Fuzzy Information and Engineering

Abuelenin, Sherif M.; Abdel-Kader, Rabab F.

2022 Fuzzy Information and Engineering

doi: 10.1080/16168658.2022.2152922

Interval type-2 fuzzy logic systems (IT2 FLSs) have a wide range of applications due to their ability to handle uncertainties. A drawback of IT2 FLSs is that their different representations generally suffer from high computational complexity. This paper discusses the representation of IT2 FLSs in closed mathematical form. The proposed form provides an easy, computationally efficient method to implement IT2 FLSs. Additionally, the closed-form is preferred in control systems. We also discuss the use of the proposed method in balancing an inverted pendulum on a cart, a common problem in control theory. Simulation results are provided to compare the performance of the proposed closed-form systems against the performance of other IT2 FLSs. The results confirm that the introduced IT2 representations perform closely to their more computationally complex counterparts.

Salari, Mehrnoosh; Ghanbari, Reza; Ghorbani-Moghadam, Khatere

2022 Fuzzy Information and Engineering

doi: 10.1080/16168658.2022.2152950

Recently, Ghanbari and Mahdavi-Amiri [2015, Soft Computing] have proposed a model to characterize exact solutions and presented an algorithm to compute approximate solutions. Here, inspired by Ghanbari and Mahdavi-Amiri, we show that solving fuzzy LR interval linear systems is equivalent to solving fuzzy LR linear systems (FLRLSs). Then we develop some necessary and sufficient conditions for the solvability of FLRLSs. We then provide a new general concept for an approximate solution when an FLRLS lacks a solution. To compute an approximate solution, we propose an algorithm using a least squares method. Finally, we show the appropriateness of our proposed approximate solution recently introduced numerically.

Salari, Mehrnoosh; Ghanbari, Reza; Ghorbani-Moghadam, Khatere

2022 Fuzzy Information and Engineering

doi: 10.1080/16168658.2022.2140479

We first investigate the solvability conditions of fuzzy LR interval algebraic linear systems with fuzzy LR interval coefficient matrix and fuzzy LR interval hand-right vector. Next, we compute the solution of FLRIALS (fuzzy LR interval algebraic linear systems) using the least squares approach. We show that solving the least squares problem is equivalent to solving a quadratic programming problem. Indeed, instead of the FLRIALS, this quadratic programming has a non-convex constraint. Thus, we relax this constraint to have a convex search space. Then, from the solution obtained from quadratic programming on convex search space, we give an approximate solution for FLRIALS.