"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 nite random variables is presented. This connection oers 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.Fuzzy systems; Degree of orness; Risk quantification; Discrete random variable JEL classification:C02,C60

The problem of collective identity in a fuzzy environment

Producción CientíficaWe define the problem of group identication in a fuzzy environment. We concentrate on the case where the society is required to self-determine the belongingness of each member to a speci_c group, characterized by a single attribute. In general terms, this case consists of a collective identity issue that can be regarded as an aggregation problem of individual assessments within a group. Here we introduce the possibility that both the original assessments and the resulting output attach partial memberships to the collectivity, for each potential member. We propose relevant classes of rules, and some are axiomatically characterized. Our new approach provides a way to circumvent classical impossibility results like Kasher and Rubinstein's.Ministerio de Economía, Industria y Competitividad (Project ECO2012-32178

Decision Making on Oil Extraction under Z-information

AbstractIn modern conditions, the refining process is complicated and ambiguous, requiring a precise knowledge of all the internal and external factors. However, in many cases, it is impossible to get complete information. Therefore, the process of oil production takes place in conditions of uncertainty accompanying the various situations. A partial absence of beliefs and fuzziness are some of the aspects of uncertainty. In this paper we consider a somewhat different framework for representing our knowledge. Zadeh suggested a Z-number notion, based on a reliability of the given information. In this study we apply Z- information to decision making on oil extraction problem and suggest the framework for decision making on a base of Z-numbers. The method associates with the construction of a non-additive measure as a lower prevision and uses this capacity in Choquet integral for constructing a utility function

A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields, and several softwares and libraries dedicated to this model have been developed.Choquet integral, Sugeno integral, capacity, bipolarity, preferences

Bridging the semantic gap in content-based image retrieval.

To manage large image databases, Content-Based Image Retrieval (CBIR) emerged as a new research subject. CBIR involves the development of automated methods to use visual features in searching and retrieving. Unfortunately, the performance of most CBIR systems is inherently constrained by the low-level visual features because they cannot adequately express the user\u27s high-level concepts. This is known as the semantic gap problem. This dissertation introduces a new approach to CBIR that attempts to bridge the semantic gap. Our approach includes four components. The first one learns a multi-modal thesaurus that associates low-level visual profiles with high-level keywords. This is accomplished through image segmentation, feature extraction, and clustering of image regions. The second component uses the thesaurus to annotate images in an unsupervised way. This is accomplished through fuzzy membership functions to label new regions based on their proximity to the profiles in the thesaurus. The third component consists of an efficient and effective method for fusing the retrieval results from the multi-modal features. Our method is based on learning and adapting fuzzy membership functions to the distribution of the features\u27 distances and assigning a degree of worthiness to each feature. The fourth component provides the user with the option to perform hybrid querying and query expansion. This allows the enrichment of a visual query with textual data extracted from the automatically labeled images in the database. The four components are integrated into a complete CBIR system that can run in three different and complementary modes. The first mode allows the user to query using an example image. The second mode allows the user to specify positive and/or negative sample regions that should or should not be included in the retrieved images. The third mode uses a Graphical Text Interface to allow the user to browse the database interactively using a combination of low-level features and high-level concepts. The proposed system and ail of its components and modes are implemented and validated using a large data collection for accuracy, performance, and improvement over traditional CBIR techniques

The posterity of Zadeh's 50-year-old paper: A retrospective in 101 Easy Pieces – and a Few More

International audienceThis article was commissioned by the 22nd IEEE International Conference of Fuzzy Systems (FUZZ-IEEE) to celebrate the 50th Anniversary of Lotfi Zadeh's seminal 1965 paper on fuzzy sets. In addition to Lotfi's original paper, this note itemizes 100 citations of books and papers deemed “important (significant, seminal, etc.)” by 20 of the 21 living IEEE CIS Fuzzy Systems pioneers. Each of the 20 contributors supplied 5 citations, and Lotfi's paper makes the overall list a tidy 101, as in “Fuzzy Sets 101”. This note is not a survey in any real sense of the word, but the contributors did offer short remarks to indicate the reason for inclusion (e.g., historical, topical, seminal, etc.) of each citation. Citation statistics are easy to find and notoriously erroneous, so we refrain from reporting them - almost. The exception is that according to Google scholar on April 9, 2015, Lotfi's 1965 paper has been cited 55,479 times