This second part of the special issue of Fuzzy Sets and Systems is composed of three more papers presented at two special sessions of the Eighth-International Conference on Fuzzy Set Theory and Applications (FSTA), which took place in Liptovský Ján, Slovakia, from January 30 till February 3, 2006. The first paper is an extended version of the contribution presented at the special session on Logical Foundations of Fuzzy Mathematics, organized by Petr Cintula and Libor Běhounek. Its title is Relational compositions in Fuzzy Class Theory and it is written by L. Běhounek and M. Daňková. The paper presents a formal representation in terms of sup-T and inf-R compositions for certain notions of the theory of fuzzy relations, including images, pre-images, height, or plinth. Bymeans of this representation, many theorems on these notions can be proved by simple calculations drawn from the properties of fuzzy relational compositions. Although the main results are with regard to the formal derivability of such theorems in Fuzzy Class Theory, the informal account of the representation and the systematized properties of fuzzy relational notions given in the paper may be of interest for a broader community of researchers. Thanks are due to S. Gottwald for handling the peer review process of this paper. The other two papers are extended versions of the contributions presented at theMinisymposium on Fuzzy Approximation, organized by Vilém Novák and Irina Perfilieva. The first paper is entitled A neural network approach to the fuzzy transform and written by M. Štěpnička and O. Polakovič. It combines a neural nets technique with the technique of fuzzy transform. Recall that the latter is a general soft-computing technique inspired by the classical transforms such as Fourier or Laplace ones. The main idea of fuzzy transform is to construct a special space in which computation is simpler and return back to the original space after the necessary computations are completed. In the paper, the method is demonstrated on an example of approximation of functions. It is shown that the neural approach is an appropriate way of finding a suitable fuzzy partition of a domain which is a first step of fuzzy transform. The proposed technique is good for on-line computation where a number of samples can increase in time. The second paper is Fuzzy rational numbers and approximation of irrationals written by J. Hančl, L. Mišík and J.T. Tóth. It focuses on a specific problem of how irrational numbers can be tackled. In computations, irrational numbers are approximated by rational ones. The question arises, which rational numbers are appropriate and how precise such approximation can be. The above paper proposes a specific technique in which an irrational number is approximated by a sequence of fuzzy intervals with rational cores. A special measure of expressibility of a given irrational number is constructed and its properties are formulated. Furthermore, a specific measure called a degree of a real number is constructed which can be applied in the general theory of Diophantine approximations.