The Development of the Generalization Algorithm Based on the Rough Set Theory

This paper considers the problem of concept generalization in decision-making systems where such features of real-world databases as large size, incompleteness and inconsistence of the stored information are taken into account. The methods of the rough set theory (like lower and upper approximations, positive regions and reducts) are used for the solving of this problem. The new discretization algorithm of the continuous attributes is proposed. It essentially increases an overall performance of generalization algorithms and can be applied to processing of real value attributes in large data tables. Also the search algorithm of the significant attributes combined with a stage of discretization is developed. It allows avoiding splitting of continuous domains of insignificant attributes into intervals.

Identifying the configurational paths to innovation in SMEs:a fuzzy-set qualitative comparative analysis

Using fuzzy-set qualitative comparative analysis (fsQCA), this study investigates the conditions leading to a higher level of innovation. More specifically, the study explores the impact of inter-organisational knowledge transfer networks and organisations' internal capabilities on different types of innovation in Small to Medium size Enterprises (SMEs) in the high-tech sector. A survey instrument was used to collect data from a sample of UK SMEs. The findings show that although individual factors are important, there is no need for a company to perform well in all the areas. The fsQCA, which enables the examination of the impacts of different combinations of factors, reveals that there are a number of paths to achieve better incremental and radical innovation performance. Companies need to choose the one that is closest to their abilities and fits best with their resources.

Modulating membership grades to gain consensus for fuzzy set uncertainty values in a clinical decision support system

This paper deals with a very important issue in any knowledge engineering discipline: the accurate representation and modelling of real life data and its processing by human experts. The work is applied to the GRiST Mental Health Risk Screening Tool for assessing risks associated with mental-health problems. The complexity of risk data and the wide variations in clinicians' expert opinions make it difficult to elicit representations of uncertainty that are an accurate and meaningful consensus. It requires integrating each expert's estimation of a continuous distribution of uncertainty across a range of values. This paper describes an algorithm that generates a consensual distribution at the same time as measuring the consistency of inputs. Hence it provides a measure of the confidence in the particular data item's risk contribution at the input stage and can help give an indication of the quality of subsequent risk predictions. © 2010 IEEE.

Partner selection for reverse logistics centres in green supply chains: a fuzzy artificial immune optimization approach

The design of reverse logistics networks has now emerged as a major issue for manufacturers, not only in developed countries where legislation and societal pressures are strong, but also in developing countries where the adoption of reverse logistics practices may offer a competitive advantage. This paper presents a new model for partner selection for reverse logistic centres in green supply chains. The model offers three advantages. Firstly, it enables economic, environment, and social factors to be considered simultaneously. Secondly, by integrating fuzzy set theory and artificial immune optimization technology, it enables both quantitative and qualitative criteria to be considered simultaneously throughout the whole decision-making process. Thirdly, it extends the flat criteria structure for partner selection evaluation for reverse logistics centres to the more suitable hierarchy structure. The applicability of the model is demonstrated by means of an empirical application based on data from a Chinese electronic equipment and instruments manufacturing company.

Entrepreneurship rates the fuzzy-set approach

A fuzzy-set qualitative comparative analysis is applied to determine the necessary and sufficient conditions for higher entrepreneur rates. Based on Global Entrepreneurship Monitor data, it is shown that the most relevant conditions are Media Attention to Entrepreneurship, as well as Perceived Capabilities and Perceived Opportunities. The non-existence of Fear of Failure is also an important factor in determining higher entrepreneurship rates. When the sample is split, this condition is more important for most developed countries. This can be viewed as relevant information for policymakers to better define their policies to promote entrepreneurship, which is a key to more sustainable growth in countries.

What are the conditions for good innovation results? A fuzzy-set approach for European Union

Innovation is one of the main concerns of European Union countries since the beginning of the century. Despite failing to reach their targets, innovation remains a priority because innovation enables countries to achieve better economic performance. This study analyzes the relation between the level of innovation and the economic effects and applies a fuzzy-set qualitative comparative analysis to study the relation between six conditions and two different outcomes. The data comes from the Union Innovation Scoreboard. The study finds that research systems, linkages and entrepreneurship, and intellectual assets are necessary conditions for the outcomes of a high level of innovation and positive economic effects. The main sufficient condition for both outcomes is a good research system.

