What is fuzzy database?

Describe the theory of Fuzzy Querying to Relational Databases?

They are used to query to fuzzy databases that are enhanced from relational databases in a way that fuzzy sets are allowed in both attribute values and truth values. A fuzzy calculus query language is constructed based on the relational calculus and a fuzzy algebra query language is also constructed based on the relational algebra. In addition, this paper proves a fuzzy relational completeness theorem such that both the languages have equivalent expressive power to each other. Index Terms-Fuzzy database, query languages, relational algebra, relational calculus, relational completeness. I. INTRODUCTION DA TABASE technology has been advanced up to the relational database stage with the purpose that user interfaces with databases may approach a level of human interfaces. It is recognized that the fuzzy theory is suitably applied to some human-oriented engineering fields, one FUZZY database ..._________________------.--- Select Name where Name I Age I Tuple truth Age i "vepy young", iiiiiiiiii=j*iiiiiiiiii..=iiii __....--___> __To. _I_ Youns _I_ t_r u e_ ...---- (---.-...-----------...----- Mary I 30 I 0.7 Tom: A r e = " ~ o u n g ' . Bob I mBddle I nearly 0 . 5 John Inearlr 401 quite true Ron I old I 0.3 ..____________________________ Fig. 1. A query to a fuzzy database. 11. A FUZZY DATABASE MODEL A fuzzy database is defined as an enhanced relational database that allows fuzzy attribute values and fuzzy truth values; both of these are expressed as fuzzy sets. An example of the fuzzy database is shown in Fig. 1. of which is information processing, in particular database retrieval. In fact, fuzzy database models that allow fuzzy attribute values and fuzzy truth values in enhanced relational databases have been studied in [3] and [4]. However, these studies are restricted to just some particular applications and not grounded on theories of fuzzy database query languages. Thus fuzzy database systems would not be systematically developed on the basis of these studies; it is due to Codd's relational database theory that relational database systems have been systematically developed. It is desirable that theoretical foundations of fuzzy databases be established in order to systematically develop fuzzy database systems. fuzzy database theory; it develops a theoretical foundation for the fuzzy functional dependencies of fuzzy databases [I]. The work encourages further research for the rest of theoretical foundations of fuzzy databases. This paper thus aims to databases. It proposes two fuzzy database query languages: a fuzzy calculus query language and a fuzzy algebra query language. In addition, it proves a relational completeness theorem such that both the languages are equivalent in expressive power to each other. With these theoretical foundations, fuzzy Truth Of any tup1es are either (= true) Or (= database query systems will be developed systematically. A. Data A fuzzy database consists of relations: a relation is a relation R(tl, ,tn) in a Cartesian product PI x PZ x ... x P, of domains Pi; each P, is a set of fuzzy sets t, over an attribute domain D, (1 5 i 5 n). It is assumed that key attributes take ordinary nonfuzzy values. For the notational convenience, fuzzy sets are identified with their representative membership functions; for example, t; also denotes a membership function. B. Fuzzy Attribute Values Attribute values such as age have nonfuzzy values such as fuzzy predicates such as ccyoung9a9n d <Gabout forty" in the fuzzy database. For example, a fuzzy attribute value of "age of Dr. x is is expressed as a possibility distribution p (age of x) = YOUNG; YOUNG denotes a fuzzy set that are identified with fuzzy sets such as YOUNG. c. Fuzzy in the relational database; truth values of any tuples are defined as fuzzy predicates such as "0.7" and "completely true" in the fuzzy database. Consider, for example, a tuple t that asserts a fuzzy proposition: "It is completely true that Dr. x iS Very much older than twenty." The truth value of t is expressed as a possibility distribution P[T(t)]= N; T( t )d enotes a truth value o f t and N denotes a fuzzy set that represents the fuzzy an work has been done in the Of the 20 in the relational database; attribute values are defined as a foundation of query languages to represents the fuzzy predicate "young." Thus attribute values Manuscript received November 21, 1989; revised September 6, 1991 and The author is with NlT Network Information Systems Laboratories, IEEE Log Number 9205829. May 29, 1992. Kanagawa, Japan. 