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.

Fuzzy ontology for knowledge mobilisation and decision support

A growing concern for organisations is how they should deal with increasing amounts of collected data. With fierce competition and smaller margins, organisations that are able to fully realize the potential in the data they collect can gain an advantage over the competitors. It is almost impossible to avoid imprecision when processing large amounts of data. Still, many of the available information systems are not capable of handling imprecise data, even though it can offer various advantages. Expert knowledge stored as linguistic expressions is a good example of imprecise but valuable data, i.e. data that is hard to exactly pinpoint to a definitive value. There is an obvious concern among organisations on how this problem should be handled; finding new methods for processing and storing imprecise data are therefore a key issue. Additionally, it is equally important to show that tacit knowledge and imprecise data can be used with success, which encourages organisations to analyse their imprecise data. The objective of the research conducted was therefore to explore how fuzzy ontologies could facilitate the exploitation and mobilisation of tacit knowledge and imprecise data in organisational and operational decision making processes. The thesis introduces both practical and theoretical advances on how fuzzy logic, ontologies (fuzzy ontologies) and OWA operators can be utilized for different decision making problems. It is demonstrated how a fuzzy ontology can model tacit knowledge which was collected from wine connoisseurs. The approach can be generalised and applied also to other practically important problems, such as intrusion detection. Additionally, a fuzzy ontology is applied in a novel consensus model for group decision making. By combining the fuzzy ontology with Semantic Web affiliated techniques novel applications have been designed. These applications show how the mobilisation of knowledge can successfully utilize also imprecise data. An important part of decision making processes is undeniably aggregation, which in combination with a fuzzy ontology provides a promising basis for demonstrating the benefits that one can retrieve from handling imprecise data. The new aggregation operators defined in the thesis often provide new possibilities to handle imprecision and expert opinions. This is demonstrated through both theoretical examples and practical implementations. This thesis shows the benefits of utilizing all the available data one possess, including imprecise data. By combining the concept of fuzzy ontology with the Semantic Web movement, it aspires to show the corporate world and industry the benefits of embracing fuzzy ontologies and imprecision.

A fuzzy grassroots ontology for improving social semantic web search

The web is continuously evolving into a collection of many data, which results in the interest to collect and merge these data in a meaningful way. Based on that web data, this paper describes the building of an ontology resting on fuzzy clustering techniques. Through continual harvesting folksonomies by web agents, an entire automatic fuzzy grassroots ontology is built. This self-updating ontology can then be used for several practical applications in fields such as web structuring, web searching and web knowledge visualization.A potential application for online reputation analysis, added value and possible future studies are discussed in the conclusion.

Remuneration Structure Definition for Distributed Generation Units and Demand Response Participants Aggregation

The implementation of competitive electricity markets has changed the consumers’ and distributed generation position power systems operation. The use of distributed generation and the participation in demand response programs, namely in smart grids, bring several advantages for consumers, aggregators, and system operators. The present paper proposes a remuneration structure for aggregated distributed generation and demand response resources. A virtual power player aggregates all the resources. The resources are aggregated in a certain number of clusters, each one corresponding to a distinct tariff group, according to the economic impact of the resulting remuneration tariff. The determined tariffs are intended to be used for several months. The aggregator can define the periodicity of the tariffs definition. The case study in this paper includes 218 consumers, and 66 distributed generation units.