Technical and economic resources management in smart grids using heuristic optimization methods

Intensive use of Distributed Generation (DG) represents a change in the paradigm of power systems operation making small-scale energy generation and storage decision making relevant for the whole system. This paradigm led to the concept of smart grid for which an efficient management, both in technical and economic terms, should be assured. This paper presents a new approach to solve the economic dispatch in smart grids. The proposed methodology for resource management involves two stages. The first one considers fuzzy set theory to define the natural resources range forecast as well as the load forecast. The second stage uses heuristic optimization to determine the economic dispatch considering the generation forecast, storage management and demand response

Análise dos métodos de seleção de fornecedores

No ambiente altamente competitivo de hoje, um processo eficaz de seleção de fornecedores é muito importante para o sucesso de qualquer organização [33]. Esta dissertação procura determinar quais os critérios e métodos mais utilizados no problema da seleção de fornecedores, contribuindo assim para o apoio a entidades que pretendam iniciar uma seleção de fornecedores de uma forma mais eficaz. Para atingir os objetivos propostos, foi realizada uma análise de artigos que fazem a revisão literária dos métodos e critérios desde o ano de 1985 até ao ano 2012. Com os dados obtidos destas revisões, foi possível identificar quais os três principais métodos utilizados ao longo dos anos, sendo eles o DEA, AHP e Fuzzy set theory e os principais critérios utilizados na seleção de fornecedores. Nesta dissertação, é apresentada uma visão geral da tomada de decisão e os métodos utilizados na tomada de decisão multicritério. É abordado o problema da seleção de fornecedores, o seu processo de seleção e as revisões literárias dos métodos e critérios de seleção utilizados nos últimos anos. Por fim, é apresentada a contribuição para a seleção de fornecedores do estudo realizado durante o desenvolvimento desta dissertação, sendo apresentados e explicados os principais métodos de seleção de fornecedores, bem como os critérios utilizados.

Three essays in financial economics: asset pricing, optimal portfolio selection and financial integration

Executive Summary The unifying theme of this thesis is the pursuit of a satisfactory ways to quantify the riskureward trade-off in financial economics. First in the context of a general asset pricing model, then across models and finally across country borders. The guiding principle in that pursuit was to seek innovative solutions by combining ideas from different fields in economics and broad scientific research. For example, in the first part of this thesis we sought a fruitful application of strong existence results in utility theory to topics in asset pricing. In the second part we implement an idea from the field of fuzzy set theory to the optimal portfolio selection problem, while the third part of this thesis is to the best of our knowledge, the first empirical application of some general results in asset pricing in incomplete markets to the important topic of measurement of financial integration. While the first two parts of this thesis effectively combine well-known ways to quantify the risk-reward trade-offs the third one can be viewed as an empirical verification of the usefulness of the so-called "good deal bounds" theory in designing risk-sensitive pricing bounds. Chapter 1 develops a discrete-time asset pricing model, based on a novel ordinally equivalent representation of recursive utility. To the best of our knowledge, we are the first to use a member of a novel class of recursive utility generators to construct a representative agent model to address some long-lasting issues in asset pricing. Applying strong representation results allows us to show that the model features countercyclical risk premia, for both consumption and financial risk, together with low and procyclical risk free rate. As the recursive utility used nests as a special case the well-known time-state separable utility, all results nest the corresponding ones from the standard model and thus shed light on its well-known shortcomings. The empirical investigation to support these theoretical results, however, showed that as long as one resorts to econometric methods based on approximating conditional moments with unconditional ones, it is not possible to distinguish the model we propose from the standard one. Chapter 2 is a join work with Sergei Sontchik. There we provide theoretical and empirical motivation for aggregation of performance measures. The main idea is that as it makes sense to apply several performance measures ex-post, it also makes sense to base optimal portfolio selection on ex-ante maximization of as many possible performance measures as desired. We thus offer a concrete algorithm for optimal portfolio selection via ex-ante optimization over different horizons of several risk-return trade-offs simultaneously. An empirical application of that algorithm, using seven popular performance measures, suggests that realized returns feature better distributional characteristics relative to those of realized returns from portfolio strategies optimal with respect to single performance measures. When comparing the distributions of realized returns we used two partial risk-reward orderings first and second order stochastic dominance. We first used the Kolmogorov Smirnov test to determine if the two distributions are indeed different, which combined with a visual inspection allowed us to demonstrate that the way we propose to aggregate performance measures leads to portfolio realized returns that first order stochastically dominate the ones that result from optimization only with respect to, for example, Treynor ratio and Jensen's alpha. We checked for second order stochastic dominance via point wise comparison of the so-called absolute Lorenz curve, or the sequence of expected shortfalls for a range of quantiles. As soon as the plot of the absolute Lorenz curve for the aggregated performance measures was above the one corresponding to each individual measure, we were tempted to conclude that the algorithm we propose leads to portfolio returns distribution that second order stochastically dominates virtually all performance measures considered. Chapter 3 proposes a measure of financial integration, based on recent advances in asset pricing in incomplete markets. Given a base market (a set of traded assets) and an index of another market, we propose to measure financial integration through time by the size of the spread between the pricing bounds of the market index, relative to the base market. The bigger the spread around country index A, viewed from market B, the less integrated markets A and B are. We investigate the presence of structural breaks in the size of the spread for EMU member country indices before and after the introduction of the Euro. We find evidence that both the level and the volatility of our financial integration measure increased after the introduction of the Euro. That counterintuitive result suggests the presence of an inherent weakness in the attempt to measure financial integration independently of economic fundamentals. Nevertheless, the results about the bounds on the risk free rate appear plausible from the view point of existing economic theory about the impact of integration on interest rates.

