The induced generalized OWA operator

[spa] Se presenta el operador OWA generalizado inducido (IGOWA). Es un nuevo operador de agregación que generaliza al operador OWA a través de utilizar las principales características de dos operadores muy conocidos como son el operador OWA generalizado y el operador OWA inducido. Entonces, este operador utiliza medias generalizadas y variables de ordenación inducidas en el proceso de reordenación. Con esta formulación, se obtiene una amplia gama de operadores de agregación que incluye a todos los casos particulares de los operadores IOWA y GOWA, y otros casos particulares. A continuación, se realiza una generalización mayor al operador IGOWA a través de utilizar medias cuasi-aritméticas. Finalmente, también se desarrolla un ejemplo numérico del nuevo modelo en un problema de toma de decisiones financieras.

The induced 2-tuple linguistic generalized OWA operator and its application in linguistic decision making

[spa] Se presenta el operador de media ponderada ordenada generalizada lingüística de 2 tuplas inducida (2-TILGOWA). Es un nuevo operador de agregación que extiende los anteriores modelos a través de utilizar medias generalizadas, variables de ordenación inducidas e información lingüística representada mediante el modelo de las 2 tuplas lingüísticas. Su principal ventaja se encuentra en la posibilidad de incluir a un gran número de operadores de agregación lingüísticos como casos particulares. Por eso, el análisis puede ser visto desde diferentes perspectivas de forma que se obtiene una visión más completa del problema considerado y seleccionar la alternativa que parece estar en mayor concordancia con nuestros intereses o creencias. A continuación se desarrolla una generalización mayor a través de utilizar medias cuasi-aritméticas, obteniéndose el operador Quasi-2-TILOWA. El trabajo finaliza analizando la aplicabilidad del nuevo modelo en un problema de toma de decisiones sobre gestión de la producción.

The generalized index of maximum and minimum level and its application in decision making

[spa] El índice del máximo y el mínimo nivel es una técnica muy útil, especialmente para toma de decisiones, que usa la distancia de Hamming y el coeficiente de adecuación en el mismo problema. En este trabajo, se propone una generalización a través de utilizar medias generalizadas y cuasi aritméticas. A estos operadores de agregación, se les denominará el índice del máximo y el mínimo nivel medio ponderado ordenado generalizado (GOWAIMAM) y cuasi aritmético (Quasi-OWAIMAM). Estos nuevos operadores generalizan una amplia gama de casos particulares como el índice del máximo y el mínimo nivel generalizado (GIMAM), el OWAIMAM, y otros. También se desarrolla una aplicación en la toma de decisiones sobre selección de productos.

Decision-making with distance measures and inducedaggregation operators

[spa] Se presenta un nuevo modelo para la toma de decisiones basado en el uso de medidas de distancia y de operadores de agregación inducidos. Se introduce la distancia media ponderada ordenada inducida (IOWAD). Es un nuevo operador de agregación que extiende el operador OWA a través del uso de distancias y un proceso de reordenación de los argumentos basado en variables de ordenación inducidas. La principal ventaja el operador IOWAD es la posibilidad de utilizar una familia parametrizada de operadores de agregación entre la distancia individual máxima y la mínima. Se estudian algunas de sus principales propiedades y algunos casos particulares. Se desarrolla un ejemplo numérico en un problema de toma de decisiones sobre selección de inversiones. Se observa que la principal ventaja de este modelo en la toma de decisiones es la posibilidad de mostrar una visión más completa del proceso, de forma que el decisor está capacitado para seleccionar la alternativa que está más cerca de sus intereses.

Decision-making with distance measures and inducedaggregation operators

[spa] Se presenta un nuevo modelo para la toma de decisiones basado en el uso de medidas de distancia y de operadores de agregación inducidos. Se introduce la distancia media ponderada ordenada inducida (IOWAD). Es un nuevo operador de agregación que extiende el operador OWA a través del uso de distancias y un proceso de reordenación de los argumentos basado en variables de ordenación inducidas. La principal ventaja el operador IOWAD es la posibilidad de utilizar una familia parametrizada de operadores de agregación entre la distancia individual máxima y la mínima. Se estudian algunas de sus principales propiedades y algunos casos particulares. Se desarrolla un ejemplo numérico en un problema de toma de decisiones sobre selección de inversiones. Se observa que la principal ventaja de este modelo en la toma de decisiones es la posibilidad de mostrar una visión más completa del proceso, de forma que el decisor está capacitado para seleccionar la alternativa que está más cerca de sus intereses.

