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nd Fuzzy object 
Algebra. 
Definition. If E is an fuzzy object algebraic expression and Q fuzzy query object 
is FOQL together define a sets fuzzy object , we say Q represent E and the opposite, 
ZHFDOO(HTXLYDOHQWWR46\PERO(Đ4
Equal representation between the query language and algebra FOQL fuzzy object 
is expressed through two theorems 1 and 2 as follows: 


Theorems 1. Every algebraic expressions are fuzzy object represented by the 
object query in FOQL. 
Theorems 2. Every Fuzzy object in FOQL queries are represented by algebraic 
expressions fuzzy object 
Thus, the rewrite a given query into algebraic expressions with algebraic set 
objects are equivalent. The algebraic expressions can be estimated with different 
abatement costs. So theoretically we wanted to find an algebraic expression 
equivalent to a query so that it can achieve a plan for more effective enforcement. 
However, in the solution installed, because the number of queries equivalent too 
large, that we only need a subset of this query. Therefore, in order to find other 
similar queries, we will need a set of rules to transform the equivalent algebraic 
expressions. However, the model fuzzy object oriented data does not have a 
standard fuzzy algebraic objects applicable to all models of fuzzy object-oriented, 
so the expectation to have a normal training include modified protection laws Full 
equivalent does not exist. So, we wanted to prove that the transformation preserved 
on a basis equivalent algebraic fuzzy objects that may be acceptable 
In order to translate a FOQL query into Fuzzy Object Algebra, query processor 
translates each SELECT clause to Project (࣊෥), FROM clause to objects name(s) 
or their Cartesian, and WHERE clause to Select (࣌෥). 
7KHTXHU\PHQWLRQHGHDUOLHUWR³UHWXUQWKHQDPHVRI<RXQJ6DOHVSHUVRQVZKR
earned Age ' very old´FDQEHZULWWHQLQ)X]]\2EMHFW$OJHEUDDVIROORZV
࣊෥ࡺࢇ࢓ࢋ ൬
࣌෥୓୪ୢୗୟ୪ୣୱ୔ୣ୰ୱ୭୬ୱǤࢌ࢕࢏ࢊୀௌ௔௟௘௦௉௘௥௦௢௡௦Ǥࢌ࢕࢏ࢊٿ ୓୪ୢୗୟ୪ୣୱ୔ୣ୰ୱ୭୬ୱǤ࡭ࢍࢋୀᇲ࢜ࢋ࢘࢟࢕࢒ࢊᇲ 
ሺŽ†ƒŽ‡•‡”•‘• ൈ෥ ݈ܵܽ݁ݏܲ݁ݎݏ݋݊ݏሻ ൰
However, query optimizer produces other equivalent alternative execution plans 
implemented in it so that a better plan in terms of execution time and resources may 
be found. 


4.2.5 $OJHEUDLF2SWLPL]DWLRQ
We previously identified the components of an algebraic optimizer. In this 
section, we discuss each of these components in some detail. 
4.2.5.1 6HDUFK6SDFHDQG7UDQVIRUPDWLRQ5XOHV
A major advantage of algebraic optimization is that an algebraic query 
expression can be transformed using well defined algebraic properties such as 
transitivity, commutatively and distributive. Therefore, each query has a 
(potentially large) number of equivalent expressions, which make up the search 
space. These expressions are equivalent in terms of the results that they generate, 
but may be widely different in terms of their costs. Thus, the query optimizers 
modify the query expressions, by means of algebraic transformation rules, in an 
attempt to obtain one which generates the same result with the lowest possible cost. 
The transformation rules are very much dependent upon the specific object algebra, 
since they are defined individually for each object algebra and for their 
combinations. The lack of a standard object algebra definition is particularly 
troubling since the community cannot benefit from generalizations of numerous 
object algebra studies. The general considerations for the definition of 
transformation are rules and the manipulation of query expressions is quite similar 
to relational systems, with one particularly important difference. Relational query 
expressions are defined on flat relations, whereas object queries are defined on 
classes (or collections or sets of objects) that have inheritance relationships among 
them. It is, therefore, possible to use the semantics of these relationships in object-
oriented query optimizers to achieve some additional transformations. 
4.2.5.2 6HDUFK$OJRULWKP
Heuristics such as performing selections and projections before joins (to reduce 
the sizes of the join operands) do not change the combinatorial nature of the 
problem. Therefore, the value of N and the threshold beyond which combinatorial 
nature of the problem makes enumerative solutions infeasible becomes an important 
issue. 


