Several fuzzy connectives, including those proposed by Lotfi Zadeh, can be seen as linear extensions of the Boolean connectives from the scale ${0,1}$ into the scale $[0,1]$. We discuss these extensions, in particular, we focus on the dualities arising from the Boolean dualities. These dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from c...

the problem of series two-block disjoint decomposition of completely specifiedboolean functions is considered. analysis and investigation of such systems are veryimportant in logical design context. recently, a good method for solving thisproblem was suggested which has been based on the ternary matrix cover approach.using this method a computer program was developed. this paper is focused onde...

the square map is one of the functions used in cryptography. for instance, the square map is used in rabin encryption scheme, block cipher rc6 and stream cipher rabbit, in different forms. in this paper, we study statistical properties of the output of the square map as a vectorial boolean function. we obtain the joint probability distribution of arbitrary number of the upper and the lower bits...