A method for decision making with the OWA operator

A new method for decision making that uses the ordered weighted averaging (OWA) operator in the aggregation of the information is presented. It is used a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index is based on distance measures and other techniques that are useful for decision making. By using the OWA operator in the IMAM, we form a new aggregation operator that we call the ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator. The main advantage is that it provides a parameterized family of aggregation operators between the minimum and the maximum and a wide range of special cases. Then, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. A further extension of this approach is presented by using hybrid averages and Choquet integrals. We also develop an application of the new approach in a multi-person decision-making problem regarding the selection of strategies.

A method for decision making with the OWA operator

A new method for decision making that uses the ordered weighted averaging (OWA) operator in the aggregation of the information is presented. It is used a concept that it is known in the literature as the index of maximum and minimum level (IMAM). This index is based on distance measures and other techniques that are useful for decision making. By using the OWA operator in the IMAM, we form a new aggregation operator that we call the ordered weighted averaging index of maximum and minimum level (OWAIMAM) operator. The main advantage is that it provides a parameterized family of aggregation operators between the minimum and the maximum and a wide range of special cases. Then, the decision maker may take decisions according to his degree of optimism and considering ideals in the decision process. A further extension of this approach is presented by using hybrid averages and Choquet integrals. We also develop an application of the new approach in a multi-person decision-making problem regarding the selection of strategies.

The induced generalized OWA operator

We present the induced generalized ordered weighted averaging (IGOWA) operator. It is a new aggregation operator that generalizes the OWA operator by using the main characteristics of two well known aggregation operators: the generalized OWA and the induced OWA operator. Then, this operator uses generalized means and order inducing variables in the reordering process. With this formulation, we get a wide range of aggregation operators that include all the particular cases of the IOWA and the GOWA operator, and a lot of other cases such as the induced ordered weighted geometric (IOWG) operator and the induced ordered weighted quadratic averaging (IOWQA) operator. We further generalize the IGOWA operator by using quasi-arithmetic means. The result is the Quasi-IOWA operator. Finally, we also develop a numerical example of the new approach in a financial decision making problem.

Indicators for the characterization of discrete Choquet integrals

Ordered weighted averaging (OWA) operators and their extensions are powerful tools used in numerous decision-making problems. This class of operator belongs to a more general family of aggregation operators, understood as discrete Choquet integrals. Aggregation operators are usually characterized by indicators. In this article four indicators usually associated with the OWA operator are extended to discrete Choquet integrals: namely, the degree of balance, the divergence, the variance indicator and Renyi entropies. All of these indicators are considered from a local and a global perspective. Linearity of indicators for linear combinations of capacities is investigated and, to illustrate the application of results, indicators of the probabilistic ordered weighted averaging -POWA- operator are derived. Finally, an example is provided to show the application to a specific context.

Past, present and future - assessing changes in aquatic environments using subfossil diatoms

