We explore a notion of fuzzy T -neighbourhood spaces, for any continuous triangular norm T , and we present on this notion a uni6ed treatment. Our theory, on one hand, generalizes the theory of Lowen (Fuzzy Sets and Systems 7 (1982) 65) from T =Min to arbitrary T , which has been the progenitor of this work, and on the other hand it is strongly related to the theory of L-neighbourhoods of H; oh...

We believe that the study of the notions of universal algebra modelled in an arbitarry topos rather than in the category of sets provides a deeper understanding of the real features of the algebraic notions. [2], [3], [4], [S], [6], [7], [13], [14] are some examples of this approach. The lattice Id(L) of ideals of a lattice L (in the category of sets) is an important ingredient of the categ...

For n, k and t such that 1 < t < k < n, a set F of subsets of [n] has the (k, t)threshold property if every k-subset of [n] contains at least t sets from F and every (k − 1)-subset of [n] contains less than t sets from F . The minimal number of sets in a set system with this property is denoted by m(n, k, t). In this paper we determine m(n, 4, 3) exactly for n sufficiently large, and we show th...

‎We study the spatial distribution of point sets on the sphere obtained from the representation of a large integer as a sum of three integer squares‎. ‎We examine several statistics of these point sets‎, ‎such as the electrostatic potential‎, ‎Ripley's function‎, ‎the variance of the number of points in random spherical caps‎, ‎and the covering radius‎. ‎Some of the results are conditional on t...

$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, w...