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Zakir Ali et al. / International Journal of Engineering Science and Technology Vol. 2(4), 2010, 358-361

POTENTIALS OF FUZZY LOGIC:AN APPROACH TO HANDLE IMPRECISE DATA *Zakir Ali **Vinod Singh Abstract The reasoning and decision-making process of human beings is often uncertain and vague in nature But traditional databases handle data, which is crisp, deterministic and precise in nature. If we want the computer system to work according to human speech, then we need to introduce Fuzziness into our databases based upon the concept of fuzzy logic, which is an extension of normal boolean logic ,representing something between absolute truth and absolute false. The concept of fuzziness in databases and the ways of handling the fuzzy queries to databases/ fuzzy databases are explained in this paper followed by a comparison between the two different set theories on which the traditional and the fuzzy databases are based. Keywords: Fuzzy Logic, Fuzzy Sets, Fuzzy Relational Databases, Fuzzy SQL 1. Introduction Most of our traditional tools for reasoning and computing are crisp, deterministic and precise in nature. But it gives birth to two major complications. Firstly, Real situations are very often not crisp and deterministic and cannot be described precisely i.e. real situations are very often uncertain or vague in a number of ways. e.g. Rather than saying “He is 6.’0” tall”, we prefer to say ,”he is very tall”. Secondly, complete description of a real system would require far more detailed data than a human being could ever recognize and process simultaneously. Since most conventional databases in use today are based on the relational model, so such kind of description becomes difficult to represent under the conventional relational model. If we want the computer system to work according to human speech, then we need to introduce Fuzziness into our databases . 2.Traditional Database Approach: An Example Consider a student record database system. Supposing we want to find all the bright (percentage above 80) and young students (age between 19 and 25) in the whole batch. For a crisp system we would specify the query as select * from student where percentage>80 and age between 19 and 25. Now this system has a major flaw. Consider a student, Zaheer whose percentage is 92% but whose age is 25 years and 2 months. He should have been selected as our requirement is to select bright students but because of the rigid boundary conditions set by the normal crisp logic, he has been rejected. 3. The Concept of Fuzziness The concept of fuzziness as described by Zadeh [1] includes imprecision, uncertainty, and degrees of truthfulness of values. Zadeh introduced a theory whose objects fuzzy sets are sets with boundaries that are not precise and the membership in this fuzzy set is not a matter of true or false, but rather a matter of degree. This concept was called Fuzziness and the theory was called Fuzzy Set Theory. It is particularly frequent in all areas in which human judgement , evaluation and decisions are important. 4. Definition of a Fuzzy Set When A is a fuzzy set and x is a relevant object then the proposition “x is a member of A” is not necessarily either true or false[2], as required by the two-valued boolean logic, but it may be true to some degrees, and the degree to which x is actually a member of A, is a real number in the interval [0,1].Theoretically F={x, µF(x))| xєX} F is the Fuzzy Set where X is a collection of objects denoted by x

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Zakir Ali et al. / International Journal of Engineering Science and Technology Vol. 2(4), 2010, 358-361 µF(x) is called the membership function(or grade of membership) of x in F. the range of the membership function is a subset of the non-negative real numbers in the interval [0,1]. 5. Comparison of Fuzzy and Boolean Logic • Boolean algebra brings logic operators AND, OR, NOT. But by using these operators when searching with imprecise or incomplete information, it is not ensured that we get the requested data. • But imagine if there is no information meeting the query conditions, still the user gets information which meet conditions to some extent/degree. • And this isn’t possible using classic approach. Only fuzzy logic can handle such queries • Hence Fuzzy logic is an extension of normal boolean logic representing something between absolute truth and absolute false. • Advantage of fuzzy logic is the mathematical ability to catch up the words described by words. This gives us the possibility to work with ambiguous terms like “small”, “near”, “far” ,”about”, ”very” and with number of other words used in human language. If 20 m is close, then what about 21 m. Will it be categorized as far? • Next difference is direct in query where fuzzy statement can be used i.e. statement which allows us to use the words like big, far, near, average etc. Hence the basic difference between fuzzy approach and boolean one is the ability to get “rated result”. 6. Classification of Fuzzy Data Fuzzy data can be further divided into two types: a) Approximate Value: The information data is not totally vague and there is some approximate value , which is known and the data lies near that value b) Linguistic Variable: This variable is used to represent a fuzzy number . A linguistic term is a name given to the fuzzy set.[3][4]. Consider a linguistic variable AGE which may have a Linguistic term YOUNG associated with it. Then the possibility distribution of this linguistic term YOUNG for the linguistic variable AGE will be as follows:

YOUNG

1

0

α

β

γ

δ

Now recall the same example of Zaheer whose percentage is 91% but whose age is 25 years and 2 months. • In fuzzy logic, we would do the same by specifying two fuzzy sets YOUNG and BRIGHT and each student will have some membership grade associated with the two sets. • So according to our definition, the student Zaheer will have a non-zero membership grade although it will be less than other students in the age group of 19-25. • Hence, using fuzzy logic even Zaheer will be included in the result set to be considered as “Zaheer also satisfies the query to some extent, which is represented by its membership grade.” 7. Fuzzy Querying to Relational Databases To incorporate fuzziness we introduce fuzzy sets/ linguistic terms on the attributes/linguistic variables[5] e.g. on the attribute HEIGHT, we may define sets as TALL,MEDIUM and SHORT. Similarly on the attribute AGE we may define sets as YOUNG, MIDDLE and OLD.

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Zakir Ali et al. / International Journal of Engineering Science and Technology Vol. 2(4), 2010, 358-361

YOUNG

MIDDLE

OLD

1

0

αY

βY

γY αM

δYβM

γM

β O δM

γO

δO

There are 4 parameters associated with the linguistic term i.e. α ,β,γ,δ as shown in the figure above. For the range [β,γ], the membership value is 1 while for the range [α ,β] and [γ,δ] , the membership value remains between [0.0,1.0] Now consider a student database which has a table STUDENTS with the following attributes:

Name Shirin

Age 20

Course B.Tech

Percentage 71

Shilpi

26

B.Tech

82

Vinay

26

B.Tech

83

Puneet

19

B.Tech

79.3

Bhanu

21

B.Tech

80

Manoveg

29

B.Tech

79.8

Now the new formulation of a base block is Select from where e.g. Select * from students where (age=middle) and (percentage =high) Today most query languages represent SQL which is based on Boolean Logic.Fuzzy SQL(SQLf) is based upon SQL with additional properties of impreciseness and fuzziness. The objective is to introduce some fuzziness in the base block of SQL as shown above[6] 8. Memory and Time Consumption of Fuzzy Databases A database that can handle imprecise information shall store not only the raw data but also the related information that shall allow us to interpret the data in a much deeper context. Hence fuzzy databases require more storage spaces as compared to traditional databases than handle crisp information. It takes more I/O time to transfer ill-known data between main memory and secondary memory than does crisp data. Furthermore, since fuzzy queries require nonboolean degrees of satisfaction to be computed, it takes more CPU time to evaluate a fuzzy query condition than does a crisp query condition. fuzzy query condition than does a crisp query condition. 9. Conclusion Today exists huge applications of fuzzy sets and their properties in areas such as Medical Diagnosis, Employment etc. One of those are databases. Fuzzy sets represent basement of fuzzy database systems , which brings opportunities to query data by language close to human speech. But fuzzy databases are still not very much in use because people are reluctant to replace their crisp data by fuzzy data before they are convinced that it is worthwhile and necessary to do so

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Zakir Ali et al. / International Journal of Engineering Science and Technology Vol. 2(4), 2010, 358-361 REFERENCES [1] [2] [3] [4] [5] [6] [7]

Zadeh, L. A. Fuzzy sets. Information and Control, 8 (1965), 338-353. Klir G. J. and Yuan B. [2001], “Fuzzy Sets and Fuzzy Logic : Theory and Applications”, Prentice Hall, Inc. Englewood Cliffs, N. J., U.S.A. W. Zhang, C. Yu, G. Wang, T. Pham, and H. Nakajima, ªA Relational Model for Imprecise Queries,º Proc. Int'l Symp.Methodologies in Intelligent Systems, 1993. H. Nakajima, T. Sogoh, and M. Arao, ªDevelopment of an Efficient Fuzzy SQL for Large Scale Fuzzy Relational Database,ºProc. Fifth Int'l Fuzzy Systems Assoc. World Congress '93, 1993. H. Prade and C. Testemale, ªFuzzy Relational Databases: Representational Issues and Reduction Using Similarity Measures,º J. Am. Soc. Information Science, vol. 38, no. 20, pp. 118-126,1988. P. Bosc, M. Galibourg, and G. Hamon, ªFuzzy Querying with SQL: Extensions and Implementation Aspects,º Fuzzy Sets and Systems, 1988. Navnit Kaur Johal, Amrit Kaur “Fuzzy Databases: Approach to handle vague information”

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