Optimization Of Fuzzy Evapotranspiration Model Through Neural Training With Input–Output Examples

In a previous study, we demonstrated that fuzzy evapotranspiration (ET) models can achieve accurate estimation of daily ET comparable to the FAO Penman–Monteith equation, and showed the advantages of the fuzzy approach over other methods. The estimation accuracy of the fuzzy models, however, depended on the shape of the membership functions and the control rules built by trial–and–error methods. This paper shows how the trial and error drawback is eliminated with the application of a fuzzy–neural system, which combines the advantages of fuzzy logic (FL) and artificial neural networks (ANN). The strategy consisted of fusing the FL and ANN on a conceptual and structural basis. The neural component provided supervised learning capabilities for optimizing the membership functions and extracting fuzzy rules from a set of input–output examples selected to cover the data hyperspace of the sites evaluated. The model input parameters were solar irradiance, relative humidity, wind speed, and air temperature difference. The optimized model was applied to estimate reference ET using independent climatic data from the sites, and the estimates were compared with direct ET measurements from grass–covered lysimeters and estimations with the FAO Penman–Monteith equation. The model–estimated ET vs. lysimeter–measured ET gave a coefficient of determination (r2) value of 0.88 and a standard error of the estimate (Syx) of 0.48 mm d–1. For the same set of independent data, the FAO Penman–Monteith–estimated ET vs. lysimeter–measured ET gave an r2 value of 0.85 and an Syx value of 0.56 mm d–1. These results show that the optimized fuzzy–neural–model is reasonably accurate, and is comparable to the FAO Penman–Monteith equation. This approach can provide an easy and efficient means of tuning fuzzy ET models

A New Approach in a Gray-Level Image Contrast Enhancement by using Fuzzy Logic Technique

Fuzzy Logic technique represents a new approach for gray level image contrast enhancement. The image contrast problem is one of the main problems that confront the researchers in the field of digital image processing, such as in the biomedical image processing like X-Ray and MRI image segmentation for disease classification. In this paper, presenting a new approach to enhancing the image contrast by using fuzzy logic algorithm, so based on the fuzzy rule, we present a new membership equation, which represents the variable threshold level. The proposed method we named it (Fuzzy Hyperbolic Threshold). By using Matlab was implemented the algorithm, and applied to difference gray level images such as old documents images, biomedical images, most of them gives very good results especially with the biomedical images, because of its significant impact on the adjustment of lighting in dark images, clarify its edges, clarify their features and improved image quality

Finite Difference Methods For Linear Fuzzy Time Fractional Diffusion And Advection-Diffusion Equation

Fractional differential equations have attracted considerable attention in the last decade or so. This is evident from the number of publications on such equations in various scientific and engineering fields. Crisp quantities in fractional differential equations which are deemed imprecise and uncertain can be replaced by fuzzy quantities to reflect imprecision and uncertainty. The fractional partial differential equation can then be expressed by fuzzy fractional partial differential equations which can give a better description for certain phenomena involving uncertainties. The analytical solution of fuzzy fractional partial differential equations is often not possible. Therefore, there is great interest in obtaining solutions via numerical methods. The finite difference method is one of the more frequently used numerical methods for solving the fractional partial differential equations due to their simplicity and universal applicability. In this thesis, the focus is the development, analysis and application of finite difference schemes of second order of accuracy and compact finite difference methods of fourth order of accuracy to solve fuzzy time fractional diffusion equation and fuzzy time fractional advection-diffusion equation. Two different fuzzy computational techniques (single and double parametric form of fuzzy number) are investigated. The Caputo formula is used to approximate the fuzzy time fractional derivative. The consistency, stability, and convergence of the finite difference methods are investigated. Numerical experiments are carried out and the results indicate the effectiveness and feasibility of the schemes that have been developed

