A two-phase algorithm for consensus building in AHP-group decision making

Group decision making through the AHP has received significant attention in contemporary research, the primary focus of which has been on the issues of consistency and consensus building. In this paper, we concentrate on the latter and present a two-phase algorithm based on the optimal clustering of decision makers (members of a group) into sub groups followed by consensus building both within sub groups and between sub groups. Two-dimensional Sammon’s mapping is proposed as a tool for generating an approximate visualization of sub groups identified in multidimensional vector space, while the consensus convergence model is suggested for reaching agreement amongst individuals in and between sub groups. As a given, all decision makers evaluate the same decision elements within the AHP framework and produce individual scores of these decision elements. The consensual scores are obtained through the iterative procedure and the final scores are declared as the group decision. The results of two selected numerical examples are compared with two sets of results: the results obtained by the commonly used geometric mean aggregation method and also the results obtained if the consensus convergence model is applied directly without the prior clustering of the decision makers. The comparisons indicated the expected differences among the aggregation schemes and the final group scores. The matrices of respect values in the consensus convergence model, obtained for cases when the decision makers are optimally clustered and when they are not, show that in the latter case the decision makers receive lower weights of respect from other members in the group. Various tests showed that our approach is efficient in cases when no clusters can be visually and undoubtedly identified, especially if the number of group members is high.     

Linear Transport Equations with μ-Monotone Coefficients

We introduce the concept of a μ-monotone function. It allows us to extend the existing theory for Filippov solutions to ODE, linear transport equations, and conservation laws for a wider range of transport velocities (A₁,…,A_d) and fluxes (f₁,…,f_d).     

General preservers of quasi-commutativity on self-adjoint operators

Let H be a separable Hilbert space and Bsa(H) the set of all bounded linear self-adjoint operators. We say that A,B∈Bsa(H) quasi-commute if there exists a nonzero ξ∈C such that AB=ξBA. Bijective maps on Bsa(H) which preserve quasi-commutativity in both directions are classified.     

Extremal generalized centralizers in matrix algebras

We describe matrices with extremal generalized centralizers over algebraically closed fields.     

Some Recent Progress and Applications in Graph Minor Theory

In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the ``rough' structure of graphs excluding a fixed minor. This result was used to prove Wagner's Conjecture that finite graphs are well-quasi-ordered under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some of these along with some other recent advances on graph minors are surveyed. Research partly supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research, Grant number 16740044, by Sumitomo Foundation, by C & C Foundation and by Inoue Research Award for Young Scientists Supported in part by the Research Grant P1–0297 and by the CRC program On leave from: IMFM & FMF, Department of Mathematics, University of Ljubljana, Ljubljana, Slovenia     

Identification of the effective distribution function for determination of the distributed activation energy models using Bayesian statistics: Application of isothermal thermogravimetric data

The new procedure for identification of the effective distribution function for determination of the distributed activation energy models, which is based on the Bayesian statistics, has been established. The five different continuous probability functions (exponential, logistic, normal, gamma and Weibull probability functions (the extended set of distributions)) were used for searching the most appropriate reactivity model for two heterogeneous processes: (a) the isothermal reduction process of nickel oxide under hydrogen atmosphere and (b) the isothermal degradation process of bisphenol‐A polycarbonate (Lexan) under nitrogen atmosphere. Using the Bayes weights, it was shown that for both processes, the most suitable distributed reactivity model is the Weibull distribution model. The kinetic parameters (ln A, E_a) attached with the Weibull distribution model were calculated for both investigated processes, using three different computational methods (the maximum likelihood method (MLM), the nonlinear regression analysis (NRA), and the posterior mean (the expected value of scale parameter η, E(η)). It was shown that there is an excellent agreement between the values of kinetic parameters calculated by the MLM, NRA, and E(η) approaches. Using Bayes weights, it is possible to discriminate between different probability models and to quantify how well a distribution fits the experimental data. For the formal reactivity model comparison, the use of the (nonnormalized) Jeffreys prior is recommended. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 641–658, 2010     

Organomercury(II) and tellurium(II) compounds with the "pincer" ligand 2,6-[O(CH2CH2)2NCH2]2C6H3--stabilization of an unusual organotellurium(II) cationic species

The reaction of RH (1) with Hg(OAc)(2), in EtOH, gave the acetate RHgOAc (2) [R = 2,6-[O(CH(2)CH(2))(2)NCH(2)](2)C(6)H(3)]. The corresponding RHgCl (3) was obtained from 2 and LiCl. The reaction of 3 with TeCl(4) (1:1 molar ratio), in anhydrous 1,4-dioxane, resulted in the transfer of the organic ligand from mercury to tellurium and the isolation of the unexpected ionic compounds [RTe](2)[Hg(2)Cl(6)] (4) and [RH(3)][HgCl(4)] (5). The molecular structures of 1-4 and 5·H(2)O were established by single-crystal X-ray diffraction. The acetate 2 and the chloride 3 are monomeric in solid state. In both mercury and tellurium organometallic compounds the organic group acts as an (N,C,N) "pincer" ligand. This coordination pattern provided stability for the rare [RTe](+) cation. Weak cation-anion interactions [Te···Cl 3.869(3) ?] are present between [RTe](+) and the dinuclear anion [Hg(2)Cl(6)](2-) in the crystal of 4. Theoretical calculations with DFT methods were performed for models of 3 and 4. The results show that in the cation of 4 the coordination of the nitrogen atoms play an important role for the stabilization of the structure found in the crystal whereas in 3 the coordination of the nitrogen atoms to the metal centre stabilizes to a less extent the structure found in solid state.