An alternative to Darwinian-like artiicial evolution is ooered by Population-Based Incremental Learning (PBIL): this algorithm memorizes the best past individuals and uses this memory as a distribution, to generate the next population from scratch. This paper extends PBIL from boolean to continuous search spaces. A Gaussian model is used for the distribution of the population. The center of thi...

The water crisis is harmful effects on human life. Also one of the most problems in the human society is water resources management. In this study, site selection of most suitable areas for artificial recharge using Boolean model. Criteria used to select the most suitable area for artificial recharge included: infiltration, slope, aquifer thickness, aquifer quality.  The layers were produced an...

It is shown that the Boolean center of complemented elements in a bounded integral residuated lattice characterizes direct decompositions. Generalizing both Boolean products and poset sums of residuated lattices, the concepts of poset product, Priestley product and Esakia product of algebras are defined and used to prove decomposition theorems for various ordered algebras. In particular, we sho...

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 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...

Boolean Networks (BNs) are established models to qualitatively describe biological systems. The analysis of BNs might be infeasible for medium large due the state-space explosion problem. We propose a novel reduction technique called Backward Equivalence (BBE), which preserves some properties interest BNs. In particular, reduced provide compact representation by grouping variables that, if init...