Pairwise comparison matrices: an empirical research

Our research focused on testing various characteristics of pairwise comparison (PC) matrices in controlled experiments. About 270 students have been involved in the test exercises and the final pool contained 450 matrices. Our team conducted experiments with matrices of different size obtained from different types of MADM problems. The matrix elements have been generated by different questioning orders, too. The cases have been divided into 18 subgroups according to the key factors to be analyzed. The testing environment made it possible to analyze the dynamics of inconsistency as the number of elements increased in a given case. Various types of inconsistency indices have been applied. The consequent behavior of the decision maker has also been analyzed in case of incomplete matrices using indicators to measure the deviation from the final ranking of alternatives and from the final score vector

On Saaty's and Koczkodaj's inconsistencies of pairwise comparison matrices

The aim of the paper is to obtain some theoretical and numerical properties of Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices (PRM). In the case of 3 × 3 PRM, a differentiable one-to-one correspondence is given between Saaty’s inconsistency ratio and Koczkodaj’s inconsistency index based on the elements of PRM. In order to make a comparison of Saaty’s and Koczkodaj’s inconsistencies for 4 × 4 pairwise comparison matrices, the average value of the maximal eigenvalues of randomly generated n × n PRM is formulated, the elements aij (i < j) of which were randomly chosen from the ratio scale ... ... with equal probability 1/(2M − 1) and a ji is defined as 1/a ij . By statistical analysis, the empirical distributions of the maximal eigenvalues of the PRM depending on the dimension number are obtained. As the dimension number increases, the shape of distributions gets similar to that of the normal ones. Finally, the inconsistency of asymmetry is dealt with, showing a different type of inconsistency

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

Información Consistente para la toma de Decisiones Empresariales

Finalmente, se propone una nueva familia de índices de valoración de productos y servicios de mayoría, y se implementa el QV-ORI que representa las opiniones en un intervalo e incorpora un índice de confiabilidad intervalar IRI, que establece la confiabilidad de las opiniones no solicitadas de los usuarios. Las mencionadas propuestas se han probado con ejemplos del mundo real, lográndose resultados acordes a lo esperado para estos casos y contexto. Fecha de lectura de Tesis Doctoral: 11 de diciembre 2019Actualmente la sociedad vive un cambio de paradigma denominado Sociedad de la información, que afecta a individuos y a empresas/organizaciones en la forma de comunicarse, informase y relacionarse. La segmentación de consumidores es mayor al existir múltiples canales de información; la diferenciación de productos y servicios es cada vez menor, entonces es necesario conocer los sentimientos basado en las experiencias propias o ajenas relacionadas con productos o servicios. En este contexto, son necesarios sistemas que ayuden en las tomas de decisiones. En este trabajo se han abordado tres retos: la calidad de los datos, en su dimensión de consistencia, la representación de la información; y, por último, índices de valoración de productos o servicios, para una valoración más representativa de la opinión de los consumidores o usuarios. Consecuentemente, se ha propuesto un índice 〖IC〗^+, que determina la consistencia de los datos en diferentes tipos de matrices de comparación entre pares: reciprocas, difusas y aditivas; y un ratio de consistencia, basado en percentiles, para aceptar o rechazar dichas matrices en los procesos de decisión. También, se propone un modelo de decisión multicriterio, que establece preferencias de productos o servicios con datos/opiniones no solicitados extraídos de los Social Media, utilizando un intervalos que posibilita mayor información; un índice de consistencia intervalar 〖ICI〗^+; los operadores ISMA-OWA y AC-OWG que ranquea las alternativas, y un algoritmo de extracción de submatrices consistentes

Densification of spatially-sparse legacy soil data at a national scale: a digital mapping approach

Digital soil mapping (DSM) is a viable approach to providing spatial soil information but its adoption at the national scale, especially in sub-Saharan Africa, is limited by low spread of data. Therefore, the focus of this thesis is on optimizing DSM techniques for densification of sparse legacy soil data using Nigeria as a case study. First, the robustness of Random Forest model (RFM) was tested in predicting soil particle-size fractions as a compositional data using additive log-ratio technique. Results indicated good prediction accuracy with RFM while soils are largely coarse-textured especially in the northern region. Second, soil organic carbon (SOC) and bulk density (BD) were predicted from which SOC density and stock were calculated. These were overlaid with land use/land cover (LULC), agro-ecological zone (AEZ) and soil maps to quantify the carbon sequestration of soils and their variation across different AEZs. Results showed that 6.5 Pg C with an average of 71.60 Mg C ha–1 abound in the top 1 m soil depth. Furthermore, to improve the performance of BD and effective cation exchange capacity (ECEC) pedotransfer functions (PTFs), the inclusion of environmental data was explored using multiple linear regression (MLR) and RFM. Results showed an increase in performance of PTFs with the use of soil and environmental data. Finally, the application of Choquet fuzzy integral (CI) technique in irrigation suitability assessment was assessed. This was achieved through multi-criteria analysis of soil, climatic, landscape and socio-economic indices. Results showed that CI is a better aggregation operator compared to weighted mean technique. A total of 3.34 x 106 ha is suitable for surface irrigation in Nigeria while major limitations are due to topographic and soil attributes. Research findings will provide quantitative basis for framing appropriate policies on sustainable food production and environmental management, especially in resource-poor countries of the world