In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

It is an important methodology to extract product’s overall KANSEI images by evaluating Critical Form Features (CFF). In this paper, Multi-class Fuzzy Support Vector Machines (MF-SVM) employing Emotional Cellular (EC) model was presented to extract KANSEI images of product’s CFF. EC is a very special kind of semantics cell, which is defined on two-dimensional (Valence-Arousal) emotional space. ...

Exploration of large and high-dimensional data sets is one of the main problems in data analysis. Self-organizing feature maps (SOFM) is a powerful technique for clustering analysis and data mining. Competitive learning in the SOFM training process focuses on finding a neuron that its weight vector is most similar to that of an input vector. SOFM can be used to map large data sets to a simpler,...

We have observed that the support vector clustering method proposed by Asa Ben Hur, David Horn, Hava T. Siegelmann, Vladimir Vapnik, (Journal of Machine Learning Research, (2001), 125–137) can provide cluster boundaries of arbitrary shape based on a Gaussian kernel abstaining from explicit calculations in the high-dimensional feature space. This allows us to apply the method to the training set...

The paper describes an approach to discover transparent fuzzy rules from data, which can be effectively used in fuzzy model-based medical diagnosis. The approach is based on three main stages. First, available symptoms measurements are clustered by our Crisp Double Clustering scheme, which identifies, in the first instance, informative prototypes in the original measurements space by a vector q...

This paper proposes a compromise model, based on the technique for order preference through similarity ideal solution (TOPSIS) methodology, to solve the multi-objective large-scale linear programming (MOLSLP) problems with block angular structure involving fuzzy parameters. The problem involves fuzzy parameters in the objective functions and constraints. This compromise programming method is ba...

Algorithms of fuzzy -means clustering with kernels employed in nonlinear transformations into high dimensional spaces in the support vector machines are studied. The objective functions in the standard method and the entropy based method are considered and iterative solutions in the alternate optimization algorithm are derived. Explicit cluster centers in the data space are not obtained by this...

“Fuzzy Functions” are proposed to be determined separately by two regression estimation models: the least squares estimation (LSE), and Support Vector Machines for Regression (SVR), techniques for the development of fuzzy system models. LSE model tries to estimate the fuzzy function parameters linearly in the original space, whereas SVR algorithm maps the data samples into higher dimensional fe...

A character recognition system using soft computing techniques is presented in this paper. We define fuzzy sets on the Hough transform of each character pattern pixel and synthesize additional fuzzy sets by t-norms. The heights of these t-norms form an n-dimensional feature vector for the character. A 3n-dimensional vector is then generated from the n-dimensional feature vector by defining thre...