2 How to Create Instances of Fuzzy Numbers 3 2.1 Arbitrary Fuzzy Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 Definition by Side Functions . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Definition by α-cut Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Definition with Generating Functions Omitted: Shadowed Sets . . . . . . 6 2.2 Us...

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 ...

In this paper, we consider a class of quadratic maximization problems. One important instance in that class is the famous quadratic maximization formulation of the max-cut problem studied by Goemans and Williamson [6]. Since the problem is NP-hard in general, following Goemans and Williamson, we apply the approximation method based on the semidefinite programming (SDP) relaxation. For a subclas...

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...

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...

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...

In this work we developed the α-cut worthy(Level) Graphs of Homomorphic, Box dot, Star Product Strong Neutrosophic Graphs. To explore some propositions, theorems and Examples.

This paper is comprised of the modeling and optimization of a multi objective linear programming problem in fuzzy environment in which some goals are fractional and some are linear. Here, we present a new approach for its solution by using α-cut of fuzzy numbers. In this proposed method, we first define membership function for goals by introducing non-deviational variables for each of objective...