Searching for the dimension of valued preference relations.

The more information a preference structure gives, the more sophisticated representation techniques are necessary, so decision makers can have a global view of data and therefore a comprehensive understanding of the problem they are faced with. In this paper we propose to explore valued preference relations by means of a search for the number of underlying criteria allowing its representation in real space. A general representation theorem for arbitrary crisp binary relations is obtained, showing the difference in representation between incomparability-related to the intersection operator-and other inconsistencies-related to the union operator. A new concept of dimension is therefore proposed, taking into account inconsistencies in source of information. Such a result is then applied to each alpha-cut of valued preference relations. (C) 2002 Elsevier Science Inc. All rights reserved

Removal of model cationic dye by adsorption onto poly(methacrylic acid)/zeolite hydrogel composites: Kinetics, equilibrium study and image analysis

Composites based on poly(methacrylic acid) (PMAA) and two types of zeolite, hydrophilic zeolite A and hydrophobic zeolite ZSM-5, were synthesized. The obtained hydrogel composites that combine well the strong interaction between PMAA and cationic species, the accessibility of active sites in the swollen network and fine mechanical stability of zeolites are considered promising candidates for removal of cationic dye, basic yellow 28 (BY28) from aqueous solutions. The adsorption was found to be highly dependent on composition of hydrogel composites, initial dye concentration, solution pH, sorbent mass and temperature, while the effect of zeolite type is less manifested. It was found that the surface adsorption influenced the kinetics of adsorption which was determined by the rate of movement of the boundary layer of BY28 adsorbed on hydrogel surface. Adsorption processes were found to be favorable and preferably physical in nature with maximum adsorption capacity that could reach up to 180 mg/g for PMAA/30A hydrogel composite. Image analysis was applied on differently colored hydrogels and revealed the linear correlation between equilibrium adsorption capacities and the mean values of pixel intensity, as well as the strong effect of initial dye concentration on uniformity of coloration along the hydrogel diameter