The deterioration of surface waters is one of the most important issues in the environmental management of the European Union. Thus, the EU Water Framework Directive 2000/60/EC (WFD) requires “good ecological and chemical status” of surface waters by 2015 allowing only a slight departure from ecological reference conditions characterized by the biological communities typical for the conditions of minimal anthropogenic impact. The WFD requires the determination of ecological reference conditions and the present ecological status of surface waters. To meet this legislative demand, sedimentary diatom assemblages were used in these studies with various methods 1) to assess natural and human activity induced environmental changes, 2) to characterize background conditions 3) to evaluate the present ecological status and 4) to predict the future of the water bodies in the light of palaeolimnological data. As the WFD refers to all surface waters, both coastal and inland sites were included. Two long and two short sediment cores from the Archipelago Sea in the northern Baltic Sea were examined for their siliceous microfossils in order to assess (1) the Holocene palaeoenvironmental history and (2) the recent eutrophication of the area. The diatom record was divided into local diatom assemblage zones (LDAZ, long cores) and diatom assemblage zones (DAZ, short cores). Locally weighted weighted averaging regression and calibration (LWWA) was applied for the quantitative reconstruction of past TN concentrations (short cores). An age model for the long cores was constructed by using independent palaeomagnetic and AMS-14C methods. The short cores were dated using radiometric (210Pb, 226Ra and 137Cs) methods. The long cores date back to the early history of the Archipelago Sea, which was freshwater – no salinity increase referable to the brackish phase of the Yoldia Sea is recognized. The nutrient status of the lacustrine phase was slightly higher in the Archipelago Sea than in the Baltic Proper. Initial brackish-water influence is observed at 8 150 ±80 cal. BP (LDAZ4), but fully brackish conditions were established at 7 700 ±80 cal. BP (LDAZ5). The diatom assemblages indicate increasing salinity, warming climate and possible eutrophic conditions during the lacustrine to brackish-water transition. The decreasing abundance of Pseudosolenia calcar-avis (Schultze) Sundström and the increasing abundance of the ice-cover indicator species Pauliella taeniata (Grunow) Round and Basson indicate decreasing salinity and climatic cooling after ca. 5 000 cal. BP. Signs of eutrophication are visible in the most recent diatom assemblage zones of both short cores. Diatom-inferred total nitrogen (DI-TN) reconstructions partially fail to trace the actual measured total nitrogen concentrations especially from the late 1980s to the mid 1990s. This is most likely due to the dominating diatom species Pauliella taeniata, Thalassiosira levanderi Van Goor and Fragilariopsis cylindrus (Grunow) W. Krieger being more influenced by factors such as the length of the ice-season rather than nutrient concentrations. It is concluded that the diatom assemblages of the study sites are principally governed by climate fluctuations, with a slight influence of eutrophication visible in the most recent sediments. There are indications that global warming, with reduced ice cover, could impact the spring blooming diatom species composition in the Archipelago Sea. In addition, increased sediment accumulation in the early 90s coincides with the short ice-seasons suggesting that warming climate with decreasing ice-cover may increase sedimentation in the study area. The diverse diatom assemblages dominated by benthic species (54 %) in DAZ1 in the Käldö Fjärd core can be taken as background diatom assemblages for the Archipelago Sea. Since then turbidity has increased and the diatom assemblages have been dominated by planktonic diatoms from around the mid 1800s onwards. The reconstructed reference conditions for the total nitrogen concentrations fluctuate around 400 μg l-1. Altogether two short sediment cores and eight short cores for top-bottom analysis were retrieved from Lake Orijärvi and Lake Määrjärvi to assess the impact of the acid mine drainage (AMD) derived metals from the Orijärvi mine tailings on the diatom communities of the lakes. The Cu (Pb, Zn) mine of Orijärvi (1757 – 1956) was the first one in Finland where flotation techniques (1911 – 1955) were used to enrich ore and large quantities of tailings were produced. The AMD derived metal impact to the lakes was found to be among the heaviest thus far recorded in Finland. Concentrations of Cu, Pb and Zn in Lake Orijärvi sediments are two to three orders of magnitude higher than background values. The metal inputs have affected Lake Orijärvi and Lake Määrjärvi diatom communities at the community levels through shifts in dominant taxa (both lakes) and at the individual level through alteration in frustule morphology (Lake Orijärvi). At present, lake water still has elevated heavy metal levels, indicating that the impact from the tailings area continues to affect both lakes. Lake Orijärvi diatom assemblages are completely dominated by benthic species and are lacking planktonic diatoms. In Lake Määrjärvi the proportion of benthic and tychoplanktonic diatoms has increased and the planktonic taxa have decreased in abundance. Achnanthidium minutissimum Kützing and Brachysira vitrea (Grun.) R. Ross in Hartley were the most tolerant species to increased metal concentrations. Planktonic diatoms are more sensitive to metal contamination than benthic taxa, especially species in the genus Cyclotella (Kützing) Brébisson. The ecological reference conditions assessed in this study for Lake Orijärvi and Lake Määrjärvi comprise diverse planktonic and benthic communitites typical of circumneutral oligotrophic lakes, where the planktonic diatoms belonging to genera Cyclotella , Aulacoseira Thwaites, Tabellaria Ehrenberg and Asterionella Hassall dominate in relative abundances up to ca. 70%. The benthic communities are more diverse than the planktonic consisting of diatoms belonging to the genera Achnanthes Bory, Fragilaria Lyngbye and Navicula St. Vincent. This study clearly demonstrates that palaeolimnological methods, especially diatom analysis, provide a powerful tool for the EU Water Frame Work Directive for defining reference conditions, natural variability and current status of surface waters. The top/bottom approach is a very useful tool in larger-scale studies needed for management purposes. This “before and after” type of sediment sampling method can provide a very time and cost effective assessment of ecological reference conditions of surface waters.