La borrosidad como epistemología de la interacción social: algunos alcances y potencialidades

En este trabajo se describen la teoría de los conjuntos borrosos de L. A. Zadeh(antecedentes, características e implicaciones) y las áreas en las que se ha aplicado laborrosidad en psicología y psicología social (desarrollo evolutivo, procesamiento deestímulos, percepción de la información, prototipos y otras aplicaciones). A partir de esto,se sugiere cómo la borrosidad podría ser útil en el estudio de la interacción social,asumiendo el carácter simultáneamente vago y preciso de la realidad, y la utilización deconceptos como la noción de sí mismo desde una visión compleja, que considere, desde laperspectiva del pluralismo, diversas posturas teóricas y metodológicas.

Linguistic models for decision support

Linguistic modelling is a rather new branch of mathematics that is still undergoing rapid development. It is closely related to fuzzy set theory and fuzzy logic, but knowledge and experience from other fields of mathematics, as well as other fields of science including linguistics and behavioral sciences, is also necessary to build appropriate mathematical models. This topic has received considerable attention as it provides tools for mathematical representation of the most common means of human communication - natural language. Adding a natural language level to mathematical models can provide an interface between the mathematical representation of the modelled system and the user of the model - one that is sufficiently easy to use and understand, but yet conveys all the information necessary to avoid misinterpretations. It is, however, not a trivial task and the link between the linguistic and computational level of such models has to be established and maintained properly during the whole modelling process. In this thesis, we focus on the relationship between the linguistic and the mathematical level of decision support models. We discuss several important issues concerning the mathematical representation of meaning of linguistic expressions, their transformation into the language of mathematics and the retranslation of mathematical outputs back into natural language. In the first part of the thesis, our view of the linguistic modelling for decision support is presented and the main guidelines for building linguistic models for real-life decision support that are the basis of our modeling methodology are outlined. From the theoretical point of view, the issues of representation of meaning of linguistic terms, computations with these representations and the retranslation process back into the linguistic level (linguistic approximation) are studied in this part of the thesis. We focus on the reasonability of operations with the meanings of linguistic terms, the correspondence of the linguistic and mathematical level of the models and on proper presentation of appropriate outputs. We also discuss several issues concerning the ethical aspects of decision support - particularly the loss of meaning due to the transformation of mathematical outputs into natural language and the issue or responsibility for the final decisions. In the second part several case studies of real-life problems are presented. These provide background and necessary context and motivation for the mathematical results and models presented in this part. A linguistic decision support model for disaster management is presented here – formulated as a fuzzy linear programming problem and a heuristic solution to it is proposed. Uncertainty of outputs, expert knowledge concerning disaster response practice and the necessity of obtaining outputs that are easy to interpret (and available in very short time) are reflected in the design of the model. Saaty’s analytic hierarchy process (AHP) is considered in two case studies - first in the context of the evaluation of works of art, where a weak consistency condition is introduced and an adaptation of AHP for large matrices of preference intensities is presented. The second AHP case-study deals with the fuzzified version of AHP and its use for evaluation purposes – particularly the integration of peer-review into the evaluation of R&D outputs is considered. In the context of HR management, we present a fuzzy rule based evaluation model (academic faculty evaluation is considered) constructed to provide outputs that do not require linguistic approximation and are easily transformed into graphical information. This is achieved by designing a specific form of fuzzy inference. Finally the last case study is from the area of humanities - psychological diagnostics is considered and a linguistic fuzzy model for the interpretation of outputs of multidimensional questionnaires is suggested. The issue of the quality of data in mathematical classification models is also studied here. A modification of the receiver operating characteristics (ROC) method is presented to reflect variable quality of data instances in the validation set during classifier performance assessment. Twelve publications on which the author participated are appended as a third part of this thesis. These summarize the mathematical results and provide a closer insight into the issues of the practicalapplications that are considered in the second part of the thesis.