Heuristic: 
1. The parser of a high-level query generates an initial internal representation; 
2. Apply heuristics rules to optimize the internal representation. 
3. A query execution plan is generated to execute groups of operations based on 
the access paths available on the files involved in the query. 
The main heuristic is to apply first the operations that reduce the size of 
intermediate results. 
E.g., Apply fuzzy SELECT and fuzzy PROJECT operations before applying the 
fuzzy JOIN, or other binary operations. 
Outline of a Heuristic Fuzzy Object Algebraic Optimization Algorithm:
1) Using rule R2, break up any select operations with conjunctive conditions into 
a cascade of select operations. 
2) Using inheritance laws for projection (R3), the selection and allows apply (R10) 
combination of projection, select a projection and a selection. 
3) For each selection, use the law (R4, R6, R7, R10) "pushed" to allow select 
components to classes or "through" connection nodes and allows creation group. 
4) For each projection (objects, sets, sets), using legislation (R3, R4, R5) to 
projection move down as far as possible. If the projected attributes include all the 
attributes of the expression, we remove that projection. 
5) Using the law (R8,R9, R10) on the object class, to remove duplicate elements 
in the object class; move allows flattened (flat), lets remove duplicates in multiple 
files (bagtoset) ahead of the group or connection operations. 
6) Creating a sequence of steps for estimating change in an order every star team 
for no group is evaluated, its subgroups. 
7) Identify sub trees that represent groups of operations that can be executed by a 
single algorithm. 


4.2.6 *HQHUDWLRQRI4XHU\([HFXWLRQ3ODQV
After the query processor translates given FOQL statement to Fuzzy object 
Algebra it forwards that expression to query optimizer which generates various 
executions plans representing different orders or combinations of operators. 
There are a number of algebraic laws implemented in query optimizer for 
generating equivalent (logical) query plans. However, following are the most 
commonly used techniques that we also consider and implement in our tool: Simple, 
Elimination of Cartesian product, and Push selection. 
A. Simple Execution plan 
Query processor generates an equivalent relational algebraic expression for the 
input query and forwards it to the query optimizer. The first algebraic expression 
generated by the query processor involves Cartesian product that we call simple 
execution plan. 
Example 1: return names of OldSalesPersons who earned Age 'very old 
In FOQL it can be represented as: 
SELECT OldSalesPersons 
FROM OldSalesPersons, SalesPersons WITH 0.5 
WHERE OldSalesPersons.FIOD=SalesPersons.FOID 
AND OldSalesPersons. Age = àvery ROGả WITH 0.8. 
In Fuzzy object Algebra above FOQL statement is represented as: 
࣊෥ࡺࢇ࢓ࢋ ቆ
࣌෥୓୪ୢୗୟ୪ୣୱ୔ୣ୰ୱ୭୬ୱǤࢌ࢕࢏ࢊୀௌ௔௟௘௦௉௘௥௦௢௡௦Ǥࢌ࢕࢏ࢊר୓୪ୢୗୟ୪ୣୱ୔ୣ୰ୱ୭୬ୱǤ࡭ࢍࢋୀᇲ௩௘௥௬௢௟ௗᇲ
ሺ݈ܵܽ݁ݏܲ݁ݎݏ݋݊ݏ ൈ෥ Ž†ƒŽ‡•‡”•‘•ሻ
ቇ


old. Such queries are written as follows. 
SELECT * FROM OldSalesPersons, SalesPersons WITH 0.6 
:+(5($1'2OG6DOHV3HUVRQV$JH àYHU\ROGả:,7+
The second query processing the extract filter data for single-case conditions 
and enable a natural join. Request query processing engine return all employees 
age is very old. Such queries are written as follows. 
SELECT Name FROM OldSalesPerson as O, SalesPersons as S WITH 0.6 
:+(5(2),2' 6)2,'$1'2$JH àYHU\ROGả:,7+
The third query processing the extract filter data for single-case conditions and 
enable a natural join. After performing the optimization algebra objects. Request 
query processing engine return all employees age is very old. Such queries are 
written as follows. 
SELECT Name FROM SalesPersons as S inner join OldSalesPersons as O on 
O.FIOD=S.FOID WI7+:+(5(2$JH àYHU\ROGả:,7+
)LJXUH4XHU\SHUIRUPDQFH
From the above experiments, results achieved confirm that the performance of 
this method is effective. As an example, we evaluate the query according to this 
approach from the chart the way the query results shown in Figure 5. 


4.4 6800$5<
This section present a new model for optimizing the efficiency of query 
processing by semantic analyzing and FO algebra transforming. Specifically, we 
develop a heuristic fuzzy object algebraic optimization algorithm relied on 
equivalent transformation rules and Fuzzy-Object-Algebra transformation. 
Analysis on several experiments using the proposed algorithm shows better 
performance of query processing, which proves the efficiency enhancement of our 
method. 


5()(5(1&(6
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 DOI: 10.14738/tmlai.52.3105 
Publication Date: 28th April, 2017 
URL:  
TMLAI TRANSACTIONS ON MACHINE LEARNING AND ARTIFICIAL INTELLIGENCE Volume 5 No. 2 ISSN 2054-7390 
SOCIETY FOR SCIENCE AND EDUCATION 
UNITED KINGDOM 
A New Approach for Query Processing and Optimization Base 
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