Félix Díaz-Hermida

A framework for fuzzy quantification models analysis

A framework for description of fuzzy quantification models is presented. Within this framework, the fuzzy quantified statements evaluation problem is described as the compatibility between the fuzzy quantifier and a fuzzy cardinality or a fuzzy aggregation measure. A list of desirable properties for quantification models is presented and those models that fit the framework are confronted with it.

Voting-model based evaluation of fuzzy quantified sentences: a general framework

The framework here presented allows the definition of new probabilistic methods for fuzzy quantification and also the description of previous ones. All of these methods are endowed with a clear semantic interpretation that is based on a voting model. The methods within the framework fulfil a number of important and adequate properties of interest for fuzzy quantification and can also deal with very different types of quantifiers, as comparative and exception ones.

Definition and classification of semi-fuzzy quantifiers for the evaluation of fuzzy quantified sentences

This paper describes a classification of semi-fuzzy quantifiers that considerably improves the division between what Zadeh calls quantifiers of the first kind and those of the second kind. A number of cases are contemplated that are not habitually described in the literature on fuzzy quantification (e.g., comparative and exception quantifiers). Models are also defined for all the types of semi-fuzzy quantifiers framed in the classification. Thus in order to construct fuzzy quantifiers it is sufficient to apply a suitable quantifier fuzzification method. This paper also deals with the application of semi-fuzzy quantifiers and fuzzy quantifiers to fuzzy relations. The solution of this problem is of interest in various fields; amongst which, perhaps the most noteworthy is that of fuzzy databases.

A Probabilistic Quantifier Fuzzification Mechanism: The Model and Its Evaluation for Information Retrieval

In this paper, we propose a new quantifier fuzzification mechanism which is deeply rooted in the theory of probability. This quantifier fuzzification mechanism skips the nested assumption, which is inherent to other probabilistic quantification methods. The new quantification approach complies with the properties required for determiner fuzzification schemes (DFS) with finite sets and, hence, its good behavior is assured. Moreover, this new approach is suitable for some application domains. In particular, the use of fuzzy quantifiers for implementing query quantified statements for information retrieval exemplifies the adequacy of the new proposal. The new quantifier fuzzification mechanism has been efficiently implemented and empirically tested for a retrieval task. This practical evaluation followed the standard methodology in the field of information retrieval and was conducted against a popular benchmark consisting of a large collection of documents. The retrieval performance evaluation made evident that: 1) the new method can work in realistic scenarios, and 2) it can overcome recent proposals for applying fuzzy quantifiers in information retrieval

Experiments on using fuzzy quantified sentences in adhoc retrieval

In this work we implement and evaluate a fuzzy approach to Information Retrieval whose query language incorporates fuzzy quantifiers. Fuzzy quantified sentences are suitable for imposing additional restrictions in the retrieval process which are not typical in classic information retrieval. Moreover, fuzzy quantifiers can be implemented in different relaxed ways leading to a wide range of methods for combining query terms. The large-scale evaluation conducted here shows clearly the practical benefits obtained in terms of retrieval performance. These empirical results strengthen previous theoretical works that already advanced the adequacy of fuzzy quantifiers for modeling information needs.

Semi-fuzzy quantifiers as a tool for building linguistic summaries of data patterns

In this paper we discuss how semi-fuzzy quantifiers are a useful tool for modeling linguistic summaries from data in two aspects: how they provide a systematic mechanism for performing the data summarization task involving fuzzy quantifiers that are different from the usual unary and binary ones and also how they can be used for the detection of quantified patterns in data.

On the analysis of set-based fuzzy quantified reasoning using classical syllogistics

Syllogism is a type of deductive reasoning involving quantified statements. The syllogistic reasoning scheme in the classical Aristotelian framework involves three crisp term sets and four linguistic quantifiers, for which the main support is the linguistic properties of the quantifiers. A number of fuzzy approaches for defining an approximate syllogism have been proposed for which the main support is cardinality calculus. In this paper we analyze fuzzy syllogistic models previously described by Zadeh and Dubois et al. and compare their behavior with that of the classical Aristotelian framework to check which of the 24 classical valid syllogistic reasoning patterns or moods are particular crisp cases of these fuzzy approaches. This allows us to assess to what extent these approaches can be considered as either plausible extensions of the classical crisp syllogism or a basis for a general approach to the problem of approximate syllogism.

On the role of fuzzy quantified statements in linguistic summarization of data

In this paper a discussion on some of the key problems in fuzzy linguistic summarization of data in introduced. Also a description on the stages that the summarization process involving fuzzy quantified statements should accomplish is presented.

Fuzzy temporal rules: a rule-based approach for fuzzy temporal knowledge representation and reasoning

In this paper a model for the representation and execution of a type of fuzzy control rules that explicitly handle time variable (Fuzzy Temporal Rules) is presented. The model here described permits using temporal references for the occurrence of events. These references are allowed to be described either in an absolute manner or related to occurrence of other events. A complete grammar that formally describes the representation language of the model is presented, together with its semantic counterpart. This knowledge and reasoning representation model is illustrated by means of a number of examples that show the substantial increase in the expresiveness that FTRs exhibit when compared to usual fuzzy control rules.

Semi-fuzzy Quantifiers for Information Retrieval

Recent research on fuzzy quantification for information retrieval has proposed the application of semi-fuzzy quantifiers for improving query languages. Fuzzy quantified sentences are useful as they allow additional restrictions to be imposed on the retrieval process unlike more popular retrieval approaches, which lack the facility to accurately express information needs. For instance, fuzzy quantification supplies a variety of methods for combining query terms whereas extended boolean models can only handle extended boolean-like operators to connect query terms. Although some experiments validating these advantages have been reported in recent works, a comparison against state-of-the-art techniques has not been addressed. In this work we provide empirical evidence on the adequacy of fuzzy quantifiers to enhance information retrieval systems. We show that our fuzzy approach is competitive with respect to models such as the vector-space model with pivoted document-length normalization, which is at the heart of some high-performance web search systems. These empirical results strengthen previous theoretical works that suggested fuzzy quantification as an appropriate technique for modeling information needs. In this respect, we demonstrate here the connection between the retrieval framework based on the concept of semi-fuzzy quantifier and the seminal proposals for modeling linguistic statements through Ordered Weighted Averaging operators (OWA).