Analysis of pairwise comparison matrices: an empirical research

Pairwise comparison (PC) matrices are used in multi-attribute decision problems (MADM) in order to express the preferences of the decision maker. Our research focused on testing various characteristics of PC matrices. In a controlled experiment with university students (N = 227) we have obtained 454 PC matrices. The cases have been divided into 18 subgroups according to the key factors to be analyzed. Our team conducted experiments with matrices of different size given from different types of MADM problems. Additionally, the matrix elements have been obtained by different questioning procedures differing in the order of the questions. Results are organized to answer five research questions. Three of them are directly connected to the inconsistency of a PC matrix. Various types of inconsistency indices have been applied. We have found that the type of the problem and the size of the matrix had impact on the inconsistency of the PC matrix. However, we have not found any impact of the questioning order. Incomplete PC matrices played an important role in our research. The decision makers behavioral consistency was as well analyzed in case of incomplete matrices using indicators measuring the deviation from the final order of alternatives and from the final score vector

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

Evolution of Global Lightning in the Transition From Cold to Warm Phase Preceding Two Super El Niño Events

Multistation observations of Schumann resonance (SR) intensity document common behavior in the evolution of continental‐scale lightning activity in two super El Niño events, occurring in 1997/98 and 2015/16. The vertical electric field component of SR at Nagycenk, Hungary and the two horizontal magnetic field components in Rhode Island, USA in 1997, and in 2014–2015, the two horizontal magnetic field components at Hornsund, Svalbard and Eskdalemuir, United Kingdom as well as in Boulder Creek, California and Alberta, Canada exhibit considerable increases in SR intensity from some tens of percent up to a few hundred percents in the transition months preceding the two super El Niño events. The UT time distribution of anomalies in SR intensity indicates that in 1997 the lightning activity increases mainly in Southeast Asia, the Maritime Continent and India, i.e. the Asian chimney region. On the other hand, a global response in lightning is indicated by the anomalies in SR intensity in 2014 and 2015. SR‐based results are strengthened by comparison to independent lightning observations from the Optical Transient Detector and the World Wide Lightning Location Network, which also exhibit increased lightning activity in the transition months. The increased lightning is attributable to increased instability due to thermodynamic disequilibrium between the surface and the midtroposphere during the transition. The main conclusion is that variations in SR intensity may act as a precursor for the occurrence and magnitude of these extreme climate events, and in keeping with earlier findings, as a precursor to maxima in global surface air temperature. Schumann resonance (SR) is a global phenomenon produced by low frequency electromagnetic radiation (\u3c100 Hz) from worldwide lightning. Lightning strokes act as wideband electromagnetic antennas transmitting in this specific frequency band, and due to the extreme low attenuation of electromagnetic waves, their radiated signals can be observed anywhere on Earth. This phenomenon enables the monitoring of global lightning with just a very few (up to four in this study) observation sites around the globe. The main advantage of the SR‐based method is the expectation that all of the worldwide lightning contributes to the measured SR field, which means the absence of detection efficiency problems which are inherent with many other lightning detection methods. In this work, we use SR measurements to monitor changes in both regional and global lightning activity in connection with two extremely large magnitude, so called “super” El Niño events (1997/98 and 2015/16). Our conclusion is that SR intensity variations in the transition months preceding these two El Niño events indicate an important increase in lightning activity attributable to thermodynamic disequilibrium. We suggest that SR intensity variations might be applied in the future to predict the occurrence of these extreme climate events. Schumann resonance intensities are analyzed from distant stations in connection with two super El Niño events Increased Schumann resonance intensity indicates enhanced lightning activity in the transition from cold to warm phase in both events Schumann resonance intensity may be a precursor for occurrence of super El Niño events and for maxima in global surface air temperature Schumann resonance intensities are analyzed from distant stations in connection with two super El Niño events Increased Schumann resonance intensity indicates enhanced lightning activity in the transition from cold to warm phase in both events Schumann resonance intensity may be a precursor for occurrence of super El Niño events and for maxima in global surface air temperatur

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

Aggregating Centrality Rankings: A Novel Approach to Detect Critical Infrastructure Vulnerabilities

Assessing critical infrastructure vulnerabilities is paramount to arrange efficient plans for their protection. Critical infrastructures are network-based systems hence, they are composed of nodes and edges. The literature shows that node criticality, which is the focus of this paper, can be addressed from different metric-based perspectives (e.g., degree, maximal flow, shortest path). However, each metric provides a specific insight while neglecting others. This paper attempts to overcome this pitfall through a methodology based on ranking aggregation. Specifically, we consider several numerical topological descriptors of the nodes’ importance (e.g., degree, betweenness, closeness, etc.) and we convert such descriptors into ratio matrices; then, we extend the Analytic Hierarchy Process problem to the case of multiple ratio matrices and we resort to a Logarithmic Least Squares formulation to identify an aggregated metric that represents a good tradeoff among the different topological descriptors. The procedure is validated considering the Central London Tube network as a case study

Evolution of global lightning in the transition from cold to warm phase preceding two super El Niño events

Multi-station observations of Schumann resonance (SR) intensity document common behavior in the evolution of continental-scale lightning activity in two super El Niño events, occurring in 1997/98 and 2015/16. The vertical electric field component of SR at Nagycenk, Hungary and the two horizontal magnetic field components in Rhode Island, USA in 1997, and in 2014–2015, the two horizontal magnetic field components at Hornsund, Svalbard and Eskdalemuir, United Kingdom as well as in Boulder Creek, California and Alberta, Canada exhibit considerable increases in SR intensity from some tens of percent up to a few hundred percents in the transition months preceding the two super El Niño events. The UT time distribution of anomalies in SR intensity indicates that in 1997 the lightning activity increases mainly in Southeast Asia, the Maritime Continent and India, i.e. the Asian chimney region. On the other hand, a global response in lightning is indicated by the anomalies in SR intensity in 2014 and 2015. SR-based results are strengthened by comparison to independent lightning observations from the Optical Transient Detector and the World Wide Lightning Location Network, which also exhibit increased lightning activity in the transition months. The increased lightning is attributable to increased instability due to thermodynamic disequilibrium between the surface and the mid-troposphere during the transition. The main conclusion is that variations in SR intensity may act as a precursor for the occurrence and magnitude of these extreme climate events, and in keeping with earlier findings, as a precursor to maxima in global surface air temperature

An impossibility theorem for paired comparisons

In several decision-making problems, alternatives should be ranked on the basis of paired comparisons between them. We present an axiomatic approach for the universal ranking problem with arbitrary preference intensities, incomplete and multiple comparisons. In particular, two basic properties -- independence of irrelevant matches and self-consistency -- are considered. It is revealed that there exists no ranking method satisfying both requirements at the same time. The impossibility result holds under various restrictions on the set of ranking problems, however, it does not emerge in the case of round-robin tournaments. An interesting and more general possibility result is obtained by restricting the domain of independence of irrelevant matches through the concept of macrovertex.Comment: 18 pages, 4 figure