We give de nitions for fuzzy subalgebras, for fuzzy relations on fuzzy sets, and for fuzzy compatibility, which generalize, improve and correct the existing ones. The unit interval is replaced here by a partially ordered algebra. Then we study their connection with the corresponding crisp concepts through their newly de ned Q-cuts.

Dynamic programming (DP) is a powerful paradigm for general, nonlinear optimal control. Computing exact DP solutions is in general only possible when the process states and the control actions take values in a small discrete set. In practice, it is necessary to approximate the solutions. Therefore, we propose an algorithm for approximate DP that relies on a fuzzy partition of the state space, a...

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...

Some IR models make use of an implication to match a document d and a query q, computing either “q implies d” (e.g. in fuzzy inclusion models) or, the other way, “d implies q” (e.g. in logical IR models). This paper analyzes, from a theoretical point of view, the IR models using both approaches. Even if the above notations seem to be opposite, it is shown that they sometimes come from different...

In this paper, the notions of   , q  -Q-fuzzy subgroup and normal subgroup are introduced and some of their properties are investigated.

∈ , ∈ ∨ q ) – fuzzy ideal (prime) of bounded lattice is introduced and its properties are studied. Mathematics Subject Classifications: 06B10, 06D72

We show that the 2-parameter Podles sphere is a q-fuzzy sphere precisely interpolating between the fuzzy sphere as quotient of the angular momentum algebra U(su2) and the standard q-sphere Cq [S] as subalgebra of the quantum group Cq [SU2]. Whereas the classical sphere as CP 1 can be defined as the algebra generated by the matrix entries of a projector e with trace(e) = 1, the fuzzy-sphere is d...

This paper presents a Dynamic Fuzzy Q-Learning (DFQL) method that is capable of tuning the Fuzzy Inference Systems (FIS) online. On-line self-organizing learning is developed so that structure and parameters identification are accomplished automatically and simultaneously. Selforganizing fuzzy inference is introduced to calculate actions and Q-functions so as to enable us to deal with continuou...