1041-4347/93$03.00 0 1993 IEEE Authorized licensed use limited to: University of Tehran. Downloaded on May 29,2010 at 10:52:24 UTC from IEEE Xplore. Restrictions apply. TAKAHASHI: FUZZY DATABASE QUERY LANGUAGES 123 predicate "completely true." Thus the truth values T(t) are identified with fuzzy sets such as N over z E [0,1]; the value z E [0,1] has the following meaning. 1) z = 0 means that the tuple t is completely false. 2) 0 < z < 1 means that the tuple t is true to the degree 3) z = 1 means that the tuple t is completely true. In particular, each tuple t of the relation R(t1, . . . , tn) is given a unique truth value T(t) by system designers at system generation time. In this case, T(t) determines a mapping T :P I x PZ x . . . x Pn + P([O1, 1) where P([O,1 1) is a set of fuzzy sets over z E [O, 11. expressed by the real number z. 111. QUERY BY TUPLE FUZZY CALCULUS A. Tuple Fuzzy Calculus A tuple fuzzy calculus (query language) is constructed as an enhancement of the tuple relational calculus. Formulas in the tuple fuzzy calculus are of the form ( t l f ( t ) )t: i s a fuzzy tuple variable each ith component ti, which is a fuzzy set in P;; f is a tuple fuzzy well-formed formula (WFF). Tuple fuzzy WFF's are enhanced from those of the tuple relational calculus as follows. 1) Atomic Tuple Fuzzy WFF's: An atomic tuple fuzzy WFF consists of fuzzy sets and a fuzzy comparison operator *. The fuzzy comparison operator * is one of the operators: equal; not equal; proper inclusion; inclusion. The fuzzy comparison operator * is an enhancement from the arithmetic comparison operator (=, #, <, >, 5,z) in the relational calculus. Then the atomic tuple fuzzy WFF's are either of the following two types: 1) (t;)* ( s j ) ; here, it is assumed that t and s are fuzzy tuple variables such that D; = Dj (1 2 ) (ti)* (c), (c) * (ti);h ere, it is assumed that c is a fuzzy set over D;. 2) Logical Connectives and Quantifiers: Logical connectives ("AND," "OR," and "NOT") are used for tuple fuzzy WFF's. Also, quantifiers ("for all" and "there exists") are used for tuple fuzzy WFF's. 3) Others: Other definitions concerning tuple fuzzy WFF's are the same as in the tuple relational calculus. Thus tuples in any relation R(tl,. . . , tn) that satisfy the formula { t l f ( t ) }fo rm a set of Cartesian products of fuzzy sets. It should be considered further whether or not to include fuzzy comparison operators * expressed by fuzzy relations such as "much greater than," "is close to," "is similar to," and "is relevant to." i , j 5 n). B. Query Evaluation Queries expressed in the tuple fuzzy calculus are evaluated by two steps as follows. (Step 1) Selecting resultant tuples: Consider that the query {tlf(t)} is issued to the relation R(t1,. . . , tn). Resultant tuples are those r E R(t1, + . . , tn) each of which satisfies the formula f(r). (Step 2) Calculating truth values of resultant tuples: Let any resultant tuple r be expressed as rkl . . . T k j ' . . rk, and r be a projection of t E R(t1,. . . , tn) onto the components ICl,...,ICj,...,km (1 5 m 5 n , l 5 k l , . . . , k j , . . . , k , 5 n). Then the truth value T(r) is defined as a projection of T(t) onto the components k l , . . . , k j , . . . IC,: T(r) = Max .T(t), where the maximum is taken over those components tk (1 5 Duplicate removal schemes are out of the scope of this paper and left for future work: if two tuples T I , r2 having different truth values T( r l ) ,T (r2)a re found to be duplicated, it is left up to fuzzy database designers which one will be selected. The fuzzy database designers will also choose which tuples from the resultant tuples r should be returned to the users: 1) full sets or appropriate subsets of resultant tuples r should be returned; 2) tuples r that contain truth values T(r) should be returned; or when users need not make use of truth values T ( r ) ,tu ples r , from which truth values T(r) are removed, should be returned. k 5 n), such that tk # tkj. IV. QUERY BY DOMAIN FUZZY CALCULUS A domain fuzzy calculus (query language) is obtained from 1) replacement of tuple variables t with domain variables, 2) replacement of the ith tuple component ti with a domain the tuple fuzzy calculus through the following replacements: 211212.. . ,Un; variable ui (1 5 i 5 n). V. QUERY BY FUZZY ALGEBRA A. Fuzzy Algebra A fuzzy algebra (query language) is constructed as an enhancement of the relational algebra. Fundamental