Fuzzy Outranking Methods Including Fuzzy PROMETHEE

Outranking methods are a family of techniques concerned with ranking the preference for alternatives based on the criteria values that describe them. The breadth of applications taking inference from such preference ranking analysis includes the areas of business, health, environment, marketing, and public services. In the context of databases, the ranking issue is closely associated with data retrieval, including the ranking of matches to queries. This chapter describes the rudiments of fuzzy outranking methods, with particular attention to one such approach, namely fuzzy PROMETHEE, compounded further with the different structures of defined fuzziness of the criteria values also considered. Alternative fuzzy PROMETHEE approaches are described, with one used in two real-life applications. The results presented, with emphasis on their graphical representation, offer insights into the appropriate application of such fuzzy outranking methods.

Fuzzy Decision-Tree-Based Analysis of Databases

The general fuzzy decision tree approach encapsulates the benefits of being an inductive learning technique to classify objects, utilising the richness of the data being considered, as well as the readability and interpretability that accompanies its operation in a fuzzy environment. This chapter offers a description of fuzzy decision tree based research, including the exposition of small and large fuzzy decision trees to demonstrate their construction and practicality. The two large fuzzy decision trees described are associated with a real application, namely, the identification of workplace establishments in the United Kingdom that pay a noticeable proportion of their employees less than the legislated minimum wage. Two separate fuzzy decision tree analyses are undertaken on a low-pay database, which utilise different numbers of membership functions to fuzzify the continuous attributes describing the investigated establishments. The findings demonstrate the sensitivity of results when there are changes in the compactness of the fuzzy representation of the associated data.

Data Dependencies in Codd's Relational Model with Similarities

This chapter deals with data dependencies in Codd’s relational model of data. In particular, we deal with fuzzy logic extensions of the relational model that consist of adding similarity relations to domains and consider functional dependencies in these extensions. We present a particular extension and functional dependencies in this extension that follow the principles of fuzzy logic in a narrow sense. We present selected features and results regarding this extension. Then, we use this extension as a reference model and compare it to several other extensions proposed in the literature. We argue that following the principles of fuzzy logic in a narrow sense, the same way we can follow the principles of classical logic in the case of the ordinary Codd relational model, helps achieve transparency, versatility, conceptual clarity, and theoretical and computational tractability of the extension. We outline several topics for future research.

Incremental Discovery of Fuzzy Functional Dependencies

Mining functional dependencies (FDs) from databases has been identified as an important database analysis technique. It has received considerable research interest in recent years. However, most current data mining techniques for determining functional dependencies deal only with crisp databases. Although various forms of fuzzy functional dependencies (FFDs) have been proposed for fuzzy databases, they emphasized conceptual viewpoints and only a few mining algorithms are given. In this research, we propose methods to validate and incrementally search for FFDs from similarity-based fuzzy relational databases. For a given pair of attributes, the validation of FFDs is based on fuzzy projection and fuzzy selection operations. In addition, the property that FFDs are monotonic in the sense that r1 ? r2 implies FDa(r1) ? FDa(r2) is shown. An incremental search algorithm for FFDs based on this property is then presented. Experimental results showing the behavior of the search algorithm are discussed.

Fuzzy Classification in Shipwreck Scatter Analysis

There are many well-known applications of fuzzy sets theory in various fields of science and technology. However, we think that the area of maritime archaeology did not attract enough attention from researchers of fuzzy sets theory in the last decades. In this chapter, we present examples of problems arising in shipwreck scatter analysis where fuzzy classification may be very useful. Using a real-world example of fragments of ceramics from an ancient shipwreck, we present an exemplary application of the fuzzy classification framework with SQL querying for data mining in archaeological information systems. Our framework can be used as a data mining tool. It can be relatively easily integrated with conventional relational databases, which are widely used in existing archaeological information systems. The main benefits of using our fuzzy classification approach include flexible and precise data analysis with userfriendly information presentation at the report generation phase.

A Tool for Fuzzy Reasoning and Querying

We present CLOUDS, which stands for C++ Library Organizing Uncertainty in Database Systems, a tool that allows the creation of fuzzy reasoning systems over classic, nonfuzzy, relational databases. CLOUDS can be used in three flavors: CLOUDS API, a C++ API; CLOUDS-L, a compiled language; and CLOUDSQL, a fuzzy extension to SQL queries (ANSI, 1992). It was developed using the objectoriented paradigm and has an extensible architecture based on a main control system that manages different models, and runs queries and commands defined in them. As a test, it was incorporated into a geographic information system and used to analyze epidemiological data.

Evaluation of Quantified Statements Using Gradual Numbers

This chapter is devoted to the evaluation of quantified statements which can be found in many applications as decision making, expert systems, or flexible querying of relational databases using fuzzy set theory. Its contribution is to introduce the main techniques to evaluate such statements and to propose a new theoretical background for the evaluation of quantified statements of type “Q X are A” and “Q B X are A.” In this context, quantified statements are interpreted using an arithmetic on gradual numbers from Nf, Zf, and Qf. It is shown that the context of fuzzy numbers provides a framework to unify previous approaches and can be the base for the definition of new approaches.

On the Versatility of Fuzzy Sets for Modeling Flexible Queries

The idea of extending the usual Boolean queries with preferences has become a hot topic in the database community. One of the advantages of this approach is to deliver discriminated answers rather than flat sets of elements. Fuzzy sets are a natural means to represent preferences, and many works have been undertaken to define queries where fuzzy predicates can be introduced inside user queries. The objective of this chapter is to illustrate the expressiveness of fuzzy sets with the division operator in the context of regular databases. Like other operators, the regular division is not flexible at all and small variations in the data may lead to totally different results. To counter this behavior, a variety of extended division operators founded on fuzzy sets are suggested. All of them obey a double requirement: to have a clear meaning from a user point of view and to deliver a resulting relation which is a quotient.

Introduction to Fuzzy Data Mining Methods

This chapter aims to give a comprehensive view about the links between fuzzy logic and data mining. It will be shown that knowledge extracted from simple data sets or huge databases can be represented by fuzzy rule-based expert systems. It is highlighted that both model performance and interpretability of the mined fuzzy models are of major importance, and effort is required to keep the resulting rule bases small and comprehensible. Therefore, in the previous years, soft computing based data mining algorithms have been developed for feature selection, feature extraction, model optimization, and model reduction (rule based simplification). Application of these techniques is illustrated using the wine data classification problem. The results illustrate that fuzzy tools can be applied in a synergistic manner through the nine steps of knowledge discovery.

Applying Fuzzy Data Mining to Tourism Area

Soaring is a recreational activity and a competitive sport where individuals fly un-powered aircrafts known as gliders. The soaring location selection process depends on a number of factors, resulting in a complex decision-making task. In this chapter, we propose the use of an extension of the FSQL language for fuzzy queries as one of the techniques of data mining that can be used to solve the problem of offering a better place for soaring given the environmental conditions and customer characteristics. The FSQL language is an extension of the SQL language that permits us to write flexible conditions in our queries to a fuzzy or traditional database. After doing a process of clustering and characterization of a large customer database in a data warehouse, we are able of classify the next clients in a cluster and offer an answer according to it.