparison of three categories of methods to reduce their computational cost. The first category consists of five enhancements to the KM algorithms, which are the most popular type-reduction algorithms to date. The second category consists of 11 alternative type-reducers, which have closed-form representations and, hence, are more convenient for analysis. The third category consists of a simplified structure for IT2 FLSs, which can be combined with any algorithms in the first or second category for further computational cost reduction. Experiments demonstrate that almost all methods in these three categories are faster than the KM algorithms. This overview and comparison will help researchers and practitioners on IT2 FLSs choose the most suitable structure and type-reduction algorithms, from a computational cost perspective. A recommendation is given in the conclusion.