**Konstantinos Ka**ff**as 1, Matthaios Saridakis 2, Mike Spiliotis 2,\*, Vlassios Hrissanthou <sup>2</sup> and Maurizio Righetti <sup>1</sup>**


Received: 29 November 2019; Accepted: 11 January 2020; Published: 16 January 2020

**Abstract:** The objective of this study is to transform the arithmetic coefficients of the total sediment transport rate formula of Yang into fuzzy numbers, and thus create a fuzzy relationship that will provide a fuzzy band of in-stream sediment concentration. A very large set of experimental data, in flumes, was used for the fuzzy regression analysis. In a first stage, the arithmetic coefficients of the original equation were recalculated, by means of multiple regression, in an effort to verify the quality of data, by testing the closeness between the original and the calculated coefficients. Subsequently, the fuzzy relationship was built up, utilizing the fuzzy linear regression model of Tanaka. According to Tanaka's fuzzy regression model, all the data must be included within the produced fuzzy band and the non-linear regression can be concluded to a linear regression problem when auxiliary variables are used. The results were deemed satisfactory for both the classic and fuzzy regression-derived equations. In addition, the linear dependence between the logarithmized total sediment concentration and the logarithmized subtraction of the critical unit stream power from the exerted unit stream power is presented. Ultimately, a fuzzy counterpart of Yang's stream sediment transport formula is constructed and made available to the readership.

**Keywords:** stream sediment transport; total load; sediment concentration; Yang formula; fuzzy regression; fuzzy coefficients; fuzzy logic
