A Type-3 Fuzzy Logic System with Uncertainty Bound Type-Reduction and Optimized Secondary Memberships and Level of Alpha-Cuts

Recently interval type-3 (IT3) fuzzy logic systems (FLSs) are applied for various high-noisy problems. However, in most presented IT3-FLSs: (1) To convert the output T3 fuzzy sets (FSs) into a crisp value just the simple weighted average type-reductions are used that these approaches weakness the main concept of IT3-FSs; (2) The secondary memberships and number, rule format, number of FSs and alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-cuts are constant in existing IT3-FLSs; (3) One of the main properties of IT3-FSs is that the upper bound (UB) and lower bound (LB) of the footprint of uncertainty (FOU) are fuzzy numbers. However, in existing FSs, it is hard to determine an uncertainty bound for UB and LB of FOU. In this paper, new type-reduction and a new learning technique are introduced. The main contributions are as follows. (1) A type-reduction based on the theorem of uncertainty bounds is developed. The suggested method has no iterative computations, and it is much closer to the Karnik-Mendel technique. (2) A new type-3 (T3) fuzzy set with triangular secondary membership, and simple interval fuzzy bounds for UB and LB of FOU is introduced and formulated. (3) A new self-structuring technique based on Invasive Weed Optimization (IWO) is suggested for optimizing rule numbers, the format of rules, the level of alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-cuts, the secondary membership, the center of FSs, and the rule parameters. (4) By several simulations on modeling of real-world data, applied control applications, and statistical analyses, the effectiveness of the schemed FLS and learning strategy is verified.