In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an examp...

The methods of fuzzy decision-making use the comparison of fuzzy numbers or sets to choose among alternatives. The linear ordering of real numbers does not extend to fuzzy numbers and fuzzy numbers can only be partially ordered and hence they cannot be compared. However, when fuzzy numbers are used in practical applications their comparison becomes necessary. Several methods of comparing fuzzy ...

Fuzzy C-means Clustering algorithm (FCM) is a method that is frequently used in pattern recognition. It has the advantage of giving good modeling results in many cases, although, it is not capable of specifying the number of clusters by itself. In FCM algorithm most researchers fix weighting exponent (m) to a conventional value of 2 which might not be the appropriate for all applications. Conse...

The primary goal of this paper is to price European options in the Merton’s framework with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes a...

Clustering is a key process in data mining for revealing structure and patterns in data. Fuzzy C-means (FCM) is a popular algorithm using a partitioning approach for clustering. One advantage of FCM is that it converges rapidly. In addition, using fuzzy sets to represent the degrees of cluster membership of each data point provides more information regarding relationships within the data than d...