Differential evolution based classification with pool of distances and aggregation operators

The objective of this thesis is to develop and generalize further the differential evolution based data classification method. For many years, evolutionary algorithms have been successfully applied to many classification tasks. Evolution algorithms are population based, stochastic search algorithms that mimic natural selection and genetics. Differential evolution is an evolutionary algorithm that has gained popularity because of its simplicity and good observed performance. In this thesis a differential evolution classifier with pool of distances is proposed, demonstrated and initially evaluated. The differential evolution classifier is a nearest prototype vector based classifier that applies a global optimization algorithm, differential evolution, to determine the optimal values for all free parameters of the classifier model during the training phase of the classifier. The differential evolution classifier applies the individually optimized distance measure for each new data set to be classified is generalized to cover a pool of distances. Instead of optimizing a single distance measure for the given data set, the selection of the optimal distance measure from a predefined pool of alternative measures is attempted systematically and automatically. Furthermore, instead of only selecting the optimal distance measure from a set of alternatives, an attempt is made to optimize the values of the possible control parameters related with the selected distance measure. Specifically, a pool of alternative distance measures is first created and then the differential evolution algorithm is applied to select the optimal distance measure that yields the highest classification accuracy with the current data. After determining the optimal distance measures for the given data set together with their optimal parameters, all determined distance measures are aggregated to form a single total distance measure. The total distance measure is applied to the final classification decisions. The actual classification process is still based on the nearest prototype vector principle; a sample belongs to the class represented by the nearest prototype vector when measured with the optimized total distance measure. During the training process the differential evolution algorithm determines the optimal class vectors, selects optimal distance metrics, and determines the optimal values for the free parameters of each selected distance measure. The results obtained with the above method confirm that the choice of distance measure is one of the most crucial factors for obtaining higher classification accuracy. The results also demonstrate that it is possible to build a classifier that is able to select the optimal distance measure for the given data set automatically and systematically. After finding optimal distance measures together with optimal parameters from the particular distance measure results are then aggregated to form a total distance, which will be used to form the deviation between the class vectors and samples and thus classify the samples. This thesis also discusses two types of aggregation operators, namely, ordered weighted averaging (OWA) based multi-distances and generalized ordered weighted averaging (GOWA). These aggregation operators were applied in this work to the aggregation of the normalized distance values. The results demonstrate that a proper combination of aggregation operator and weight generation scheme play an important role in obtaining good classification accuracy. The main outcomes of the work are the six new generalized versions of previous method called differential evolution classifier. All these DE classifier demonstrated good results in the classification tasks.

Younger Dryas and Allerød summer temperatures at Gerzensee (Switzerland) inferred from fossil pollen and cladoceran assemblages

Linear- and unimodal-based inference models for mean summer temperatures (partial least squares, weighted averaging, and weighted averaging partial least squares models) were applied to a high-resolution pollen and cladoceran stratigraphy from Gerzensee, Switzerland. The time-window of investigation included the Allerød, the Younger Dryas, and the Preboreal. Characteristic major and minor oscillations in the oxygen-isotope stratigraphy, such as the Gerzensee oscillation, the onset and end of the Younger Dryas stadial, and the Preboreal oscillation, were identified by isotope analysis of bulk-sediment carbonates of the same core and were used as independent indicators for hemispheric or global scale climatic change. In general, the pollen-inferred mean summer temperature reconstruction using all three inference models follows the oxygen-isotope curve more closely than the cladoceran curve. The cladoceran-inferred reconstruction suggests generally warmer summers than the pollen-based reconstructions, which may be an effect of terrestrial vegetation not being in equilibrium with climate due to migrational lags during the Late Glacial and early Holocene. Allerød summer temperatures range between 11 and 12°C based on pollen, whereas the cladoceran-inferred temperatures lie between 11 and 13°C. Pollen and cladocera-inferred reconstructions both suggest a drop to 9–10°C at the beginning of the Younger Dryas. Although the Allerød–Younger Dryas transition lasted 150–160 years in the oxygen-isotope stratigraphy, the pollen-inferred cooling took 180–190 years and the cladoceran-inferred cooling lasted 250–260 years. The pollen-inferred summer temperature rise to 11.5–12°C at the transition from the Younger Dryas to the Preboreal preceded the oxygen-isotope signal by several decades, whereas the cladoceran-inferred warming lagged. Major discrepancies between the pollen- and cladoceran-inference models are observed for the Preboreal, where the cladoceran-inference model suggests mean summer temperatures of up to 14–15°C. Both pollen- and cladoceran-inferred reconstructions suggest a cooling that may be related to the Gerzensee oscillation, but there is no evidence for a cooling synchronous with the Preboreal oscillation as recorded in the oxygen-isotope record. For the Gerzensee oscillation the inferred cooling was ca. 1 and 0.5°C based on pollen and cladocera, respectively, which lies well within the inherent prediction errors of the inference models.

