SOFT COMPUTING TECHNIQUES FOR STATISTICAL DATABASES Miroslav Hudec

SOFT COMPUTING TECHNIQUES FOR STATISTICAL DATABASES Miroslav Hudec INFOSTAT – Bratislava MSIS 2009

Introduction • • • Soft computing (by fuzzy logic) Database query (SQL - fuzzy) case study Data classification (usual - fuzzy) case study Conclusion

Soft computing The essential property of soft computing (SC) is to “soften” hard computing (HC) techniques for coping with the imprecision, ambiguity and uncertainty. HC uses two-valued logic (e. g. the element satisfies or not the criterion) Fuzzy logic as a part of SC uses many valued logic (e. g. the element can partly satisfy the criterion) Computing with words is inspired by the human capability to perform a wide variety of tasks without exact measurements and computations. (Flexible database query. Interesting for statistical IS? )

Database queries (SQL) two-valued logic select * from Table where attribute_p > P and attribute_r < R.

SQL and fuzzy queries two-valued logic SQL conditions >=, <=, = logical operators and, or: 1 and 1 =1 0 and 1 =0 one function for and or operator many-valued logic fuzzy big small about 0, 7 and 0, 358=? (0. 358) (0. 2506) for {0, 1} logic minimum and product become ordinary and operator

Case study select district, roads, area from T where roads is Big and area is Small The length of road indicator is represented by „Big value“ fuzzy set with these parameters Ld=200 km and Lp =300 km. The „Small value“ fuzzy set with parameters Lp=450 km 2 and Lg =650 km 2 describes the area of district attribute.

Solution If SQL was used, this additional valuable information would remain hidden.

Discussion For the very soft gradation, the infinite number of SQL queries has to be used. In case of fuzzy queries, one query is sufficient. The advantages of this approach for users are as follows: • the connection to a database (connection string) and data accessing (SQL command) do not have to be modified; • users do not need to learn a new query language; • the interface supports (quasi) natural language; • presenting of obtained data is in similar way as from SQL but with additional valuable information; • users see data “behind the corner“ (colored areas in table) and can take into account possible interested data.

Data classification two-valued logic How to solve this problem without additional calculation? Approximate reasoning and fuzzy logic

Data classification many-valued logic classify_into [class. Cx] select [attributes] from [tables, views] The same GLC

Case study In this case study municipalities are classified according to the percentage of needs for the winter road maintenance. This example contains following fuzzy rules : If Road is Small and Snow is Small Then Maintenance is Small; (0. 1) If Road is Small and Snow is Big Then Maintenance is Medium; If Road is Big and Snow is Small Then Maintenance is Medium; (0. 5) If Road is Big and Snow is Big Then Maintenance is Big. (0. 9)

Case study classify_into S select * from Table where roads is Small and snow is Small; classify_into M select * from Table where (roads is Small and snow is Big) or (roads is Big and snow is Small); classify_into B select * from Table where roads is Big and snow is Big.

Case study If classical classification were used, this additional valuable information would remain hidden (Softer classification between objects T 1 -T 4).

Implementation

SQL and fuzzy approach SQL queries are useful when a clean and exact boundary between selected and non selected data is required (faster and less calculations). Fuzzy queries provide flexibility for the definition of query and inclusion of records that almost meet the query criterion (more operations, more information). User decides which type of query is better for each task.

Conclusion This approach allows users of statistical information systems to use their approximate reasoning during work with data. When users work with usual software tools they have to change their many-valued logical thinking (approximate reasoning) into the two-valued computer logic. This fuzzy approach supports work with linguistic expressions on the client side, nevertheless it does not need any modification of relational databases.

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