International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

We provide a survey of recent developments about capacities (or fuzzy measures) and cooperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of usual tools in these theories, such as the Choquet integral, the Möbius transform, and the Shapley value.

The majority of approaches to multicriteria optimization are based on quantitative representations of preferences of a decision maker, in which numerical procedures of multicriteria analysis are used for aggregation purposes. However, very often qualitative data cannot be known in terms of absolute values so that a qualitative approach is needed. Moreover, the multicriteria methods are directly applicable when alternatives are individuals-then they may be explicitly listed and ordered by an agent. However, sometimes the set of alternatives has combinatorial structure and it must be selected from the set of Cartesian products of value domains of attributes satisfying certain constraints. Then, the space of possible alternatives has a size exponential in the number of variables and ranking all alternatives explicitly is a complex and tedious task. In this paper we propose logic programming with ordered disjunction as a qualitative approach to combinatorial multicriteria decision making, allowing a concise representation of the preference structures, and a human-like form of expressions, being close to natural language, hence providing a good readability and simplicity. A combinatorial multicriteria decision making problem is encoded as a logic program, in which preferences of the decision maker are represented qualitatively. The optimal decision corresponds exactly to the preferred answer set of the program, obtained via the well-known methods of multicriteria analysis.

OWA (Ordered Weighted Averaging) aggregation operators have been extensively adopted to handle MCDM (multiple criteria decision making) problems. However, additive or multiplicative preferences should be aggregated with feasible operators. To resolve this problem, this study proposes a new MCDM aggregation model, capable of handling situational group MCDM problems based on the ME-OWA (maximal entropy ordered weighted averaging) and ME-OWGA (maximal entropy ordered weighted geometric averaging) operators. The proposed model is also applied not only to evaluate the service quality of airlines but also select the most appropriate desalination technology. The results of previous MCDM methods can be covered with proposed model.

In this paper, we present a statistical criterion for accepting/rejecting the pairwise reciprocal comparison matrices in the analytic hierarchy process. We have studied the consistency in random matrices of different sizes. We do not agree with the traditional criterion of accepting matrices due to their inflexibility and because it is too restrictive when the size of the matrix increases. Our system is capable of adapting the acceptance requirements to different scopes and consistency necessities. The advantages of our consistency system are the introduction of adaptability in the acceptance criterion and the simplicity of the index we have used, the eigenvalue (λ_max) and the simplicity of the criterion.

In this paper, attribute reduction in variable precision rough set model is discussed. Several kinds of reducts preserving some of lower approximations, upper approximations, boundary regions and the unpredictable region are discussed. Relations among those kinds of reducts are investigated. As a basis for reduct computation, Boolean function representations of the preservation of lower approximations, upper approximations, boundary regions and the unpredictable region are discussed. Throughout this paper, the great difference between the analysis using variable precision rough sets and the classical rough set analysis is emphasized.

Recently kernel methods in support vector machines have widely been used in machine learning algorithms to obtain nonlinear models. Clustering is an unsupervised learning method which divides whole data set into subgroups, and popular clustering algorithms such as c-means are employing kernel methods. Other kernel-based clustering algorithms have been inspired from kernel c-means. However, the formulation of kernel c-means has a high computational complexity. This paper gives an alternative formulation of kernel-based clustering algorithms derived from competitive learning clustering. This new formulation obviously uses sequential updating or on-line learning to avoid high computational complexity. We apply kernel methods to related algorithms: learning vector quantization and self-organizing map. We moreover consider kernel methods for sequential c-means and its fuzzy version by the proposed formulation.

Data mining aims at extracting knowledge from data. Sometimes this requires the data owner to make data available to the data analyst. Unless the analyst is trusted by the data owner, the latter may wish to have his intellectual property rights protected. Watermarking is a way to provide some protection, not only for multimedia data, but also for numerical data. It consists of imperceptibly embedding a secret mark into the data to be protected. The mark can later be used to resolve any subsequent disputes on data ownership. This paper presents a watermarking method that embeds a watermark into each attribute of a multivariate continuous numerical dataset. This watermarking method is shown to be robust against random noise addition attacks. Data quality is assured to the extent that the watermarked data nearly preserve the attribute means and the covariance matrix from the original dataset. Our proposal is the first known watermarking system for multivariate numerical datasets with such robustness and quality properties.

An improvement to the content-based image retrieval (CBIR) system for kaou images which has been developed by the authors group is introduced. Kaous are handwritten monograms found on old Japanese documents in a Chinese character-like shapes with artistic decorations. Kaous play an important role in the research of historical documents, which involve browsing and comparison of numerous samples. In this work, a novel method of kaou image modeling for CBIR is introduced, which incorporates the shade information of a closed kaou region in addition to the conventionally used contour characteristics. Dissimilarity of query and dictionary images were calculated as a weighted sum of elementary differences in the positions, contour shapes and colors of the component regions. These elementary differences were evaluated using relaxation matching and empirically defined distance functions. In the experiments, a set of 2455 kaou images were used. It was found that apparently similar kaou images could be retrieved by the proposed method, improving the retrieval quality..

This section is maintained by Vladik Kreinovich. Please send your abstracts (or copies of papers that you want to see reviewed here) to vladik@utep.edu, or by regular mail to: V. Kreinovich, Department of Computer Science, University of Texas, El Paso, TX 79968, USA.