A New Method for the Design of Interval Type-3 Fuzzy Logic Systems With Uncertain Type-2 Non-Singleton Inputs (IT3 NSFLS-2): A Case Study in a Hot Strip Mill

Abstract

This paper presents a new method for the construction and training of interval type-3 fuzzy logic systems whose inputs are uncertain type-2 non-singleton numbers (IT3 NSFLS-2). The proposed methodology is divided in two processes: 1) The novel construction of the structure of the IT3 NSFLS-2 systems based on: a) The level-alpha-0 of the interval type-2 fuzzy logic system (IT2-alpha-0 FLS), and on b) The secondary membership function using Gaussian modeling to construct each rule of the alpha-k fuzzy rule base (FRB), the firing intervals of the antecedent and the centroids of the consequent, and 2) The training methodology based on gradient descent algorithm to train the antecedent and consequent parameters of the alpha-0 FRB. The primary membership functions (MF) of the antecedents of the IT3 NSFLS-2 system are modeled as Gaussians with uncertain means and with common standard deviation. The proposal was applied and tested with the prediction of a transfer bar's surface temperature in an industrial hot strip mill facility located in Monterrey México. The modeling results show that the proposal supports the stability required by this critical process and shows the best performance when compared with similar methods.INDEX TERMS General type-2 fuzzy systems, gradient descent algorithm, hot strip mill, interval type-2 fuzzy systems, interval type-3 fuzzy systems, temperature prediction, type-2 non-singleton inputs.

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“…Type-3 fuzzy logic systems (T3 FLS) make it possible to model the effects of uncertainties and to minimize them by optimizing the parameters during the learning process. They can approximate any real continuous function on a compact set to arbitrary accuracy [47,48].…”

“…1. By the math model used in the consequent section [47][48][49]: (a) Mamdani, with a single value [ 𝑐 ], or interval value 𝑐 , 𝑐 , (b) Takagi-Sugeno-Kang (TSK), a linear function of 𝑝 + 1 𝑥 inputs 𝐶 + 𝐶 𝑥 + ⋯ 𝐶 𝑥 + ⋯ + 𝐶 𝑥 , where 𝐶 is a numerical value of the rule 𝑖, and (c) Takagi-Sugeno (TS), with a nonlinear function of the state space 𝑥 (𝑡) = 𝐴 𝑥(𝑡) + 𝐵 𝑢(𝑡), where 𝑥(𝑡) is the state vector, 𝐴 is the system matrix, 𝐵 is the input matrix, and 𝑢(𝑡) is the input vector at time (𝑡).…”

“…2. By the math model used as a primary membership function (MF) [47][48][49]: (a) type-1 (T1), with a single primary MF, and (b) type-2 (T2), with a double primary MF. 3.…”