Let Q be a given n× n square symmetric matrix of nonnegative elements between 0 and 1, e.g. similarities. Fuzzy clustering results in fuzzy assignment of individuals to K clusters. In additive fuzzy clustering, the n × K fuzzy memberships matrix P is found by leastsquares approximation of the off-diagonal elements of Q by inner products of rows of P. By contrast, kernelized fuzzy c-means is not...

In intuitionistic fuzzy sets, there is a natural symmetry between degrees of truth and falsity. As a result, for such sets, natural similarity measures are symmetric relative to an exchange of true and false values. It has been recently shown that among such measures, the most intuitively reasonable are the ones which are also symmetric relative to an arbitrary permutation of degrees of truth, ...

in this paper, rstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases de ned by shi and huang, is equivalent to the family of its bases de ned by p. lubczonok. secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however,...

In this paper, the extension principle is used in order to fuzzify location and scale estimators when used on fuzzy numbers. First, fuzzy nonlinear means, such as arithmetic, harmonic, geometric and fuzzy L p mean are deened as extensions of the corresponding crisp means. Fuzzy maximum and minimum operators are used to deene order statistics of fuzzy numbers. Fuzzy L location and scale estimato...

Wewill define a notion for a quasi fuzzy p-normed space, then we use the fixed point alternative theorem to establish Hyers–Ulam– Rassias stability of the quartic functional equation where functions map a linear space into a complete quasi fuzzy p-normed space. Later, we will show that there exists a close relationship between the fuzzy continuity behavior of a fuzzy almost quartic function, co...

In this paper we propose a parallel structure of I-P-D (Integral minus Proportional minus Derivative) type fuzzy controller based on the conventional PID control theory, used to control the speed of DC motor. The conventional PID controller exhibit poor performance when applied to DC motor, it fails to perform satisfactory under parameter variation or load changes. The parallel I-P-D type fuzzy...