Let V and W be n-dimensional vector spaces over GF (2). A mapping Q : V →W is called crooked if it satisfies the following three properties: Q(0) = 0; Q(x) +Q(y) +Q(z) +Q(x+ y + z) 6= 0 for any three distinct x, y, z; Q(x) +Q(y) +Q(z) +Q(x+ a) +Q(y + a) +Q(z + a) 6= 0 if a 6= 0 (x, y, z arbitrary). We show that every crooked function gives rise to a distance regular graph of diameter 3 having λ...

Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with 13 some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic submeasures and more general semi-copula-based probabilistic submeasures. Some algebraic properties of classes of such submeasures are also studied. 15 © 2012 Else...