M. A. Vila

On aggregation operations of linguistic labels

This article is devoted to defining some aggregation operations between linguistic labels. First, from some remarks about the meaning of label addition, a formal and general definition of a label space is introduced. After, addition, difference, and product by a positive real number are formally defined on that space. the more important properties of these operations are studied, paying special attention to the convex combination labels. the article concludes with some numerical examples.

Linguistic decision-making models

Using linguistic values to assess results and information about external factors is quite usual in real decision situations. In this article we present a general model for such problems. Utilities are evaluated in a term set of labels and the information is supposed to be a linguistic evidence, that is, is to be represented by a basic assignment of probability (in the sense of Dempster‐Shafer) but taking its values on a term set of linguistic likelihoods. Basic decision rules, based on fuzzy risk intervals, are developed and illustrated by several examples. the last section is devoted to analyzing the suitability of considering a hierarchical structure (represented by a tree) for the set of utility labels.

Fuzzy association rules: general model and applications

The theory of fuzzy sets has been recognized as a suitable tool to model several kinds of patterns that can hold in data. In this paper, we are concerned with the development of a general model to discover association rules among items in a (crisp) set of fuzzy transactions. This general model can be particularized in several ways; each particular instance corresponds to a certain kind of pattern and/or repository of data. We describe some applications of this scheme, paying special attention to the discovery of fuzzy association rules in relational databases.

On a canonical representation of fuzzy numbers

Abstract Fuzzy numbers, and more generally linguistic values, are approximate assessments, given by experts and accepted by decision-makers when obtaining more accurate values is impossible or unnecessary. To simplify the task of representing and handling fuzzy numbers, several authors have introduced real indices in order to capture the information contained in a fuzzy number. In this paper we propose two parameters, value and ambiguity, for this purpose. We use these parameters to obtain canonical representations and to deal with fuzzy numbers in decision-making problems. Several examples illustrate these ideas.

About the use of fuzzy clustering techniques for fuzzy model identification

Abstract In this work we present an alternative approach to generate fuzzy rules with a functional consequent associated to the TSK fuzzy model. In our case, using fuzzy clustering algorithms that look for linear behaviours in the product space of the input-output data, we analyse different methods to generate the associated fuzzy rules using in some cases multidimensional reference fuzzy sets in the product space of the input variables and in other cases fuzzy sets in each of the different dimensions. In any case the rules being generated correspond to a TSK fuzzy model.

GEFRED: a generalized model of fuzzy relational databases

Abstract In this paper, we present a Fuzzy Relational Databases model whose main characteristics are: the integration of previous models in the same framework, representation capabilities for a wide series of fuzzy information, and a coherent and flexible handling of it. This model aims to solve each problem of representation and handling of fuzzy information taking into account its specific nature, and hence it allows the user to choose the comparison operator and the fuzzy compatibility measure to be used in a query. Besides, it permits the user to specify the precision with which the conditions involved in a query are satisfied.

Fuzzy cardinality based evaluation of quantified sentences

Abstract Quantified statements are used in the resolution of a great variety of problems. Several methods have been proposed to evaluate statements of types I and II. The objective of this paper is to study these methods, by comparing and generalizing them. In order to do so, we propose a set of properties that must be fulfilled by any method of evaluation of quantified statements, we discuss some existing methods from this point of view and we describe a general approach for the evaluation of quantified statements based on the fuzzy cardinality and fuzzy relative cardinality of fuzzy sets. In addition, we discuss some concrete methods derived from the mentioned approach. These new methods fulfill all the properties proposed and, in some cases, they provide an interpretation or generalization of existing methods.

A procedure for ranking fuzzy numbers using fuzzy relations

Abstract This paper presents a method to give fuzzy order relations between fuzzy numbers. These are founded on the concept of ‘comparison function’ (defined in the paper), and the use of fuzzy measures related with the same numbers. The link of such relations with fuzzy operations is investigated too.

Association rules applied to credit card fraud detection

Association rules are considered to be the best studied models for data mining. In this article, we propose their use in order to extract knowledge so that normal behavior patterns may be obtained in unlawful transactions from transactional credit card databases in order to detect and prevent fraud. The proposed methodology has been applied on data about credit card fraud in some of the most important retail companies in Chile.

A new definition of fuzzy functional dependency in fuzzy relational databases

The need to incorporate and treat information given in fuzzy terms in Relational Databases has concentrated a great effort in the last years. This article focuses on the treatment of functional dependencies (f.d.) between attributes of a relation scheme. We review other approaches to this problem and present some of its missfunctions concerning intuitive properties a fuzzy extension of f.d. should verify. Then we introduce a fuzzy extension of this concept to overcome the previous anomalous behaviors and study its properties. of primary interest is the completeness of our fuzzy version of Armstrong axioms in order to derive all the fuzzy functional dependencies logically implied by a set of f.f.d. just using these axioms.