fuzzy algebraic operations are union, set difference, Cartesian product, projection, and selection, which are defined as follows. I ) Union: Let R and S denote any relations in the fuzzy database. The union of R and S is a set of tuples that belongs to R or S. The union is equal to that in set theory. Any resultant tuple t by the union of R and S inherits the truth value T(t) from its original tuple in R or S. 2) Set Difference: The difference R - S of R from S is a set of tuples, each of which belongs to R and does not belong to S. The difference is equal to that in set theory. Any resultant tuple t by the set difference R - S inherits the truth value T(t) from its original tuple in R. 3) Cartesian Product: The Cartesian product R x S of R and S is a set of tuples, {(r, s ) l r : tuple in R, s: tuple in S}. The Cartesian product is equal to that in set theory. The truth value T(t) of the resultant tuple t = (rl s) by the Cartesian product R x S is the minimum of T(r) and T(s) where T(r) and T(s) are truth values of r and s, respectively. 4) Projection: The projection Proj(IC1, . . . , kj, . . . , k,)(R) of R onto the lcjth attributes is a set of tuples of the lcjth attribute values. The projection is equal to that in set theory. Let r denote any resultant tuple of the projection Proj(i1,i z,. . . , im) (R)o f t E R. Then the truth value T( r )i s Authorized licensed use limited to: University of Tehran. Downloaded on May 29,2010 at 10:52:24 UTC from IEEE Xplore. Restrictions apply. - 124 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 5, NO. 1, FEBRUARY 1993 the maximum of T(t) taken over those components tk, such 5) Selection: Let G denote a fuzzy WFF involving the i) operands that are constant fuzzy sets and attribute item ii) the fuzzy set comparison operators * (equal, not equal, iii) logical connectives "OR," "AND," and "NOT." The selection SelG(R) of the relation R is a set of tuples t in R each of which satisfies the fuzzy WFF G when any occurrences of the number i in G are replaced with the ith component of T in R. When any resultant tuple T is made by the selection SelG(R)t, E R inherits the truth value T( t )f rom the original tuple t in R: T(T) = T(t). Some additional fuzzy algebraic operations such as intersection, quotient, &join, and natural join are defined as combinations of the fundamental fuzzy algebraic operations defined previously in the same way as in the relational algebra. For example, the &join and the natural join are defined as follows. 6) 0-Join: The &join of R and 5' is defined as a combination of two fundamental fuzzy algebraic operations: the Cartesian product and the selection where 8 is enhanced to a fuzzy comparison operator * (equal, not equal, proper inclusion, inclusion). Truth values of resultant tuples by the &join are calculated as those of combinations of the two fundamental fuzzy algebraic operations. 7) Natural Join: The natural join of R and S is defined as a combination of three fundamental fuzzy algebraic operations: the Cartesian product, the selection, and the projection. Truth values of resultant tuples by the natural join are calculated as those of combinations of the three fundamental fuzzy algebraic operations. that tk # tkj. following constituents: numbers of the relation R; proper inclusion, inclusion); B. Que? Evaluation Any query by the fuzzy algebra is expressed as a combination of the fundamental fuzzy algebraic operations. Thus the resultant tuples T and their truth values T ( T )by this query are obtained as combinations of its constituent fundamental fuzzy algebraic operations. Duplicate removal schemes and return methods of resultant tuples to users are the same as described in the fuzzy calculus. VI. RELATIONACLO MPLETENESTSH EOREM FOR FUZZY DATABASE QUERY LANGUAGES The relational database theory establishes the relational completeness theorem such that the relational calculus is equivalent in expressive power to the relational algebra [2]. A similar theorem in the fuzzy database is given. Theorem: The following three fuzzy database query languages have the same expressive power: 1) tuple fuzzy calculus; 2) domain fuzzy calculus; 3) fuzzy algebra. Proof: The fundamental idea of the proof of this theorem is given by Ullman [2, pp. 114-1221; it presents the proof of the relational completeness theorem for the relational database query languages. Ullman's proof techniques consist of the following three reduction techniques: i) reduction of the relational algebra to the tuple relational calculus; ii) reduction of the tuple relational calculus to the domain relational calculus; iii) reduction of the domain relational calculus to the relational algebra. The reduction technique ii) is just the transformation between variable expressions, and thus is not influenced by the enhancements of the fuzzy database query languages. Therefore, it should be proved here that the reduction techniques i) and iii) can also be extended to cover the enhancements of the fuzzy database query languages. There are two essential enhancements in the fuzzy database query languages from the relational database. 