A fuzzy approach to similarity in Case-Based Reasoning suitable to SQL implementation

The aim of this paper is to formally introduce a notion of acceptance and similarity, based on fuzzy logic, among case features in a case retrieval system. This is pursued by rst reviewing the relationships between distance-based similarity (i.e. the standard approach in CBR) and fuzzy-based similarity, with particular attention to the formalization of a case retrieval process based on fuzzy query specication. In particular, we present an approach where local acceptance relative to a feature can be expressed through fuzzy distributions on its domain, abstracting the actual values to linguistic terms. Furthermore, global acceptance is completely grounded on fuzzy logic, by means of the usual combinations of local distributions through specic dened norms. We propose a retrieval architecture, based on the above notions and realized through a fuzzy extension of SQL, directly implemented on a standard relational DBMS. The advantage of this approach is that the whole power of an SQL engine can be fully exploited, with no need of implementing specic retrieval algorithms. The approach is illustrated by means of some examples from a recommender system called MyWine, aimed at recommending the suitable wine bottles to a customer providing her requirements in both crisp and fuzzy way

Possibilistic functional dependencies and their relationship to possibility theory

This paper introduces possibilistic functional dependencies. These dependencies are associated with a particular possibility distribution over possible worlds of a classical database. The possibility distribution reflects a layered view of the database. The highest layer of the (classical) database consists of those tuples that certainly belong to it, while the other layers add tuples that only possibly belong to the database, with different levels of possibility. The relation between the confidence levels associated with the tuples and the possibility distribution over possible database worlds is discussed in detail in the setting of possibility theory. A possibilistic functional dependency is a classical functional dependency associated with a certainty level that reflects the highest confidence level where the functional dependency no longer holds in the layered database. Moreover, the relationship between possibilistic functional dependencies and possibilistic logic formulas is established. Related work is reviewed, and the intended use of possibilistic functional dependencies is discussed in the conclusion

A Relational Model for the Possibilistic Valid-time Approach

In real world, it is very common that some objects or concepts have properties with a time-variant or timerelated nature. Modelling this kind of objects or concepts in a (relational) database schema is possible, but time-variant and time-related attributes have an impact on the consistency of the entire database and must be appropriately managed. Therefore, temporal database models have been proposed to deal with this problem in the literature. Time can be affected by imprecision, vagueness and / or uncertainty, since existing time measuring devices are inherently imperfect. Additionally, human beings manage time using temporal indications and temporal notions, which may also be imprecise. However, the imperfection in human-used temporal indications is supported by human interpretation, whereas information systems need appropriate support in order to accomplish this task. Several proposals for dealing with such imperfections when modelling temporal data exist. Some of these proposals transform the temporal data into a compact representation but there is not a formal model for managing and handling uncertainty regarding temporal information. In this work we present a novel model to deal with imprecision in valid-time databases together with the definition and implementation of the data manipulation language, DML.Junta de Andalucia P07-TIC-03175 BES-2009-013805 TIN2008-0206

The legacy of 50 years of fuzzy sets: A discussion

International audienceThis note provides a brief overview of the main ideas and notions underlying fifty years of research in fuzzy set and possibility theory, two important settings introduced by L.A. Zadeh for representing sets with unsharp boundaries and uncertainty induced by granules of information expressed with words. The discussion is organized on the basis of three potential understanding of the grades of membership to a fuzzy set, depending on what the fuzzy set intends to represent: a group of elements with borderline members, a plausibility distribution, or a preference profile. It also questions the motivations for some existing generalized fuzzy sets. This note clearly reflects the shared personal views of its authors