In 1972, M. Rosenfeld asked if every triangle-free graph could be embedded in the unit sphere S in such a way that two vertices joined by an edge have distance more than √ 3 (i.e. distance more than 2π/3 on the sphere). In 1978, D. Larman [4] disproved this conjecture, constructing a triangle-free graph for which the minimum length of an edge could not exceed p 8/3. In addition, he conjectured ...

Distinct Trypanosoma cruzi genotypes have been considered relevant for patient management and therapeutic response of Chagas disease. However, typing strategies for genotype-specific serodiagnosis of Chagas disease are still unavailable and requires standardization for practical application. In this study, an innovative TcI/TcVI/TcII Chagas Flow ATE-IgG2a technique was developed with applicabil...

Let G= (V,E,σ,μ) be a simple connected undirected fuzzy graph. In this paper, we use a fuzzy graph model to represent a traffic network of a city and discuss a method to find the different type of accidental zones in a traffic flows. Depending on the possibility of accident, this paper classifies accidental zone of a traffic flow into three type’s namely α-strong, β-strong and δ-strong accident...

Rule interpolation methods deal with sparse fuzzy rule bases. The KH interpolation method, which has advantageous computational behaviour, can produce ,,abnormal” output in certain cases. Recently a new method has been proposed to eliminate this property. The goal of this paper is to investigate the mathematical stability of the new α-cut based interpolation approach originated from the KH inte...

In this article, we solve the second type of nonlinear Volterra picture fuzzy integral equation (NVPFIE) using an accelerated form Adomian decomposition method (ADM). Based on (α,δ,β)-cut, convert NVPFIE to equations in a crisp form. An version ADM is used transformed system, which based new formula for polynomial. The sufficient condition that guarantees unique solution obtained polynomial, er...

The fuzzy regression control chart is a functional technique to evaluate the process in which the average has a trend and the data represents a linguistic or approximate value. In this study, the theoretical structure of the “α-level fuzzy midrange for α-cut fuzzy X ~ -regression control chart” is proposed for triangular (TFN) and trapezoidal (TrFN) membership functions. In addition, the real w...

This paper investigates the approximation behaviour of the α-cut based fuzzy interpolators. First, it is shown that the so-called KH fuzzy interpolator is a fuzzy generalization of a well-known and thoroughly investigated parameterized interpolatory operator from approximation theory, the Shepard operator. Exploiting the aforementioned relationship, we establish analog results on the approximat...