1) The fuzzy database allows fuzzy sets as attribute values; the fuzzy comparison operators * (equal, not equal, proper inclusion, inclusion) are used in the fuzzy database query languages instead of the arithmetic comparison operators (=, # , <, > ,z2,) used in the relational database query languages. 2) The fuzzy database allows fuzzy sets as truth values T(t),t E R; truth values T(r) of resultant tuples T are inherited from T(t) of original tuples t E R, or calculated as combinations of Cartesian products or projections of T(t) of original tuples t E R. The enhancement 1) is easily incorporated into the reduction techniques i) and iii) by replacing the arithmetic comparison operators with the fuzzy comparison operators. Next, consider the enhancement 2). Remember that the truth value T(t) of the tuple t is defined just depending on the fuzzy set and fuzzy set operations that have been established in fuzzy theory; calculations of T(r) are made independently of any of the definitions of the fuzzy database query languages. Thus the reduction techniques i) and iii) can be extended to incorporate the enhancement 2). This completes the proof. QED VII. CONCLUDINGR EMARKS This paper proposes two fuzzy database query languages (fuzzy relational calculus and fuzzy relational algebra) based on the relational database query languages. In addition, it proves the relational completeness theorem such that both the languages are equivalent in expressive power to each other. As in the case of the relational database, this relational completeness theorem in the fuzzy database is expected to provide a criterion for the minimum fuzzy database query capability that must be implemented in any reasonable real fuzzy database query languages. There are interesting further theoretical studies still left. More complicated fuzzy queries, including more general fuzzy comparison operators such as "much greater than," and "is close to", need to be studied. Such queries include, for example, a statement "select several persons where their age is Authorized licensed use limited to: University of Tehran. Downloaded on May 29,2010 at 10:52:24 UTC from IEEE Xplore. Restrictions apply. TAKAHASHI: FUZZY DATABASE QUERY LANGUAGES 125 a little over than that of v,o ung bovs." Other studies need to be 131 M. Umano. "Relational algebra in fuzzy database," IEICE Tech. Rep. U , . > devoted to duplicate removal schemes and query optimization cih Japanese) v01r86, no. 192>-PP. 1986. [4] M. Zemankova-Leech and A. Kandel, "Fuzzy relational databases-A techniques to improve execution efficiency of the fuzzy query key to expert systems," Verlag TUV Rheinland GmbH, 1984. I . - languages; both of these are completely out of the scope of this paper though these are essential to the fuzzy database. Practically, there also should be an interesting further study how to implement the fuzzy database query languages in this paper by extending the existing real relational database query languages, such as the international standard database language SQL. REFERENCES [l] K. V. S. V. N. Raju and A. K. Majumdar, "Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems," ACM Trans. Database Sysr., vol. 13, no. 2, pp. 129-166, June 1 OR!? Yoshikane Takahashi received the M.Sc. degree in mathematics from the University of Tokyo, Tokyo, Japan in 1975. He is currently with NlT Network Information Systems Laboratories, Kanagawa, Japan. His research fields include communications protocol, fuzzy theory, neural networks, nonmonotonic logic, genetic algorithms, and knowledge information theory. Mr. Takahashi was awarded the Moto-oka Commemorative Award in 1986. He is a member of the [Z] J. D. Ullman, Principles of Database Systems. Rockville, MD: Com- Japanese Institute of Electronics, Information, and Communication Engineers, puter Science, 1980. and the Information Processing Society of Japan. Authorized