Decision making techniques with similarity measures and OWA operators

We analyse the use of the ordered weighted average (OWA) in decision-making giving special attention to business and economic decision-making problems. We present several aggregation techniques that are very useful for decision-making such as the Hamming distance, the adequacy coefficient and the index of maximum and minimum level. We suggest a new approach by using immediate weights, that is, by using the weighted average and the OWA operator in the same formulation. We further generalize them by using generalized and quasi-arithmetic means. We also analyse the applicability of the OWA operator in business and economics and we see that we can use it instead of the weighted average. We end the paper with an application in a business multi-person decision-making problem regarding production management

Decision making techniques with similarity measures and OWA operators

We analyse the use of the ordered weighted average (OWA) in decision-making giving special attention to business and economic decision-making problems. We present several aggregation techniques that are very useful for decision-making such as the Hamming distance, the adequacy coefficient and the index of maximum and minimum level. We suggest a new approach by using immediate weights, that is, by using the weighted average and the OWA operator in the same formulation. We further generalize them by using generalized and quasi-arithmetic means. We also analyse the applicability of the OWA operator in business and economics and we see that we can use it instead of the weighted average. We end the paper with an application in a business multi-person decision-making problem regarding production management

The connection between distortion risk measures and ordered weighted averaging operators

Distortion risk measures summarize the risk of a loss distribution by means of a single value. In fuzzy systems, the Ordered Weighted Averaging (OWA) and Weighted Ordered Weighted Averaging (WOWA) operators are used to aggregate a large number of fuzzy rules into a single value. We show that these concepts can be derived from the Choquet integral, and then the mathematical relationship between distortion risk measures and the OWA and WOWA operators for discrete and finite random variables is presented. This connection offers a new interpretation of distortion risk measures and, in particular, Value-at-Risk and Tail Value-at-Risk can be understood from an aggregation operator perspective. The theoretical results are illustrated in an example and the degree of orness concept is discussed.

Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

About Strictly Hyperbolic Operators with Non-Regular Coefficients

2002 Mathematics Subject Classification: 35L15, 35L80, 35S05, 35S30

Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.

Fluorescence, Aggregation Properties And Ft-ir Microspectroscopy Of Elastin And Collagen Fibers.

Histological and histochemical observations support the hypothesis that collagen fibers can link to elastic fibers. However, the resulting organization of elastin and collagen type complexes and differences between these materials in terms of macromolecular orientation and frequencies of their chemical vibrational groups have not yet been solved. This study aimed to investigate the macromolecular organization of pure elastin, collagen type I and elastin-collagen complexes using polarized light DIC-microscopy. Additionally, differences and similarities between pure elastin and collagen bundles (CB) were investigated by Fourier transform-infrared (FT-IR) microspectroscopy. Although elastin exhibited a faint birefringence, the elastin-collagen complex aggregates formed in solution exhibited a deep birefringence and formation of an ordered-supramolecular complex typical of collagen chiral structure. The FT-IR study revealed elastin and CB peptide NH groups involved in different types of H-bonding. More energy is absorbed in the vibrational transitions corresponding to CH, CH2 and CH3 groups (probably associated with the hydrophobicity demonstrated by 8-anilino-1-naphtalene sulfonic acid sodium salt [ANS] fluorescence), and to νCN, δNH and ωCH2 groups of elastin compared to CB. It is assumed that the α-helix contribution to the pure elastin amide I profile is 46.8%, whereas that of the B-sheet is 20% and that unordered structures contribute to the remaining percentage. An FT-IR profile library reveals that the elastin signature within the 1360-1189cm(-1) spectral range resembles that of Conex-Toray aramid fibers.

Metallochlorophylls of magnesium, copper and zinc: evaluation of the influence of the first coordination sphere on their solvatochromism and aggregation properties

In this study the role of different metal centers (magnesium, zinc and copper) on the enhancement of the hydrophilic character of metallochlorophylls, was evaluated. The solvatochromism as well as the aggregation process for these compounds in water/ethanol mixtures at different volume ratios were evaluated using Fluorescence, and Resonant Light Scattering (RLS) measurements, aiming to characterize the behavior of these compounds. Independently on the studied metallochlorophyll, the presence of at least 60% of water results in a considerable increase in the fluorescence emission, probably a direct consequence of a lower aggregation of these compounds, which is confirmed by the results from RLS measurements. Additionally, the results suggest that magnesium and zinc chlorophyll should be promising phototherapeutic agents for Photodynamic Therapy.