Numerical Solution of Fuzzy Fractional Differential Equation By Haar Wavelet

In this paper, we deal with a wavelet operational method based on Haar wavelet to solve the fuzzy fractional differential equation in the Caputo derivative sense. To this end, we derive the Haar wavelet operational matrix of the fractional order integration. The given approach provides an efficient method to find the solution and its upper bond error. To complete the discussion, the convergence theorem is subsequently expressed in detail. So far, no paper has used the Harr wavelet method using generalized difference and fuzzy derivatives, and this is the first time we have done so. Finally, the presented examples reflect the accuracy and efficiency of the proposed method

Fuzzy Least Squares Twin Support Vector Machines

Least Squares Twin Support Vector Machine (LST-SVM) has been shown to be an efficient and fast algorithm for binary classification. It combines the operating principles of Least Squares SVM (LS-SVM) and Twin SVM (T-SVM); it constructs two non-parallel hyperplanes (as in T-SVM) by solving two systems of linear equations (as in LS-SVM). Despite its efficiency, LST-SVM is still unable to cope with two features of real-world problems. First, in many real-world applications, labels of samples are not deterministic; they come naturally with their associated membership degrees. Second, samples in real-world applications may not be equally important and their importance degrees affect the classification. In this paper, we propose Fuzzy LST-SVM (FLST-SVM) to deal with these two characteristics of real-world data. Two models are introduced for FLST-SVM: the first model builds up crisp hyperplanes using training samples and their corresponding membership degrees. The second model, on the other hand, constructs fuzzy hyperplanes using training samples and their membership degrees. Numerical evaluation of the proposed method with synthetic and real datasets demonstrate significant improvement in the classification accuracy of FLST-SVM when compared to well-known existing versions of SVM

Spectrum of the three dimensional fuzzy well

We develop the formalism of quantum mechanics on three dimensional fuzzy space and solve the Schr\"odinger equation for a free particle, finite and infinite fuzzy wells. We show that all results reduce to the appropriate commutative limits. A high energy cut-off is found for the free particle spectrum, which also results in the modification of the high energy dispersion relation. An ultra-violet/infra-red duality is manifest in the free particle spectrum. The finite well also has an upper bound on the possible energy eigenvalues. The phase shifts due to scattering around the finite fuzzy potential well have been calculated

Extruder for food product (otak–otak) with heater and roll cutter

Food extrusion is a form of extrusion used in food industries. It is a process by which a set of mixed ingredients are forced through an opening in a perforated plate or die with a design specific to the food, and is then cut to a specified size by blades [1]. Summary of the invention principal objects of the present invention are to provide a machine capable of continuously producing food products having an’ extruded filler material of meat or similarity and an extruded outer covering of a moldable food product, such as otak-otak, that completely envelopes the filler material

A decomposition theorem for fuzzy set-valued random variables and a characterization of fuzzy random translation

Let $X$ be a fuzzy set--valued random variable (\frv{}), and \huku{X} the family of all fuzzy sets $B$ for which the Hukuhara difference X\HukuDiff B exists $\mathbb{P}$--almost surely. In this paper, we prove that $X$ can be decomposed as X(\omega)=C\Mink Y(\omega) for $\mathbb{P}$--almost every $\omega\in\Omega$, $C$ is the unique deterministic fuzzy set that minimizes $\mathbb{E}[d_2(X,B)^2]$ as $B$ is varying in \huku{X}, and $Y$ is a centered \frv{} (i.e. its generalized Steiner point is the origin). This decomposition allows us to characterize all \frv{} translation (i.e. X(\omega) = M \Mink \indicator{\xi(\omega)} for some deterministic fuzzy convex set $M$ and some random element in \Banach). In particular, $X$ is an \frv{} translation if and only if the Aumann expectation $\mathbb{E}X$ is equal to $C$ up to a translation. Examples, such as the Gaussian case, are provided.Comment: 12 pages, 1 figure. v2: minor revision. v3: minor revision; references, affiliation and acknowledgments added. Submitted versio