A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets

Wu, Dongrui; Mendel, Jerry M.

doi:10.1016/j.ins.2008.12.010

Cited by 322 publications

(150 citation statements)

References 42 publications

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“…Equation (6) yields a value of 1 when the fuzzy sets are identical and 0 when they are completely disjoint. Note that the Jaccard similarity measure has been extended for interval type-2 [15], [16] and general type-2 fuzzy sets [17]; though, this is not discussed here.…”

Section: B Jaccard Similarity Measurementioning

confidence: 99%

Novel similarity measure for interval-valued data based on overlapping ratio

Kabir

Wagner

Havens

et al. 2017

2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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Abstract-In computing the similarity of intervals, current similarity measures such as the commonly used Jaccard and Dice measures are at times not sensitive to changes in the width of intervals, producing equal similarities for substantially different pairs of intervals. To address this, we propose a new similarity measure that uses a bi-directional approach to determine interval similarity. For each direction, the overlapping ratio of the given interval in a pair with the other interval is used as a measure of uni-directional similarity. We show that the proposed measure satisfies all common properties of a similarity measure, while also being invariant in respect to multiplication of the interval endpoints and exhibiting linear growth in respect to linearly increasing overlap. Further, we compare the behavior of the proposed measure with the highly popular Jaccard and Dice similarity measures, highlighting that the proposed approach is more sensitive to changes in interval widths. Finally, we show that the proposed similarity is bounded by the Jaccard and the Dice similarity, thus providing a reliable alternative.

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Section: B Jaccard Similarity Measurementioning

confidence: 99%

Novel similarity measure for interval-valued data based on overlapping ratio

Kabir

Wagner

Havens

et al. 2017

2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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“…We apply local similarity measure to each corresponding feature-value pair of the problem parts of the cases under comparison. In implementation, we use Jaccard similarity measure (as it is proven to be better than other similarity measures for IT2 FSs [67]) formulated as follows [67]:…”

Section: Granulation In the Proposed Cwws Frameworkmentioning

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.

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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 ...

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“…Though additional measures exist, the measures presented in this section are the most common and provide a good overview of the interval T2 SMs available. A more detailed comparison of these and other interval T2 SMs has been presented by Wu and Mendel in [11] and [8]. 1) Zeng and Li: Zeng and Li [7] proposed the following SM for interval T2 FSs,Ã andB, in a discrete universe of discourse:…”

Section: B Similarity Measuresmentioning

confidence: 99%

“…Examples of trapezoidal and triangular FSs are presented, however the SM will work for any type of sets. These demonstrations use the SMs by Zeng and Li, Jaccard, Gorzałczany and Bustince; as defined in (6), (7), (8) and (9), respectively. Demonstration 2 employs the zSlices-based SM on trapezoidal general T2 FSs that are based on the interval T2 FSs used in demonstration 1.…”

Section: B Demonstrations Of Zslices-based General Type-2 Approachesmentioning

confidence: 99%

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Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets

McCulloch

Wagner

Aickelin

2013

2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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Abstract-Similarity measures provide one of the core tools that enable reasoning about fuzzy sets. While many types of similarity measures exist for type-1 and interval type-2 fuzzy sets, there are very few similarity measures that enable the comparison of general type-2 fuzzy sets. In this paper, we introduce a general method for extending existing interval type-2 similarity measures to similarity measures for general type-2 fuzzy sets. Specifically, we show how similarity measures for interval type-2 fuzzy sets can be employed in conjunction with the zSlices based general type-2 representation for fuzzy sets to provide measures of similarity which preserve all the common properties (i.e. reflexivity, symmetry, transitivity and overlapping) of the original interval type-2 similarity measure. We demonstrate examples of such extended fuzzy measures and provide comparisons between (different types of) interval and general type-2 fuzzy measures.

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A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets

Cited by 322 publications

References 42 publications

Novel similarity measure for interval-valued data based on overlapping ratio

Novel similarity measure for interval-valued data based on overlapping ratio

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

Extending similarity measures of interval type-2 fuzzy sets to general type-2 fuzzy sets

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