On reducing inconsistency of pairwise comparison matrices below an acceptance threshold

A recent work of the authors on the analysis of pairwise comparison matrices that can be made consistent by the modification of a few elements is continued and extended. Inconsistency indices are defined for indicating the overall quality of a pairwise comparison matrix. It is expected that serious contradictions in the matrix imply high inconsistency and vice versa. However, in the 35-year history of the applications of pairwise comparison matrices, only one of the indices, namely CR proposed by Saaty, has been associated to a general level of acceptance, by the well known ten percent rule. In the paper, we consider a wide class of inconsistency indices, including CR, CM proposed by Koczkodaj and Duszak and CI by Pel\'aez and Lamata. Assume that a threshold of acceptable inconsistency is given (for CR it can be 0.1). The aim is to find the minimal number of matrix elements, the appropriate modification of which makes the matrix acceptable. On the other hand, given the maximal number of modifiable matrix elements, the aim is to find the minimal level of inconsistency that can be achieved. In both cases the solution is derived from a nonlinear mixed-integer optimization problem. Results are applicable in decision support systems that allow real time interaction with the decision maker in order to review pairwise comparison matrices.Comment: 20 page

Source apportionment of carbonaceous chemical species to fossil fuel combustion, biomass burning and biogenic emissions by a coupled radiocarbon-levoglucosan marker method

An intensive aerosol measurement and sample collection campaign was conducted in central Budapest in a mild winter for 2 weeks. The online instruments included an FDMS-TEOM, RT-OC/EC analyser, DMPS, gas pollutant analysers and meteorological sensors. The aerosol samples were collected on quartz fibre filters by a low-volume sampler using the tandem filter method. Elemental carbon (EC), organic carbon (OC), levoglucosan, mannosan, galactosan, arabitol and mannitol were determined, and radiocarbon analysis was performed on the aerosol samples. Median atmospheric concentrations of EC, OC and PM2.5 mass were 0.97, 4.9 and 25 mu g m(-3), respectively. The EC and organic matter (1.6 x OC) accounted for 4.8 and 37 %, respectively, of the PM2.5 mass. Fossil fuel (FF) combustion represented 36% of the total carbon (TC = EC + OC) in the PM2.5 size fraction. Biomass burning (BB) was a major source (40 %) for the OC in the PM2.5 size fraction, and a substantial source (11 %) for the PM10 mass. We propose and apply here a novel, straightforward, coupled radiocarbon-levoglucosan marker method for source apportionment of the major carbonaceous chemical species. The contributions of EC and OC from FF combustion (ECFF and OCFF to the TC were 11.0 and 25 %, respectively, EC and OC from BB (ECBB and OCBB were responsible for 5.8 and 34 %, respectively, of the TC, while the OC from biogenic sources (OCBIO made up 24% of the TC. The overall relative uncertainty of the OCBIO and OCBB contributions was assessed to be up to 30 %, while the relative uncertainty for the other apportioned species is expected to be below 20 %. Evaluation of the apportioned atmospheric concentrations revealed some of their important properties and relationships among them. ECFF and OCFF were associated with different FF combustion sources. Most ECFF was emitted by vehicular road traffic, while the contribution of non-vehicular sources such as domestic and industrial heating or cooking using gas, oil or coal to OCFF was substantial. The mean contribution of BB to EC particles was smaller by a factor of approximately 2 than that of road traffic. The main formation processes of OCFF, OCBB and OCBIO from volatile organic compounds were jointly influenced by a common factor, which is most likely the atmospheric photochemistry, while primary organic emissions can also be important. Technological improvements and control measures for various BB appliances, together with efficient education and training of their users, in particular on the admissible fuel types, offer an important potential for improving the air quality in Budapest, and likely in other cities as well

Pairwise comparison matrices and the error-free property of the decision maker

Pairwise comparison is a popular assessment method either for deriving criteria-weights or for evaluating alternatives according to a given criterion. In real-world applications consistency of the comparisons rarely happens: intransitivity can occur. The aim of the paper is to discuss the relationship between the consistency of the decision maker—described with the error-free property—and the consistency of the pairwise comparison matrix (PCM). The concept of error-free matrix is used to demonstrate that consistency of the PCM is not a sufficient condition of the error-free property of the decision maker. Informed and uninformed decision makers are defined. In the first stage of an assessment method a consistent or near-consistent matrix should be achieved: detecting, measuring and improving consistency are part of any procedure with both types of decision makers. In the second stage additional information are needed to reveal the decision maker’s real preferences. Interactive questioning procedures are recommended to reach that goal

Comparison of weighting methods used in multicriteria decision analysis frameworks in healthcare with focus on low- and middle-income countries

Criteria weighting is a key element of multicriteria decision analysis that is becoming extensively used in healthcare decision-making. In our narrative review we describe the advantages and disadvantages of various weighting methods.An assessment of the eight identified primary criteria weighting methods was compiled on domains including their resource requirements, and potential for bias.In general, we found more complex methods to have less potential for bias; however, resource intensity and general participant burden is greater for these methods.The selection of the most appropriate method depends on the decision-making context. The simple multiattribute rating technique (SMART) method combined with swing-weighting technique and the analytic hierarchy process methods may be the most feasible approaches for low- and middle-income countries

Chemical characterization of laboratory-generated tar ball particles

The chemical properties of laboratory-generated tar ball (Lab-TB) particles produced from dry distillate (wood tars) of three different wood species in the laboratory were investigated by analytical techniques that had never been used before for their characterization. The elemental compositions of laboratory-generated tar balls (Lab- TBs) from three tree species were very similar to one another and to those characteristic of atmospheric tar balls (TBs) collected from the savanna fire during the SAFARI 2000 sampling campaign. The O=C and H= C molar ratios of the generated Lab-TBs were at the upper limit characteristic of soot particles. The Fourier transform infrared spectroscopy (FTIR) spectra of the generated Lab-TBs were very similar to one another as well and also showed some similarity with those of atmospheric humic-like substances (HULIS). The FT-IR measurements indicated that Lab-TBs have a higher proportion of aromatic structure than HULIS and the oxygen atoms of Lab-TBs are mainly found in hydroxyl and keto functional groups. Whereas Raman activity was detected in the starting materials of the Lab-TBs (wood tars) in the range of 1000–1800 c