In this article two point fuzzy boundary value problem is defined under the approach generalized Hukuhara differentiability (gH-differentiability). We research the solution method of the fuzzy boundary problem with the basic solutions Φ (x, λ) and χ (x, λ) which are defined by the special procuder. We give operator-theoretical formulation, construct fundamental solutions and investigate some properties of the eigenvalues and corresponding eigenfunctions of the considered fuzzy problem. Then results of the proposed method are illustrated with a numerical example.

Development of new flexible distributions for modeling non-negative measurements occuring in lifetime or reliability studies is a prominent research area in Statistics. As being the most favoured positive definite form, the Gamma distribution poses a basis for such improvements. It is well known that transforming a Gamma variable with another continuous random variable (X) creates Gamma-X family of distributions. Following this principle, we here attempted to define the X variable as Folded-Normal distributed which is also positive definite so as to propose a new family of distributions. Named as Gamma Folded-Normal distribution (GFN), our proposal is a generalization of Gamma Half-Normal distribution and contains more freely estimated parameters. This study evaluates some mathematical properties of GFN distribution such as moments and illustrates the estimation procedure for unknown parameters through a simulation study. A separate simulation is also conducted to compare the performance of this new distribution with the Folded-Normal, Half-Normal and Gamma Half-Normal distributions. Besides, the practical importance of our new proposal is illustrated by analyzing a real world data set.

ÖZET: Bu makalede iki nokta sınır değer problemi genelleştirilmiş Hukuhara türevi (gh-türev) ile incelenmiştir. Bu yöntemin dört farklı çözümü vardır. Bu çözümler ayrı ayrı incelenerek elde edilen sonuçlar sunulmuştur. Yöntemin uygulanabilirliği bir örnekle gösterilmiştir.

In this study, it was aimed to reveal the importance of microbiological factors in water quality determination studies based on fuzzy logic and to determine the usability of management in water quality. Six critical parameters for water quality detection are included. In the study of Avsar [1], only bacteriological data were emphasized, and no information was obtained about quantitative data on water quality. It was found that fecal coliform was more effective on the changes in water quality compared to fecal coliform and temperature based fuzzy quality indexes. When the fuzzy quality values were determined, the effect of seasonal changes did not appear to be high, but the change in pH and coliform values affected the quality. This showed that water quality assessment would not be accurate without microbiological data. As a result, the proposed data can be considered accurate and reliable, so we recommend that microbiological data should be included in the evaluation of water quality determination studies. In addition, we can say that fuzzy logic technique will be a comprehensive and reliable technique in the assessment of the quality of the streams that are used in irrigation, fishing and recreational areas.

In this paper we deal with the fuzzy eigenfunctions of the two point fuzzy boundary value problem (FBVP) with fuzzy coefficient of the boundary conditions. The fuzzy solution is obtained from the Zadeh's extension principle using the Heaviside function. The eigenvalues and the fuzzy eigenfunctions of the boundary value problem are found using the Wronskian functions. We present an example in order to compare the proposed solution.