Fuzziness in Information Systems

How to Deal with Crisp and Fuzzy Data in Selection, Classification, and Summarization

verfasst von: Miroslav Hudec

Verlag: Springer International Publishing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book is an essential contribution to the description of fuzziness in information systems. Usually users want to retrieve data or summarized information from a database and are interested in classifying it or building rule-based systems on it. But they are often not aware of the nature of this data and/or are unable to determine clear search criteria. The book examines theoretical and practical approaches to fuzziness in information systems based on statistical data related to territorial units.
Chapter 1 discusses the theory of fuzzy sets and fuzzy logic to enable readers to understand the information presented in the book. Chapter 2 is devoted to flexible queries and includes issues like constructing fuzzy sets for query conditions, and aggregation operators for commutative and non-commutative conditions, while Chapter 3 focuses on linguistic summaries. Chapter 4 presents fuzzy logic control architecture adjusted specifically for the aims of business and governmental agencies, and shows fuzzy rules and procedures for solving inference tasks. Chapter 5 covers the fuzzification of classical relational databases with an emphasis on storing fuzzy data in classical relational databases in such a way that existing data and normal forms are not affected. This book also examines practical aspects of user-friendly interfaces for storing, updating, querying and summarizing. Lastly, Chapter 6 briefly discusses possible integration of fuzzy queries, summarization and inference related to crisp and fuzzy databases.
The main target audience of the book is researchers and students working in the fields of data analysis, database design and business intelligence. As it does not go too deeply into the foundation and mathematical theory of fuzzy logic and relational algebra, it is also of interest to advanced professionals developing tailored applications based on fuzzy sets.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Fuzzy Set and Fuzzy Logic Theory in Brief

Abstract

A set consists of elements sharing the same property. This property is essential for setting set boundaries. Hence, the following question appears: Can we always unambiguously define these boundaries? The answer is, no. We can unambiguously define a set containing all municipalities belonging to the district D. Municipality either belongs to the district D (from administrative point of view), or does not belong. However, for the set expressing high distance we cannot clearly define sharp boundary to distinguish high from non-high distance. This section begins with the classical sets in order to smoothly continue to fuzzy sets. Next, relevant properties and operations of fuzzy sets are discussed. Further, the concept of fuzzy number, as a subcategory of fuzzy sets, is explained. Fuzzy sets and many-valued logics are basis for fuzzy logic. Fuzzy logic facilitates commonsense reasoning with imprecise predicates expressed as fuzzy sets. In the second part fuzzy conjunction, negation, disjunction, implication and quantifiers are examined. Mentioned concepts are used throughout the book.

Miroslav Hudec

Chapter 2. Fuzzy Queries

Abstract

The goal of database queries is to separate relevant tuples from non-relevant ones. The common way to realize such a query is to formulate a logical condition. In classical queries, we use crisp conditions to describe tuples we are looking for. According to the condition, a relational database management system returns a list of records. However, user’s preferences in what should be retrieved, are often vague or imprecise. These preferences can be expressed in atomic conditions and/or between them. For example, the meaning of a query: find municipalities with small population density and altitude about 1000 m above sea level can be understood at the first glance. The linguistic terms clearly suggest that there is a smooth transition between acceptable and unacceptable records. This chapter is focused on the construction of fuzzy sets, the aggregations functions and the issues of fuzzy logic in queries which should not be attenuated.

Miroslav Hudec

Chapter 3. Linguistic Summaries

Abstract

In many tasks, users are not interested in data stored in relational databases, but in summarized relational knowledge and “abstracts” from the data which are expressed in a useful and understandable way by linguistic terms. Linguistic Summaries (LSs) are able to express the knowledge in the data that is concise and easily understandable by users. LSs are quantified sentences of natural language such as most of municipalities of high altitude and low pollution have small number of respiratory diseases. The truth value of summaries gets values from the unit interval as it is common in the fuzzy logic world. We start with simple LSs and continue with more complex ones. In this direction, selecting appropriate t-norms for aggregation and quality measures are discussed. Furthermore, a system for calculating summaries will not work properly, if it uses ill-defined membership functions. Focus is also on constructing these functions for summarizers, restrictions and quantifiers. The quality measures are also analysed, because the high truth value of sentence is not always a sufficient measure. Finally, possible applications are considered.

Miroslav Hudec

Chapter 4. Fuzzy Inference

Abstract

In practice we can find many examples of inference rules, where relation between antecedent and consequence is expressed by linguistic terms, e.g. if turnover is high, then provide high discount in business or if temperature is low and humidity is medium then turn valve slightly up in controlling technical systems. Furthermore, attributes’values either measured or estimated are of both kinds: crisp and vague or fuzzy. We start by formalizing single fuzzy rule with one antecedent and finish with formalizing multiple fuzzy rules containing several antecedents. Both models of fuzzy inference (Mamdani and Sugeno) are examined. The solution depends on chosen fuzzy sets, logical connectives and defuzzification strategy. Throughout the book the first and the second topic were discussed. In this chapter focus is on defuzzification strategies. Finally, classification by IF-THEN rules with support of fuzzy queries is examined.

Miroslav Hudec

Chapter 5. Fuzzy Data in Relational Databases

Abstract

Many agree that relational databases, like any other model of the real world, are imperfect artefacts. Hence, they cannot cover all occurrences and variety of data, in our case fuzzy data. Fuzzy values of attributes cannot be directly stored in traditional relational databases due to the first normal form. On the other hand, relational databases are broadly used. We firstly examine the way, how to store fuzzy data in traditional relational databases by satisfying normal forms in order to keep the integrity of a database in an usual way. Databases which are in use should be straightforwardly converted into fuzzy relational databases, when users decide that some attributes are better expressed by fuzzy data than by crisp values. Moreover, attributes which remain crisp, should not be affected. This improvement can be realized by fuzzy meta model of relational database. The second part of the chapter is focused on querying and summarizing fuzzy databases.

Miroslav Hudec

Chapter 6. Perspectives, Synergies and Conclusion

Abstract

Fuzziness can be found in many areas of daily life. Hence, fuzziness cannot be always expressed with one aspect and solved by one approach. It implies that different approaches should cooperate. In addition, many tasks, for example, in smaller businesses are not extremely demanding for complex tools, but rather they look for overviews of problems from different aspects. This short concluding chapter is focused on cooperation between fuzzy queries, summaries and inferences with respect to fuzzy and crisp data.

Miroslav Hudec

Backmatter

Titel: Fuzziness in Information Systems
verfasst von: Miroslav Hudec
Verlag: Springer International Publishing
Electronic ISBN: 978-3-319-42518-4
Print ISBN: 978-3-319-42516-0
DOI: https://doi.org/10.1007/978-3-319-42518-4