Type-2 fuzzy linear systems

Najariyan, Marzieh; Mazandarani, Mehran; John, Robert

doi:10.1007/s41066-016-0037-y

Cited by 26 publications

(15 citation statements)

References 34 publications

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“…A comparison between the solutions obtained by the present method and by Najariyan et al 11 is also discussed in Table 1 to check the validation of the proposed method. Table 1 compares the results obtained by the current method and that by Najariyan et al 11 The solutions obtained by the present method are given in the second column of Table 1, and the solutions given in Najariyan et al 11 are mentioned in the third column. It's easy to see that both solutions are nearly identical.…”

Section: Numerical Examplesmentioning

confidence: 96%

Type‐2 fuzzy linear system of equations with application in static problem of structures

Mohapatra

Chakraverty

2022

Math Methods in App Sciences

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In this paper, a new method is proposed to solve type-2 fuzzy linear system of equations by converting the system into three interval linear systems and one crisp linear system of equations. In this work, three possible cases of type-2 fuzzy linear system is considered depending upon uncertainty (as type-2 fuzzy number) in right-hand side vector B, in co-efficient matrix Ã, and both in co-efficient matrix Ã as well as right-hand side vector B. Triangular perfect quasi type-2 fuzzy numbers are taken to propose the new method. The main significance of the proposed method is that it uses the arithmetic of interval theory, which makes this method easier to handle. Five numerical examples are solved to show the validation of the proposed technique. Further, two application problems related to 6-bar truss and rectangular sheet are encountered in type-2 fuzzy environment. Comparison among the results obtained by the present method and previously achieved results is also made in this work, which shows that the results are close enough and, in some cases, better bounds for the solution are obtained.

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Section: Numerical Examplesmentioning

confidence: 96%

Type‐2 fuzzy linear system of equations with application in static problem of structures

Mohapatra

Chakraverty

2022

Math Methods in App Sciences

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“…Type-2 fuzzy sets, as well as relevant techniques such as Ref. [34,40], are not necessary in this case.…”

Section: Semantics Of Ltwhs Based On Uniformly Distributed Domainmentioning

confidence: 99%

Linguistic terms with weakened hedges: A model for qualitative decision making under uncertainty

Wang

Zhang

Zeng

2018

Information Sciences

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When expressing the experts' opinions in qualitative decision making (QDM), linguistic hedges can be considered to modify the force expressed by a predefined linguistic term. If an expert is not sure to select one term, weakened hedges would be a natural way to express the uncertainty. This is usually implemented by using a hedge to modify the most possible term, like the expression "more or less good". To model the uncertainty implied by hedges in QDM, this paper presents a novel linguistic representational and computational model in which the linguistic expressions take the form of a weakened hedge and a linguistic term, which is named as linguistic term with weakened hedge (LTWH). The syntax of LTWHs is defined by a set of hedges and a set of linguistic terms. The semantics of a LTWH is determined, objectively, based on the semantics of the term and a similarity measure of the reference domain. Accordingly, the negation, order relations and some basic operations of LTWHs are defined. To illustrate the effectiveness of LTWHs in granular computing, the connection to some multi-granularity linguistic models is exploited and a process for unifying multi-granularity linguistic information is developed. The major contritions of this paper are: (1) The proposed model enables a new manner to express and operate uncertain linguistic information in QDM; (2) it possesses clear syntax and semantics and the computational results are very interpretable; and (3) the proposed solution of multi-granularity linguistic unification maintains the semantics of the original linguistic information.

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“…Takagi-Sugeno (T-S) systems are a kind of the fuzzy system introduced in Tanaka and Wang (2004) to facilitate the use of fuzzy system tools for some nonlinear systems. Because of the effective representation of a nonlinear system as a set of local linear models that are interpolated by nonlinear functions, T-S fuzzy methods have proved useful in a variety of problems (Ammar et al 2018;Tuan VLB, and Hajjaji 2018;Chaibi et al 2019;Naami et al 2019;Ejegwa 2020;Yang et al 2020;Saif et al 2020;Dutta and Doley 2021;Zhang and Huang 2021;Kchaou and Jerbi 2021;Ech-charqy et al 2020; D'Urso 2017; Najariyan et al 2017). Stability analysis and controller design can then be handled with this technique (Takagi and Sugeno 1985;Tanaka et al 1998) for nonlinear systems (Xie et al (2020)), by an equivalent combination of linear systems.…”

Section: Introductionmentioning

confidence: 99%

Design of robust control for uncertain fuzzy quadruple-tank systems with time-varying delays

et al. 2022

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The robust $$H_\infty$$ H ∞ observer-based control design is addressed here for non-linear Takagi-Sugeno (T-S) fuzzy systems with time-varying delays, subject to uncertainties and external disturbances. This is motivated by the quadruple-tank with time delay control problem. The observer design methodology is based on constructing an appropriate Lyapunov–Krasovskii functional (LKF) for an augmented system formed from the original and the delayed states. The bilinear terms are transferred to the linear matrix inequalities, thanks to a change of variables which can be solved in one step. Furthermore, by employing the $$\mathcal {L}_2$$ L 2 performance index, the adverse effects of persistent bounded disturbances is largely avoided. The proposed method has the advantage of relating the controller and Lyapunov function to both the original and delayed states. Then, the controller and observer gains are obtained simultaneously by solving these inequalities with off-the-shelf software (Yalmip/MATLAB toolbox). Finally, an application to a simulated quadruple-tank system with time delay is carried out to demonstrate the benefits of the proposed technique, showing a compromise between controller simplicity and robustness that outperforms previous approaches.

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Type-2 fuzzy linear systems

Cited by 26 publications

References 34 publications

Type‐2 fuzzy linear system of equations with application in static problem of structures

Type‐2 fuzzy linear system of equations with application in static problem of structures

Linguistic terms with weakened hedges: A model for qualitative decision making under uncertainty

Design of robust control for uncertain fuzzy quadruple-tank systems with time-varying delays

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