General Type-2 Fuzzy Inference Systems: Analysis, Design and Computational Aspects

Lucas, Luís A.; Centeno, Tania Mezzadri; Delgado, Myriam Regattieri

doi:10.1109/fuzzy.2007.4295522

Cited by 71 publications

(44 citation statements)

References 17 publications

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“…As such, the cylindrical extension of F s (x ) can be seen as a copy of F s (x ) for every g ∈ G. 3) In a Multiple-Input-Single-Output (MISO) FLS, the inferred output µB S (g) of each rule s is computed as follows [7]:…”

Section: Fuzzy Inference Enginementioning

confidence: 99%

“…Coupland and John [4] have presented a geometric representation of general type-2 sets, and, recently, other forms of representation have been introduced, where Mendel and Liu [5], [6] have put forward a representation based on alpha planes, while Wagner and Hagras [9] have introduced the zSlices-based representation. Furthermore, several other advances have been made in trying to reduce the complexity associated with general type-2 fuzzy systems [2], [7], [8], [11]. Coupland et al [16] have investigated the potential of general type-2 FLSs in robot control.…”

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confidence: 99%

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Toward General Type-2 Fuzzy Logic Systems Based on zSlices

Wagner

Hagras

2010

IEEE Trans. Fuzzy Syst.

370

215

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Abstract-Higher order fuzzy logic systems (FLSs), such as interval type-2 FLSs, have been shown to be very well suited to deal with the high levels of uncertainties present in the majority of real-world applications. General type-2 FLSs are expected to further extend this capability. However, the immense computational complexities associated with general type-2 FLSs have, until recently, prevented their application to real-world control problems. This paper aims to address this problem by the introduction of a complete representation framework, which is referred to as zSlicesbased general type-2 fuzzy systems. The proposed approach will lead to a significant reduction in both the complexity and the computational requirements for general type-2 FLSs, while it offers the capability to represent complex general type-2 fuzzy sets. As a proof-of-concept application, we have implemented a zSlicesbased general type-2 FLS for a two-wheeled mobile robot, which operates in a real-world outdoor environment. We have evaluated the computational performance of the zSlices-based general type-2 FLS, which is suitable for multiprocessor execution. Finally, we have compared the performance of the zSlices-based general type-2 FLS against type-1 and interval type-2 FLSs, and a series of results is presented which is related to the different levels of uncertainty handled by the different types of FLSs.Index Terms-General type-2 fuzzy logic systems (FLSs), type-2 FLSs, zSlices.

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Section: Fuzzy Inference Enginementioning

confidence: 99%

mentioning

confidence: 99%

Toward General Type-2 Fuzzy Logic Systems Based on zSlices

Wagner

Hagras

2010

IEEE Trans. Fuzzy Syst.

370

215

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“…Lucas et al [14] have proposed first computing the centroids of vertical slices and then computing the centroid of the resulting function. Although ad hoc, this is a rather novel idea.…”

Section: Recent Work On Centroid Trmentioning

confidence: 99%

“…Others suggest first developing a restricted T2 FLS in which all of the secondary membership functions (MFs) are symmetrical triangles [25]. While it is very tempting to immediately develop a full-blown T2 FLS, to do so is fraught with computational difficulties (e.g., how to compute set theoretic and arithmetic operations and perform type-reduction (TR) for general T2 fuzzy sets (FSs) are active areas of research [1], [5]- [7], [12], [14], [20], [26]). Even developing a restricted T2 FLS has similar problems, although approximations for set theoretic operations and TR are possible.…”

Section: Introductionmentioning

confidence: 99%

On new quasi-type-2 fuzzy logic systems

Mendel¹,

Liu²

2008

2008 IEEE International Conference on Fuzzy Systems (IEEE World Congress on Computational Intelligence)

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Abstract-This paper provides an answer to the question that the type-2 fuzzy logic community is now asking: "What comes after interval type-2 fuzzy logic systems (IT2 FLSs)?" It demonstrates, through a geometrical understanding of the type-reduced set, that logical next steps in the progression from type-1 to interval type-2 to type-2 FLSs are quasi-T2 FLSs, either an interconnection of a T1 FLS and an IT2 FLS, or an interconnection of two IT2 FLSs, in which both FLSs are designed simultaneously. The quasi-T2 FLSs overcome the computational difficulties that are associated with set theoretic operations and type-reduction (TR) for general T2 FSs and FLSs, because all set theoretic operations can be performed as in existing T1 or IT2 FLSs, and because TR for an IT2 FLS can be performed using existing KM Algorithms.

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“…3. The vertical slice centroid type-reducer (VSCTR) which was initially proposed by John [25] then detailed by Lucas et al [33] . It does not calculate the union for all the embedded sets involved in the general type-2 fuzzy sets.…”

Section: The Choice For the Defuzzification Methodsmentioning

confidence: 99%

Learning of interval and general type-2 fuzzy logic systems using simulated annealing: Theory and practice

Almaraashi

John

Hopgood

et al. 2016

Information Sciences

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a b s t r a c tThis paper reports the use of simulated annealing to design more efficient fuzzy logic systems to model problems with associated uncertainties. Simulated annealing is used within this work as a method for learning the best configurations of interval and general type-2 fuzzy logic systems to maximize their modeling ability. The combination of simulated annealing with these models is presented in the modeling of four benchmark problems including real-world problems. The type-2 fuzzy logic system models are compared in their ability to model uncertainties associated with these problems. Issues related to this combination between simulated annealing and fuzzy logic systems, including type-2 fuzzy logic systems, are discussed. The results demonstrate that learning the third dimension in type-2 fuzzy sets with a deterministic defuzzifier can add more capability to modeling than interval type-2 fuzzy logic systems. This finding can be seen as an important advance in type-2 fuzzy logic systems research and should increase the level of interest in the modeling applications of general type-2 fuzzy logic systems, despite their greater computational load.

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General Type-2 Fuzzy Inference Systems: Analysis, Design and Computational Aspects

Cited by 71 publications

References 17 publications

Toward General Type-2 Fuzzy Logic Systems Based on zSlices

Toward General Type-2 Fuzzy Logic Systems Based on zSlices

On new quasi-type-2 fuzzy logic systems

Learning of interval and general type-2 fuzzy logic systems using simulated annealing: Theory and practice

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