Morphological variation within the diatom taxon Cyclotella comensis and its importance for quantitative temperature reconstructions

1. The morphologically complex taxon Cyclotella comensis Grunow had no clear relationship with environmental parameters in a study using sediment surface samples from the Swiss Alps. The morphological heterogeneity of the taxon was investigated by applying a principal component analysis (PCA) to 9000 presence/absence descriptions of valves from surface samples of six lakes from different altitudes (15 characteristics, 100 valves each lake). The PCA allowed the classification of six morphs, which differed mainly in size and length of striae. Photographs of the morphs are shown in this paper. 2. Sixty-eight sediment surface samples were analysed using these newly defined six morphs. Summer temperature explained a major part of the variance between the morphs as assessed by a redundancy analysis (RDA). Summer temperature optima and tolerances were estimated using weighted averaging. 3. The influence of the revised C. comensis taxonomy on the diatom inferred summer temperature of a high alpine lake is discussed in a multiproxy context for the past 800 years.

Modern diatom, cladocera, chironomid, and chrysophyte cyst assemblages as quantitative indicators for the reconstruction of past environmental conditions in the Alps. II. Nutrients

Surface sediments from 68 small lakes in the Alps and 9 well-dated sediment core samples that cover a gradient of total phosphorus (TP) concentrations of 6 to 520 μg TP l-1 were studied for diatom, chrysophyte cyst, cladocera, and chironomid assemblages. Inference models for mean circulation log10 TP were developed for diatoms, chironomids, and benthic cladocera using weighted-averaging partial least squares. After screening for outliers, the final transfer functions have coefficients of determination (r2, as assessed by cross-validation, of 0.79 (diatoms), 0.68 (chironomids), and 0.49 (benthic cladocera). Planktonic cladocera and chrysophytes show very weak relationships to TP and no TP inference models were developed for these biota. Diatoms showed the best relationship with TP, whereas the other biota all have large secondary gradients, suggesting that variables other than TP have a strong influence on their composition and abundance. Comparison with other diatom – TP inference models shows that our model has high predictive power and a low root mean squared error of prediction, as assessed by cross-validation.

An intercontinental comparison of chironomid palaeotemperature inference models: Europe vs North America

Chironomid-temperature inference models based on North American, European and combined surface sediment training sets were compared to assess the overall reliability of their predictions. Between 67 and 76 of the major chironomid taxa in each data set showed a unimodal response to July temperature, whereas between 5 and 22 of the common taxa showed a sigmoidal response. July temperature optima were highly correlated among the training sets, but the correlations for other taxon parameters such as tolerances and weighted averaging partial least squares (WA-PLS) and partial least squares (PLS) regression coefficients were much weaker. PLS, weighted averaging, WA-PLS, and the Modern Analogue Technique, all provided useful and reliable temperature inferences. Although jack-knifed error statistics suggested that two-component WA-PLS models had the highest predictive power, intercontinental tests suggested that other inference models performed better. The various models were able to provide good July temperature inferences, even where neither good nor close modern analogues for the fossil chironomid assemblages existed. When the models were applied to fossil Lateglacial assemblages from North America and Europe, the inferred rates and magnitude of July temperature changes varied among models. All models, however, revealed similar patterns of Lateglacial temperature change. Depending on the model used, the inferred Younger Dryas July temperature decrease ranged between 2.5 and 6°C.