Encoding Words Into Normal Interval Type-2 Fuzzy Sets: HM Approach

Hao, Minshen; Mendel, Jerry M.

doi:10.1109/tfuzz.2015.2486814

Cited by 61 publications

(68 citation statements)

References 42 publications

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“…The encoder is designed by deciding a problem specific vocabulary of 'words' and then collecting the data intervals from a group of subjects. These data intervals are processed using the Interval Approach (IA) (Liu and Mendel 2008), Enhanced Interval Approach (EIA) (Wu et al 2012) or the Hao-Mendel Approach (HMA) (Hao and Mendel 2016). All the IA, EIA and HMA (Mendel 2016) have a number of data processing steps divided into two broad categories: the data part and the FS part.…”

Section: -Tuple Based Cww Methodology For Student Strategy Evaluationmentioning

confidence: 99%

Computing with words for student strategy evaluation in an examination

Gupta

Muhuri

2018

Granul. Comput.

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In the framework of Granular Computing (GC), Interval type 2 Fuzzy Sets (IT2 FSs) play a prominent role by facilitating a better representation of uncertain linguistic information. Perceptual Computing (Per-C), a well-known computing with words (CWW) approach, and in its various applications have nicely exploited this advantage. This paper reports a novel Per-C based approach for student strategy evaluation. Examinations are generally oriented to test the subject knowledge of students. The number of questions they are able to solve accurately judges success rates of students in the examinations. However, we feel that not only the solutions of questions, but also the strategy adopted for finding those solutions are equally important. More marks should be awarded to a student, who solves a question with a better strategy compared to a student whose strategy is relatively not that good. Furthermore, the student's strategy can be taken as a measure of his/ her learning outcome as perceived by a faculty member. This can help to identify students whose learning outcomes are not good and thus, can be provided with any relevant help, for improvement. The main contribution of this paper is to illustrate the use of CWW for student strategy evaluation and present a comparison of the recommendations generated by different CWW approaches. CWW provides us with two major advantages. Firstly, it generates a numeric score for the overall evaluation of strategy adopted by a student in the examination. This enables comparison and ranking of the students based on their performances. Secondly, a linguistic evaluation describing the student strategy is also obtained from the system. Both these numeric score and linguistic recommendation are together used to assess the quality of a student's strategy. Furthermore, the linguistic recommendation is useful for human beings as they naturally understand and express themselves using 'words', 'words' being treated as fuzzy information granules in the GC paradigm, which is perhaps the case with most of the human reasoning and concepts. Also, through the comparison of the recommendations generated by different CWW approaches, we found that Per-C outperforms the others CWW approaches by generating unique recommendations in all the cases as well as modeling the word uncertainty in the best possible way.

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Section: -Tuple Based Cww Methodology For Student Strategy Evaluationmentioning

confidence: 99%

Computing with words for student strategy evaluation in an examination

Gupta

Muhuri

2018

Granul. Comput.

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“…Having defined each zSlice, γ(M ) can be calculated by replacing the equation above in (10) and using (7) such that we obtain:…”

Section: (8)mentioning

confidence: 99%

“…There is a growing body of literature within the Fuzzy Set (FS) community and in particular within the Computing With Words area [1] that is based on the premise that "words mean different things to different people" [2]. It is this premise that has motivated the development of robust techniques for modelling and reasoning [3]- [7] using a number of different types of FS based models in respect to inter-individual uncertainty associated with terms.…”

Section: Introductionmentioning

confidence: 99%

Measuring Inter-group Agreement on zSlice Based General Type-2 Fuzzy Sets

Navarro

Wagner

2019

2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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Recently, there has been much research into modelling of uncertainty in human perception through Fuzzy Sets (FSs). Most of this research has focused on allowing respondents to express their (intra) uncertainty using intervals. Here, depending on the technique used and types of uncertainties being modelled different types of FSs can be obtained (e.g., Type-1, Interval Type-2, General Type-2). Arguably, one of the most flexible techniques is the Interval Agreement Approach (IAA) as it allows to model the perception of all respondents without making assumptions such as outlier removal or predefined membership function types (e.g. Gaussian). A key aspect in the analysis of interval-valued data and indeed, IAA based agreement models of said data, is to determine the position and strengths of agreement across all the sources/participants. While previously, the Agreement Ratio was proposed to measure the strength of agreement in fuzzy set based models of interval data, said measure has only been applicable to type-1 fuzzy sets. In this paper, we extend the Agreement Ratio to capture the degree of inter-group agreement modelled by a General Type-2 Fuzzy Set when using the IAA. This measure relies on using a similarity measure to quantitatively express the relation between the different levels of agreement in a given FS. Synthetic examples are provided in order to demonstrate both behaviour and calculation of the measure. Finally, an application to realworld data is provided in order to show the potential of this measure to assess the divergence of opinions for ambiguous concepts when heterogeneous groups of participants are involved.1 The rationale of doing so is due to the use of the Jaccard similarity measure [23] which is simplified to the case of |A| |B| when A ⊆ B.

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“…3.13 in Mendel and Wu (2010) and Fig. 8 in Liu and Mendel (2008) In the IA (Liu and Mendel 2008;Mendel and Wu 2010, Ch. 3) and the EIA (Wu et al 2012) this processing appears in their data part, but in the HMA (Hao and Mendel 2015) it appears in the fuzzy set part. For this article all statistical information processing has been moved into the data part, so that the three approaches can be compared.…”

Section: Establish Nature Of the Fou (Table 6)mentioning

confidence: 99%

“…In the HMA, the average of the centroid 17 of each triangular FOU is equated to the sample mean of the set of m smaller-length data intervals, and the upper bound of the standard deviation 18 interval for each triangular FOU is equated to the sample standard deviation of the set of m smaller-length data intervals. Hao and Mendel (2015) obtain closed-form formulas for both the average of the centroid and the upper bound of the standard The Unreasonable Region is so named because it would be unreasonable for a word shoulder FOU to extend so far either to the left or to the right into that region (Liu andMendel 2008: Ó 2008, IEEE) Map the set(s) of smaller intervals into the two parameters that define the respective FOU. There is one FOU for the shoulder FOUs, but two FOUs for the interior FOU.…”

Section: Establish the Fou (Tables 7 8)mentioning

confidence: 99%

A comparison of three approaches for estimating (synthesizing) an interval type-2 fuzzy set model of a linguistic term for computing with words

Mendel

2015

Granul. Comput.

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130

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This article compares three methods [Interval Approach (IA), Enhanced Interval Approach (EIA) and Hao-Mendel Approach (HMA)] for estimating (synthesizing) an interval type-2 fuzzy set (IT2 FS) model for a word, beginning with data that are collected from a group of subjects, or from a single subject. It summarizes the stages for each of the methods in tables so it is possible to compare the steps of each stage side-by-side. It also demonstrates, by means of an example of three words, that using more information contained in the collected data intervals is equivalent to reducing the uncertainty in the IT2 FS model. It recommends the HMA because it uses more information contained in the collected data intervals than does the IA or the EIA, and because it is the only method to-date that leads to normal IT2 FSs. Such fuzzy sets are easier to compute with than are non-normal IT2 FSs.

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Encoding Words Into Normal Interval Type-2 Fuzzy Sets: HM Approach

Cited by 61 publications

References 42 publications

Computing with words for student strategy evaluation in an examination

Computing with words for student strategy evaluation in an examination

Measuring Inter-group Agreement on zSlice Based General Type-2 Fuzzy Sets

A comparison of three approaches for estimating (synthesizing) an interval type-2 fuzzy set model of a linguistic term for computing with words

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