On various approaches to normalization of interval and fuzzy weights

Pavlačka, Ondřej

doi:10.1016/j.fss.2013.07.026

Cited by 15 publications

(11 citation statements)

References 29 publications

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“…Users can select any one from them according to the real situation of the application. [1,2], [2,3], [3,4]). According to above new method, we can find the midpoints being 0.5, 1.5, 2.5, 3.5.…”

Section: Criterion Of Goodness For Normalizing Interval Weightsmentioning

confidence: 99%

“…MCDA is an important part of modern scientific decisionmaking and its theory and method have been widely used in engineering, economics, management and military as well as many other fields. The MCDA reasonably determined by the normalization of interval weight is very important because it is related to the reliability and accuracy of decision outcomes [2]. Therefore, the study of MCDA determined by the index weight has important theoretical and practical value.…”

Section: Introductionmentioning

confidence: 99%

“…In the following examples, using an n-tupe to express a weights is convenient.Example 3. Given interval weights ([0, 2],[2,5],[5, 9]). The midpoints are 1, 3.5, 5 respectively.…”

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confidence: 99%

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Discussion on Normalization Methods of Interval Weights

Sui

Wang

2016

SJAMS

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This paper is collecting the classic and newly normalization methods, finding deficiency of existing normalization methods for interval weights, and introducing a new normalization methods for interval weights. When we normalize the interval weights, it is very important and necessary to check whether, after normalizing, the location of interval centers as well as the length of interval weights keep the same proportion as those of original interval weights. It is found that, in some newly normalization methods, they violate these goodness criteria. In current work, for interval weights, we propose a new normalization method that reserves both proportions of the distances from interval centers to the origin and of interval lengths, and also eliminates the redundancy from the original given interval weights. This new method can be widely applied in information fusion and decision making in environments with uncertainty.

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Section: Criterion Of Goodness For Normalizing Interval Weightsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Discussion on Normalization Methods of Interval Weights

Sui

Wang

2016

SJAMS

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“…To do so, we will consider different ways for normalizing intervals [9] and study their effects in the resulting intervals both from the theoretical and applied point of view. That is, we will not only evaluate their performance in IVOVO, but we will also study whether the different normalizations are able to maintain the order established between intervals as well as other properties that may be expected after normalization.…”

Section: Introductionmentioning

confidence: 99%

On the Influence of Interval Normalization in IVOVO Fuzzy Multi-class Classifier

Uriz

Paternain

Bustince

et al. 2019

Advances in Intelligent Systems and Computing

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IVOVO stands for Inverval-Valued One-Vs-One and is the combination of IVTURS fuzzy classifier and the One-Vs-One strategy. This method is designed to improve the performance of IVTURS in multi-class problems, by dividing the original problem into simpler binary ones. The key issue with IVTURS is that intervalvalued confidence degrees for each class are returned and, consequently, they have to be normalized for applying a One-Vs-One strategy. However, there is no consensus on which normalization method should be used with intervals. In IVOVO, the normalization method based on the upper bounds was considered as it maintains the admissible order between intervals and also the proportion of ignorance, but no further study was developed. In this work, we aim to extend this analysis considering several normalizations in the literature. We will study both their main theoretical properties and empirical performance in the final results of IVOVO.

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“…In the literature, interval-valued weights are used in several contexts, in order to face the problem of real-world applications in which there are a lot of uncertainty involved and lack of consensus among the modeling experts. Pavlacka [47] presented a review of the existing methods for normalization of interval weights. For example, in the context of multicriterion decision making, Wang and Li [56] used a hierarchical structure to aggregate local interval weights into global interval weights, by means of a pair of linear programming models to maximize the lower and upper bounds of the aggregated interval value.…”

Section: Introductionmentioning

confidence: 99%

Generalized interval-valued OWA operators with interval weights derived from interval-valued overlap functions

Bedregal

Bustince

Palmeira

et al. 2017

International Journal of Approximate Reasoning

105

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In this work we extend to the interval-valued setting the notion of an overlap functions and we discuss a method which makes use of interval-valued overlap functions for constructing OWA operators with interval-valued weights. . Some properties of intervalvalued overlap functions and the derived interval-valued OWA operators are analysed. We specially focus on the homogeneity and migrativity properties.

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On various approaches to normalization of interval and fuzzy weights

Cited by 15 publications

References 29 publications

Discussion on Normalization Methods of Interval Weights

Discussion on Normalization Methods of Interval Weights

On the Influence of Interval Normalization in IVOVO Fuzzy Multi-class Classifier

Generalized interval-valued OWA operators with interval weights derived from interval-valued overlap functions

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