We survey current term-wise techniques for quadratizing high-degree pseudo-Boolean functions and introduce a new one, which allows multiple splits of terms. We also introduce the first aggregative approach, which splits a collection of terms based on their common parts.

Three important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the Cauchy functional equation in several variables. We show that these properties are equivalent and we completely describe the functions characterized by them. By adding some regularity condition...

Let A be a finite set and B an arbitrary set with at least two elements. The arity gap of a function f : An → B is the minimum decrease in the number of essential variables when essential variables of f are identified. A non-trivial fact is that the arity gap of such B-valued functions on A is at most |A|. Even less trivial to verify is the fact that the arity gap of B-valued functions on A wit...

This work aims to investigate the competitive time-dependent desorption rate of heavy metals (lead, zinc, nickel) coexisting with phenanthrene from natural high buffering soil. Two non-ionic surfactants (Tween 80 and Brij 35) combined with disodium ethylene diamine tetraacetate salt (Na2-EDTA) were utilized as the reagents. The contaminants’ time-dependent desorption data was fitted with five k...

Reversible logic is becoming more and more prominent as the technology sets higher demands on heat, power, scaling and stability. Reversible gates are able at any time to ”undo” the current step or function. Multiple-valued logic has the advantage of transporting and evaluating higher bits each clock cycle than binary. Moreover, we demonstrate in this paper, combining these disciplines we can c...

We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lovász extension of a pseudo-Boolean function which vanishes at the origin. We present axiomatizations of this generalized Choquet integral, given in terms of certain functional equations, as well as by necessary and sufficient conditions which reveal desirable propertie...

the removal of cd2+ and pb2+ ions from wastewater using p-tert-butyl-calix[4] arene was investigated in terms of initial ph, initial concentration, adsorbent dosage, contact time and temperature. the maximum adsorption occurred at the ph value of 6. the adsorbent studied exhibits high efficiency for cd (ii)and pb (ii) adsorption and the equilibrium states could be achieved in 10 min. adsorption...

A function f : {−1, 1} → R is called pseudo-Boolean. It is wellknown that each pseudo-Boolean function f can be written as f(x) =

The aim of this paper is to completely classify all aggregation functions based on the notion of arity gap. We first establish explicit descriptions of the arity gap of the Lovász extensions of pseudo-Boolean functions and, in particular, of the Choquet integrals. Then we consider the wider class of order-preserving functions between arbitrary, possibly different, posets, and show that similar ...