With the capability of dealing with vague and incomplete data, the study of fuzzy time series has attracted great interest and is expected to expand rapidly. Song and Chissom (1993) first proposed the seven-step forecasting framework of fuzzy time series which are composed of (1) definition of the universe of discourse, (2) partitioning of the universe of discourse, (3) definition of fuzzy sets...

Comparison and data analysis to the similarity measures and entropy for fuzzy sets are studied. The distance proportional value between the fuzzy set and the corresponding crisp set is represented as fuzzy entropy. We also verified that the sum of the similarity measure and the entropy between fuzzy set and the corresponding crisp set constitutes the total information. Finally, we derive a simi...

Let F*(K) be the set of all fuzzy complex numbers. In this paper some classical and measure-theoretical notions are extended to the case of complex fuzzy sets. They are fuzzy complex number-valued distance on F*(K), fuzzy complex number-valued measure on F*(K), and some related notions, such as null-additivity, pseudo-null-additivity, null-subtraction, pseudo-null-subtraction, autocontionuous f...

This paper proposes a new fuzzy similarity measure to calculate the degree of similarity of generalized fuzzy numbers (GFN’s).The fuzzy similarity measure is developed by integrating the concept of centre of gravity (COG) points and fuzzy difference of distance of points of fuzzy numbers. A fuzzy description for difference of distances between fuzzy numbers in its turn exploits appropriate simi...

This study is to propose a new approach for medical diagnosis using the distance between interval-valued intuitionistic fuzzy sets. For this purpose, we developed an interview chart with interval fuzzy degrees based on the relation between symptoms and diseases (three types of headache), and utilized the interval-valued intuitionistic fuzzy weighted arithmetic average operator to aggregate fuzz...

This paper deals with ridge estimation of fuzzy nonparametric regression models using triangular fuzzy numbers. This estimation method is obtained by implementing ridge regression learning algorithm in the La- grangian dual space. The distance measure for fuzzy numbers that suggested by Diamond is used and the local linear smoothing technique with the cross- validation procedure for selecting t...

The distance measure is an important criterion in any clustering algorithm. This paper shows how fuzzy clustering results can be improved by introducing a weighting factor in the inter-objects distance measures. New weighted versions of four well-known distance measures are considered. These distances are tested, using the fuzzy c-means algorithm, on three datasets. Experimental results show th...

FCM (fuzzy c-means algorithm) based on Euclidean distance function converges to a local minimum of the objective function, which can only be used to detect spherical structural clusters. The added fuzzy covariance matrices in their distance measure were not directly derived from the objective function. In this paper, an improved Normalized Clustering Algorithm Based on Mahalanobis distance by t...

fuzzy measures are suitable in analyzing human subjective evaluation processes. several different strategies have been proposed for distance of fuzzy numbers. the distances introduced for fuzzy numbers can be categorized in two groups:1. the crisp distances which explain crisp values for the distance between two fuzzy numbers.2. the fuzzy distance which introduce a fuzzy distance for normal fuz...