A classification of Hermitian representations for the recently introduced fuzzy torus algebra is presented. This is carried out by regarding the fuzzy torus algebra as a q-deformation of parafermion. In addition to the known representations, new representations of both finite and infinite dimension are found. Using the infinite dimensional representation, coherent state for the fuzzy torus is c...

In (Chaudhuri and Rosenfeld, 1996), metrics were developed for fuzzy sets u and v defined on the same support set S. These metrics are based on applying the Hausdorff metric to pairs of membership level sets (u 1 ( [ tk, 1 ] ), v1 ( [ tk, 1 ] ) ), where tk E [0, 1] is a (possible) membership value of u or v. The metrics of (Chaudhuri and Rosenfeld, 1996) give nice comparisons of fuzzy sets by m...

In this paper, first of all the distance measure entitled generalized Hausdorff distance is defined between two generalized fuzzy numbers that has been introduced by Chen [3]. Then using another distance and combining it with the generalized Hausdorff distance, a fuzzy distance measure is introduced with the help of fuzzy distance measure proposed in [1] to generalize fuzzy numbers. The concept...

Exploratory data analysis heavily relies on methods to visualize data and models in a user friendly and interpretable manner. We show how models consisting of a collection of fuzzy points can be visualized in parallel coordinates. In contrast to existing techniques that display only lines representing centroids or shaded areas showing the general variance of cluster centers, the proposed techni...

We prove recognition theorems for codimension one manifold factors of dimension n ≥ 4. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that X ×R is a manifold in the cases when X is a resolvable generalized manifold of finite dimension n ≥ 3 wit...

It has been developed a C++ program that generates random fuzzy relations of a given dimension and computes their T-transitive closure (that contains the initial relation) and the new T-transitivized relation (that is contained in the initial relation) for the t-norms minimum, product and Lukasiewicz. It has been computed several distances between both transitive closure and transitivized relat...

In these notes we give an extensive survey of the recent progress for critical spread-out oriented percolation above the upper critical dimension. We describe the main tools, which are the lace expansion and the inductive method. The lace expansion gives a recursion relation for the two-point functions involved, and the inductive method gives an inductive analysis of the arising recursion relat...

The inductive learning of fuzzy rule-based classification systems usually encounters an issue of exponential growth of the fuzzy rulesearch space when the number of patternsand/or variables becomes large.This issue makes the learning process more difficultand, in most cases, may lead to scalability problems. Alcalá-Fdezet al.proposed a fuzzy association rule-based classification method for high...

Individual vehicle information, especially, vehicle classification data play a key role in Advanced Traffic Management and Information Systems (ATMIS). In inductive loop and piezo-sensor fusion systems, traffic data such as the vehicle length and the distance between axles are used for vehicle classification. However, classification errors often occur in distinguishing passenger cars from small...