If fuzzy wuzzy wasn't fuzzy why is he fuzzy wuzzy?

because fuzzy wazzy was fuzzy

When you call fuzzy set as fuzzy graph?

fuzzy graph is not a fuzzy set, but it is a fuzzy relation.

Why is fuzzy bear so fuzzy?

fuzzy wuzzy had no hair... therefore he cannot be fuzzy

What is fuzzy system?

 Fuzzy inference is a computer paradigm based on fuzzy set theory, fuzzy if-then- rules and fuzzy reasoning  Applications: data classification, decision analysis, expert systems, times series predictions, robotics & pattern recognition  Different names; fuzzy rule-based system, fuzzy model, fuzzy associative memory, fuzzy logic controller & fuzzy system Fuzzy inference is a computer paradigm based on fuzzy set theory, fuzzy if-then- rules and fuzzy reasoning  Applications: data classification, decision analysis, expert systems, times series predictions, robotics & pattern recognition  Different names; fuzzy rule-based system, fuzzy model, fuzzy associative memory, fuzzy logic controller & fuzzy system

Fuzzy logic previous papers please?

fuzzy logic papers fuzzy logic papers fuzzy logic papers

Fuzzy wuzzy was a bear?

Fuzzy wuzzy was a bear But Fuzzy wuzzy had no hair So he wasn't fuzzy, wuzzy?

Fuzzy Wuzzy was a bear Fuzzy Wuzzy had no hair Fuzzy Wuzzy wasn't fuzzy was he?

Fuzzy-Wuzzy (a poem by English author and poet Rudyard in 1892) refers to the Hadenoda warriors who fought the British army in North Africa and the respect of the ordinary British soldier toward them. The name "Fuzzy-Wuzzy" could be entirely English in origin, or it could combine some sort of Arabic pun (by chance based on ghazī, "warrior"). It refers to their butter-matted hair that gave them a unique "fuzzy" look.

Is salt fuzzy?

Salt is not fuzzy.

Are fuzzy putunias fuzzy?

Yes they are.

What is check point in DBMS?

fuzzy checkpointIn a fuzzy checkpoint, the database server does not flush the modified pages in the shared-memory buffer pool to disk for certain types of operations, called fuzzy operations. When a fuzzy checkpoint completes, the pages might not be consistent with each other, because the database server does not flush all data pages to disk. A fuzzy checkpoint completes much more quickly than a full checkpoint and reduces the amount of physical logging during heavy update activity. When necessary, the database server performs a full checkpoint to ensure the physical consistency of all data on disk. Fuzzy OperationsThe following commonly used operations are fuzzy for built-in data types:InsertsUpdatesDeletesThe following operations are nonfuzzy:Inserts, updates, and deletes for rows that contain user-defined data types, smart large objects (CLOB and BLOB data types), or simple large objects (TEXT and Byte data types)Table alters and loadsOperations that create or modify indexes (B-tree, R-tree, or user-defined indexes)The database server flushes all the modified data pages for nonfuzzy operations to disk during a fuzzy checkpoint in the same way as for a full checkpoint.Important:Fuzzy checkpoints are disabled for the primary and secondary servers in a High-Availability Data Replication pair.Write-Ahead Logging and Fast RecoveryFuzzy checkpoint uses write-ahead logging for fast recovery. Write-ahead logging means that the logical-log records representing changes to fuzzy data must be on disk before the changed data replaces the previous version of the data on disk. Fast recovery begins with the oldest update not yet flushed to disk rather than with the previous checkpoint.Fuzzy checkpoints result in slightly longer roll-forward fast-recovery times. The database server occasionally performs a full checkpoint to prevent loss of old logical-log records.Fuzzy Checkpoints Improve PerformanceFuzzy checkpoints are much faster than full checkpoints and improve transaction throughput. Because the database server does not log fuzzy operations in the physical log, the physical log does not fill as quickly, and checkpoints occur less often. For example, if you are inserting and updating a lot of data, checkpoints occur less frequently and are shorter.The database server skips a full checkpoint if all data is physically consistent when the checkpoint interval expires. It skips a fuzzy checkpoint only if no pages have been dirtied since the last checkpoint.To improve transaction throughput, use the BUFFERPOOL configuration parameter to increase thelru_max_dirty and lru_max_dirty values. However, do not change the gap between the lru_max_dirty andlru_max_dirty values.

Are the webkinz still fuzzy?

yes, webkinz are still fuzzy they always were and always will be fuzzy

What is fuzzy database?

What else can I help you with?

Data base state vs database schema?

What are names of databases?

What is the scientific name for the american fuzzy lop?

What diff between the database and database system?

What factors determine the database you search?