A Probabilistic and Statistical View of Fuzzy Methods

Laviolette, Michael; Seaman, John W.; Barrett, J. Douglas; Woodall, William H.

doi:10.2307/1269905

Cited by 80 publications

(32 citation statements)

References 54 publications

(37 reference statements)

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“…While we introduce here a model that addresses the fuzziness kind of uncertainty in inflow variables we ascertain that this modelling paradigm can include a measure of ambiguity using fuzzy set theory or possibility theory. We consider fuzziness in historical inflow input data variables by modelling inflow interval data through the use of membership functions to address our uncertainty in classifying observations (Laviolette et al, 1995). In other words, considering an inflow observation "Q", the membership function μ A (Q) that lies between 0 and 1 symbolizes the assessor's view of the extent to which Q belongs to the fuzzy set A.…”

Section: Fuzzy Modelingmentioning

confidence: 99%

“…The capability of fuzzy systems thus lies in being subjective (thus includes uncertainty) as being dependent on the assessor's view (represented mathematically by the shape and overlap of the membership functions). However, in doing so we assume that for any inflow measurement Q we shall be able to assign a membership value μ Ai (Q) for all 1 ≤ i ≤ N where N represents the number of all fuzzy subsets that can be recognized within the inflow measurement space (Laviolette et al, 1995 andSingpurwall andBooker, 2004).…”

Section: Fuzzy Modelingmentioning

confidence: 99%

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A neuro-fuzzy model for inflow forecasting of the Nile river at Aswan high dam

El-Shafie

Taha

Noureldin

2006

Water Resour Manage

172

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River flow forecasting is an essential procedure that is necessary for proper reservoir operation. Accurate forecasting results in good control of water availability, refined operation of reservoirs and improved hydropower generation. Therefore, it becomes crucial to develop forecasting models for river inflow. Several approaches have been proposed over the past few years based on stochastic modeling or artificial intelligence (AI) techniques.In this article, an adaptive neuro-fuzzy inference system (ANFIS) model is proposed to forecast the inflow for the Nile River at Aswan High Dam (AHD) on monthly basis. A major advantage of the fuzzy system is its ability to deal with imprecision and vagueness in inflow database. The ANFIS model divides the input space into fuzzy sub-spaces and maps the output using a set of linear functions. A historical database of monthly inflows at AHD recorded over the past 130 years is used to train the ANFIS model and test its performance. The performance of the ANFIS model is compared to a recently developed artificial neural networks (ANN) model. The results show that the ANFIS model was capable of providing higher inflow forecasting accuracy specially at extreme inflow events compared with that of the ANN model. It is concluded that the ANFIS model can be quite beneficial in water management of Lake Nasser reservoir at AHD.

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Section: Fuzzy Modelingmentioning

confidence: 99%

Section: Fuzzy Modelingmentioning

confidence: 99%

A neuro-fuzzy model for inflow forecasting of the Nile river at Aswan high dam

El-Shafie

Taha

Noureldin

2006

Water Resour Manage

172

View full text Add to dashboard Cite

show abstract

“…They defined fuzzy unnatural pattern rules based on the probabilities of fuzzy events. Using the defuzzification method to simplify the fuzzy observations into real numbers causes the loss of original data information as it has been pointed out by Cheng [5], Grzegorzewski [9], and Laviolette et al [16]. Kaya and Kahraman [15] introduced fuzzy rules method for symmetrical fuzzy numbers.…”

Section: Introductionmentioning

confidence: 99%

X-MR control chart for autocorrelated fuzzy data using D p,q -distance

Gildeh

Shafiee

2015

Int J Adv Manuf Technol

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A control chart is a tool for investigating whether the variation in a production process is random or assignable. X − MR control chart is a binary control chart on which average values of process and moving range between observations are used to discover the variability in the process. In an ordinary control chart, the data are crisp values but sometimes, the data are generated as vague and uncertain values because of some of environmental conditions and other factors. In such cases, fuzzy sets theory is a useful tool for analyzing data. On the other hand, the assumption of independence between observations cannot be accepted because the probability of false warning will increase if the data are autocorrelated and their correlation is ignored. In this article, we will discuss the construction of fuzzy control charts for autocorrelated fuzzy observations and employment of ranking method in order to find out whether the observations are in or out of control. In fact, by using defined D p,q -distance between fuzzy numbers, we calculate their variance, covariance, and autocorrelation coefficient. The autocorrelation coefficient is used in order to modify the limit of control chart. By using D p,q -distance, we present a new approach for constructing control charts.

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“…By considering the underlying probability distributions of the linguistic data, Kanagawa et al (1993) further constructed a more feasible chart than that of Wang and Raz (1990). Nevertheless, both of the researches have a core controversial issue; that is, the scales of membership functions for the linguistic terms are arbitrarily given by lack of on-site data collection or exclusion of experts' knowledge and judgment (Laviolette et al, 1995;Shu and Wu, 2011;Woodall et al, 1997). More recently, Gülbay and Kahraman (2007) considered fuzzy measurements directly gathered from the key quality characteristic and employed a fuzzy approach with an acceptable percentage index to build a Shewhart-type fuzzy control chart.…”

Section: Introductionmentioning

confidence: 99%