Multi Objective Evolutionary Algorithm Applied to the Optimal Power Flow Problem

This work presents the application of a multiobjective evolutionary algorithm (MOEA) for optimal power flow (OPF) solution. The OPF is modeled as a constrained nonlinear optimization problem, non-convex of large-scale, with continuous and discrete variables. The violated inequality constraints are treated as objective function of the problem. This strategy allows attending the physical and operational restrictions without compromise the quality of the found solutions. The developed MOEA is based on the theory of Pareto and employs a diversity-preserving mechanism to overcome the premature convergence of algorithm and local optimal solutions. Fuzzy set theory is employed to extract the best compromises of the Pareto set. Results for the IEEE-30, RTS-96 and IEEE-354 test systems are presents to validate the efficiency of proposed model and solution technique.

Uma abordagem nebulosa de raciocínio baseado em casos para recomendação de sistemas marítimos de produção de petróleo

Pós-graduação em Ciência da Computação - IBILCE

On the Arithmetic of Errors

An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of real numbers. We focus on certain operations of errors which seem not to have been sufficiently studied algebraically. In this work we restrict ourselves to arithmetic operations for errors related to addition and multiplication by scalars. We pay special attention to subtractability-like properties of errors and the induced “distance-like” operation. This operation is implicitly used under different names in several contemporary fields of applied mathematics (inner subtraction and inner addition in interval analysis, generalized Hukuhara difference in fuzzy set theory, etc.) Here we present some new results related to algebraic properties of this operation.

Oil spill environmental risk assessment of stationary sources in offshore zones (Innovating a mathematical model)

Nowadays, risks arising from the rapid development of oil and gas industries are significantly increasing. As a result, one of the main concerns of either industrial or environmental managers is the identification and assessment of such risks in order to develop and maintain appropriate proactive measures. Oil spill from stationary sources in offshore zones is one of the accidents resulting in several adverse impacts on marine ecosystems. Considering a site's current situation and relevant requirements and standards, risk assessment process is not only capable of recognizing the probable causes of accidents but also of estimating the probability of occurrence and the severity of consequences. In this way, results of risk assessment would help managers and decision makers create and employ proper control methods. Most of the represented models for risk assessment of oil spills are achieved on the basis of accurate data bases and analysis of historical data, but unfortunately such data bases are not accessible in most of the zones, especially in developing countries, or else they are newly established and not applicable yet. This issue reveals the necessity of using Expert Systems and Fuzzy Set Theory. By using such systems it will be possible to formulize the specialty and experience of several experts and specialists who have been working in petroliferous areas for several years. On the other hand, in developing countries often the damages to environment and environmental resources are not considered as risk assessment priorities and they are approximately under-estimated. For this reason, the proposed model in this research is specially addressing the environmental risk of oil spills from stationary sources in offshore zones.