An approach for parameterized shadowed type-2 fuzzy membership functions applied in control applications

  • Patricia Melin
  • Emanuel Ontiveros-Robles
  • Claudia I. Gonzalez
  • Juan R. Castro
  • Oscar CastilloEmail author
Methodologies and Application


At present time, general type-2 fuzzy logic provides better uncertainty modeling when compared to interval type-2 fuzzy logic, and this has been shown with the improvement in the performance of fuzzy logic controllers and fuzzy edge detectors. However, higher computational cost represents a limitation for many applications and implementation platforms, and it is because of this that the computational cost reduction is the main goal of this paper. The aim of this work is to model a GT2 FLS based on shadowed type-2 fuzzy sets (ST2 FS) and apply this approach to control problems. The ST2 FS consists of approximating the secondary membership function by shadowed sets and is because of this, that we present an analytic approach to obtain the shadowed set for triangular and Gaussian membership functions for any parameters. Based on this, we achieve a representation of the ST2 FS as a parameterized function, facilitating its implementation. The results are compared against the performance when a generalized type-2 fuzzy inference system is approximated using α-planes for control applications.


General type-2 fuzzy sets Shadowed sets Interval type-2 fuzzy sets Shadowed type-2 fuzzy sets 


Compliance with ethical standards

Conflict of interest

All the authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Tijuana Institute of TechnologyTijuanaMexico

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