$\alpha$-Plane Representation for Type-2 Fuzzy Sets: Theory and Applications

Mendel, Jerry M.; Liu, Feilong; Zhai, Daoyuan

doi:10.1109/tfuzz.2009.2024411

Cited by 298 publications

(155 citation statements)

References 47 publications

Supporting

Mentioning

149

Contrasting

Unclassified

Order By: Relevance

“…There are some representations for type-2 fuzzy sets that have been proposed in the literature such as vertical-slice representation [36, p. 83] [38] , wavy-slice representation [38] , geometric representation [15] , alpha-planes [41] , alpha cuts [22] and Z-slices [45] . The most well-known representations among them are the vertical-slice and wavy-slice representations.…”

Section: Type-2 Fuzzy Sets and Systemsmentioning

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

View full text Add to dashboard Cite

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.

show abstract

Section: Type-2 Fuzzy Sets and Systemsmentioning

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

View full text Add to dashboard Cite

show abstract

“…Furthermore, it has been concluded by Hisdal [29] that increased fuzziness in a description means increased ability to handle inexact information in a logically correct manner. Recently, the introduction of zSlices [31] and alpha-planes [79] [87] has helped to bridge the gap caused by the complexity of the design and implementation of GT2 FSs.…”

Section: Linear General Type-2 Fuzzy Sets (Lgt2 Fss)mentioning

confidence: 99%

“…However, the equivalence between alpha-plane and zSlices representations has been proven in [80]. Accordingly, LGT2 FSs can also be represented using alpha-planes introduced by Liu [87] and Mendel et al [79].…”

Section: A Mathematical Definition Of the Lgt2 Fssmentioning

confidence: 99%

A Linear General Type-2 Fuzzy-Logic-Based Computing With Words Approach for Realizing an Ambient Intelligent Platform for Cooking Recipe Recommendation

Bilgin

Hagras

Helvert

et al. 2016

IEEE Trans. Fuzzy Syst.

View full text Add to dashboard Cite

Abstract-This paper addresses the need to enhance transparency in Ambient Intelligent Environments by developing more natural ways of interaction, which allow the users to communicate easily with the hidden networked devices rather than embedding obtrusive tablets and computing equipment throughout their surroundings. Ambient Intelligence vision aims to realize digital environments that adapt to users in a responsive, transparent and context aware manner in order to enhance users' comfort. It is therefore appropriate for employing the paradigm of 'Computing With Words' (CWWs), which aims to mimic the ability of humans to communicate transparently and manipulate perceptions via words. One of the daily activities that would increase the comfort levels of the users (especially people with disabilities) is cooking and performing tasks in the kitchen. Existing approaches on food preparation, cooking, and recipe recommendation stress on healthy eating and balanced meal choices while providing limited personalization features through the use of intrusive user interfaces. Herein, we present an application, which transparently interacts with users based on a novel CWWs approach in order to predict the recipe's difficulty level and to recommend an appropriate recipe depending on the user's mood, appetite and spare time. The proposed CWWs framework is based on Linear General Type-2 (LGT2) Fuzzy Sets, which linearly quantify the linguistic modifiers in the third dimension in order to better represent the user perceptions while avoiding the drawbacks of type-1 and interval type-2 fuzzy sets. The LGT2 based CWWs framework can learn from user experiences and adapt to them in order to establish more natural human-machine interaction. improvement when general type-2 fuzzy sets are used than when interval type-2 fuzzy sets are used instead. The quantitative and qualitative analysis both show the success of the system in providing a natural interaction with the users for recommending food recipes where the quantitative analysis shows the high statistical correlation between the system output and the users' feedback; and the qualitative analysis presents social science evaluation confirming the strong user acceptance of the system. Index Terms-ambient intelligence, computing with words, general type-2 fuzzy sets I. INTRODUCTIONhe recent years have witnessed a rapid increase in the miniaturization of computers which enabled to embed computing throughout our spaces in familiar objects such as home appliances (e.g. washing machines, refrigerators, etc.), portable devices (e.g. mobile phones, tablets, etc.), cars, etc. In addition, the advances in communications allowed such devices to be networked and connected to the Internet. Among the highlights of the connected and miniaturized devices bring to real life is the opportunity of customization and therefore personalization. Lately, it is getting more important to deliver personalized content in areas such as food planning which is becoming an important personal issue that affects the ...

show abstract

“…In 2008 Liu [9,22] proposed the α-planes representation. Via this technique a generalised type-2 fuzzy set is decomposed into a set of α-planes, which are horizontal slices akin to interval type-2 fuzzy sets.…”

Section: Definition 9 (Stratum [20]) Let T Be the Trs Of A Discretisementioning

confidence: 99%

The Structure of the Type-Reduced Set of a Continuous Type-2 Fuzzy Set

Greenfield¹,

Chiclana²

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

View full text Add to dashboard Cite

This paper is concerned with the structure of the type-reduced set (TRS) of the continuous type-2 fuzzy set, in both its interval and generalised forms. In each case the TRS structure is approached by first investigating the discretised set. The TRS of a continuous interval type-2 fuzzy set is shown to be a continuous straight line, and that of a generalised type-2 fuzzy set, a continuous, convex curve.

show abstract

$\alpha$-Plane Representation for Type-2 Fuzzy Sets: Theory and Applications

Cited by 298 publications

References 47 publications

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

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

A Linear General Type-2 Fuzzy-Logic-Based Computing With Words Approach for Realizing an Ambient Intelligent Platform for Cooking Recipe Recommendation

The Structure of the Type-Reduced Set of a Continuous Type-2 Fuzzy Set

Contact Info

Product

Resources

About