Topological properties of fuzzy numbers

Goetschel, Roy H.; Voxman, William

doi:10.1016/s0165-0114(83)80107-9

Cited by 179 publications

(46 citation statements)

References 3 publications

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“…In literature one may find a number of definitions for a fuzzy number. One of the most detailed definitions was proposed by Goetschel and Voxmann [3]. A fuzzy number A is a specific type of a fuzzy set determined on the set of real numbers (X = R), which, additionally, fulfils the following conditions:…”

Section: Elements Of Fuzzy Sets Used In Schedule Makingmentioning

confidence: 99%

Creating a Construction Schedule Specyfing Fuzzy Norms and the Number of Workers

Plebankiewicz¹,

Karcińska²

2016

Archives of Civil Engineering

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The basic element of a project organizing construction works is a schedule. The preparation of the data necessary to specify the timings of the construction completion as indicated in the schedule involves information that is uncertain and hard to quantify. The article presents the methods of building a schedule which includes a fuzzy amount of labour, time standards and number of workers. The proposed procedure allows determining the real deadline for project completion, taking into account variable factors affecting the duration of the individual works.

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Section: Elements Of Fuzzy Sets Used In Schedule Makingmentioning

confidence: 99%

Creating a Construction Schedule Specyfing Fuzzy Norms and the Number of Workers

Plebankiewicz¹,

Karcińska²

2016

Archives of Civil Engineering

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“…By a fuzzy number (sometimes referred to as Zadeh's fuzzy number -see, for instance, Herencia and Lamata [18,19]-) we mean (see Goetschel and Voxman [11]) a fuzzy subset of the space of real numbers R, that is, a mapping U : R → [0, 1], which is convex, normal and upper semi-continuous with compact support.…”

Section: Original Definition Interpretation and Metric Propertiesmentioning

confidence: 99%

Bertoluzza et al.’s metric as a basis for analyzing fuzzy data

Casals

Corral

Gil

et al. 2013

METRON

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Since Bertoluzza et al. 's metric between fuzzy numbers has been introduced, several studies involving it have been developed. Some of these studies concern equivalent expressions for the metric which are useful for either theoretical, practical or simulation purposes. Other studies refer to the potentiality of Bertoluzza et al.'s metric to establish statistical methods for the analysis of fuzzy data. This paper shortly reviews such studies and examine part of the scientific impact of the metric.

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“…Moreover, when k = −1, we have k ⊗ũ = −ũ. The Hausdorff distance between fuzzy numbers given by D : Note that (R F , D) is a complete metric space (see [3,11,13]) and has the following properties, …”

Section: Preliminariesmentioning

confidence: 99%

Integrating Ridge-type regularization in fuzzy nonlinear regression

Farnoosh¹,

Ghasemian²,

Fard³

2012

Comput. Appl. Math.

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Abstract. In this paper, we deal with the ridge-type estimator for fuzzy nonlinear regression models using fuzzy numbers and Gaussian basis functions. Shrinkage regularization methods are used in linear and nonlinear regression models to yield consistent estimators. Here, we propose a weighted ridge penalty on a fuzzy nonlinear regression model, then select the number of basis functions and smoothing parameter. In order to select tuning parameters in the regularization method, we use the Hausdorff distance for fuzzy numbers which was first suggested by Dubois and Prade [8]. The cross-validation procedure for selecting the optimal value of the smoothing parameter and the number of basis functions are fuzzified to fit the presented model. The simulation results show that our fuzzy nonlinear modelling performs well in various situations.Mathematical subject classification: Primary: 62J86; Secondary: 62J07.

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Topological properties of fuzzy numbers

Cited by 179 publications

References 3 publications

Creating a Construction Schedule Specyfing Fuzzy Norms and the Number of Workers

Creating a Construction Schedule Specyfing Fuzzy Norms and the Number of Workers

Bertoluzza et al.’s metric as a basis for analyzing fuzzy data

Integrating Ridge-type regularization in fuzzy nonlinear regression

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