Assessment of the Couple between the Historical Sample and the Theoretical Probability Distributions for Maximum flow Values Based on a Fuzzy Methodology

Saridakis, Matthaios; Spiliotis, Mike; Angelidis, Panagiotis; Papadopoulos, Basil K.

doi:10.3390/environsciproc2020002022

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…From the theorem of global existence for the maxima and minima of functions with many variables, it is known that if the domain of a real function is closed and bounded and the real function is continuous, then the function will have its absolute minimum and maximum values at some points in the domain (Marsden & Tromba 2003). Based on this theorem, it is evident that the α-cut for any real continuous function with real variables in this domain can be determined, given that the inputs are fuzzy triangular numbers (Tsakiris & Spiliotis 2016;Saridakis et al 2020).…”

Section: Fundamentals Of Fuzzy Logic and Setsmentioning

confidence: 99%

Fuzzy linear regression analysis for groundwater response to meteorological drought in the aquifer system of Xanthi plain, NE Greece

Papadopoulos

Spiliotis

Gkiougkis

et al. 2021

Journal of Hydroinformatics

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This paper studies, through the principles of fuzzy set theory, groundwater response to meteorological drought in the case of an aquifer system located in the plains at the southeast of Xanthi, NE Greece. Meteorological drought is expressed through standardized Reconnaissance Drought Index (RDISt) and Standardized Precipitation Index (SPI), which are calculated for various reference periods. These drought indices are considered as independent variables in multiple fuzzy linear regression based on Tanaka's model, while the observed water table regarding two areas is used as a dependent variable. The fuzzy linear regression of Tanaka is characterized by the inclusion constraints where all the observed data must be included in the produced fuzzy band. Hence, each fuzzy output can get an interval of values where a membership degree corresponds to each of them. A modification of the Tanaka model by adding constraints is proposed in order to avoid irrational behavior. The results show that there was a significant influence of the meteorological drought of the previous hydrological year, while geology plays an important role. Furthermore, the use of RDISt improves the results of fuzzy linear regressions in all cases. Two suitability measures and a measure of comparison between fuzzy numbers are used.

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Section: Fundamentals Of Fuzzy Logic and Setsmentioning

confidence: 99%

Fuzzy linear regression analysis for groundwater response to meteorological drought in the aquifer system of Xanthi plain, NE Greece

Papadopoulos

Spiliotis

Gkiougkis

et al. 2021

Journal of Hydroinformatics

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“…Thus, a crisp function can The extension principle is a fundamental principle in fuzzy set theory. In brief, with the use of the extension principle all the operations of the crisp functions can be extended as the fuzzy arithmetic and fuzzy algebraic operations [37,38]. Thus, a crisp function can be performed on a fuzzy number and the result of this operation should also be a fuzzy number.…”

Section: Basic Consepts Of Fuzzy Logic and Setsmentioning

confidence: 99%

Relating Hydro-Meteorological Variables to Water Table in an Unconfined Aquifer via Fuzzy Linear Regression

Papadopoulos¹,

Spiliotis²,

Gkiougkis³

et al. 2021

Environments

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This study aims to assess the short-term response of groundwater to the main hydro-meteorological variables of drought in a coastal unconfined aquifer. For this purpose, a multiple fuzzy linear regression-based methodology is implemented in order to relate rainfall, streamflow and the potential evapotranspiration to groundwater. Fuzzy regression analysis is recommended when there is a lack of data. The uncertainty of the system is incorporated into the regression coefficients which, in this study, are considered to be fuzzy symmetrical triangular numbers. Two objective functions are used producing a fuzzy band in which all the observed data must be included. The first objective function, based on Tanaka’s model, minimizes the total width of the produced fuzzy band. The second one includes the first while additionally minimizing the distance between the central value of the fuzzy output of the model and the observed value. Validity of the model is checked through suitability measures. The present methodology is applied at the east part of the Nestos River Delta in the Prefecture of Xanthi (Greece), where the observed values of the depth of groundwater level of four wells are examined.

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Assessment of the Couple between the Historical Sample and the Theoretical Probability Distributions for Maximum flow Values Based on a Fuzzy Methodology

Cited by 2 publications

References 11 publications

Fuzzy linear regression analysis for groundwater response to meteorological drought in the aquifer system of Xanthi plain, NE Greece

Fuzzy linear regression analysis for groundwater response to meteorological drought in the aquifer system of Xanthi plain, NE Greece

Relating Hydro-Meteorological Variables to Water Table in an Unconfined Aquifer via Fuzzy Linear Regression

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