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Attribute Weights Mining for Case-Intelligent System Reasoning on
Similarity Rough Sets
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IMMAEE 2018
IOP Conf. Series: Materials Science and Engineering452 (2018) 042110 IOP Publishing
doi:10.1088/1757-899X/452/4/042110
1
Attribute Weights Mining for Case-Intelligent System
Reasoning on Similarity Rough Sets
Jianyang Li 1, 2, *, Changtong Song 2 and Qi Wang 2
1School of Electrical Engineering, Zhenjiang Institute, Zhenjiang, China
2School of Computer Engineering, Hefei University of Technology, Hefei, China
*Corresponding author e-mail: lijianyang@sina.com
Abstract. Attribute Weights Assignment is an important method to solve real world
problems full of uncertainty, for it is difficult to acquire a comprehensive formula
theoretically with which so many empirical calculations have to be drilled out of domain
experts. Case-Intelligent System based on CBR (case-based reasoning), which is a
human creative thinking and useful reasoning model for problem-solving, can acquire
prior knowledge from the former stored cases implicating decision strategy empirical
and powerful, and construct a flexible system integrated with efficient machine learning
methods coping with uncertainty. Attribute weights also are the key for case similarity
measurement and optimal case selection in CBR cycle, so the similarity Rough Sets is
proposed for case attributes reduction, knowledge obtainment and objective weights
acquiring in our case-intelligent system, which performs well in real experiments on
decision-making and achieves reasonable explanations.
1. Introduction
Due to our recognition limited, our world are full of uncertainty for us to explore which is a situation of
our knowledge unknown for exactly describing the existing state. Uncertainty involves imperfect or
unknown information and can be described in the following three aspects, (1) Decision making- a
situation where the current order or nature of things is unknown, the consequences is unpredictable and
credible probabilities is undesirable (2) Information theory- a certain degree to which available choices
are free from constraints. (3) Statistics- a situation where neither the probability distribution of a variable
nor its mode of occurrence is known.
Different experts are obliged to find out a conclusion to explain the uncertainty. for example,
Vagueness is a form of uncertainty such as long/short distance where we cannot clearly distinguish the
two, and this form of vagueness can be modeled by some variation on Zadeh's fuzzy logic or subjective
logic [1]. Ambiguity is a form of uncertainty for word in natural language has different meaning and its
interpretation depends on the writer [2,3]. Uncertainty may be a lack of knowledge of complex facts for
that if we had acquired knowledge enough for those impact factors, it could have been removed with
further analysis and experimentation. Due to ignorance, indolence, or the both, our learning is a process
with uncertainty though we want to reach a more precise result. We must deal with the real world
problems full of uncertainty, and tolerate uncertainty existing in problems to get a feasible results;
moreover how to explain the results obtained from uncertain knowledge reasoning chains many
researches have proposed is a more difficult task.
IMMAEE 2018
IOP Conf. Series: Materials Science and Engineering452 (2018) 042110 IOP Publishing
doi:10.1088/1757-899X/452/4/042110
2
As the great achievement for the simulation of human analogy learning, CBR originates from human
experience learning, which obtains the similar former cases and appropriately adapts to a new situation
for the new problem-solving. CBR allows similar knowledge reasoning even though some attributes
missing as long as they are similar in a certain degree, and knowledge space mapping is the key for
analogy learning. Cases are the presentation implicit of human sense, logics and creativity, which many
artificial intelligences and cognitive psychologies are exploring the synthesis-reasoning, and naturally
become a common artifice when people process experiential decision-making [4-6]. So case-intelligent
system based on CBR is constructed to express human learning ability for problem-solving, where
attribute weights Acquirement and assignment is a effective way to conquer the complexity and
uncertainty and got a reasonable results [7,8].
2. Attributes Weighting Methods
2.1. Complicated Decision-making
Many researches have done lots from different perspective, and several corresponding decision-making
methods have been proposed. But they are so complicated characteristics with uncertainty-(1)
uncertainty or unknown state of running environments; (2) complicated decision-making environment
and development situation; (3) decision maker having the expected requirement but not a expected value;
(4) undetermined candidate alternative or estimating the implementation effect difficultly; (5)
establishing decision-making model difficultly. Summarized the all, uncertainty comes from the both
sides, the one is that we haven’t got clear knowledge for the problem, which is objective for our cognitive
process; the other is that our decision-making is subjective. So case-intelligent system is chosen for the
complicated decision-making from extracting and analyzing the former cases to solve similar problems
[9].
CBR systems retrieve and reuse solutions from previous solved problems that have stored as cases,
searching their relations by similarity measurement at a certain level, through which solves the new
issues by appropriate knowledge transformation. The process of matching is based on the similar
information in the case library; and the matching methods can be composed by partial similar attributes,
partial matching feature, even by interpretable matching, where the chief task is the similarity
measurement [10]. kNN (k Nearest Neighbor) is the foundation for case similarity measurement, let’s
see how the attributes weighting influence the similarity result.
Assume case 1 2
( , ,..., )
n
X X X X
with vector
i
X
(i=1 to n), and case 1 2
( , ,..., )
n
Y Y Y Y
with
vector
i
Y
(i=1 to n), then their distance can be computed:
1/
( , ) ( , )
r r
i i
i
DIST X Y D X Y
. If
i
W
is
found as the weight of attribute
i
X
, then
1/
( , ) * ( , )
r r
i i i
i
DIST X Y W D X Y
. DIST(X,Y) can be
measured in Hausdorff distance, Minkowsky distance, Mahalanobis distance, Manhattan distance, Euler
distance (r=2), Hamming distance (r=1), etc. so the similarity between X and Y is:
1/
( , ) 1 ( , ) 1 * ( , )
r r
i i i
i
SIM X Y DIST X Y W D X Y
Due to the weights changing, their similarity value may be close, and the two cases can be treated in
similar state, thus it has a significant impact on the correctness of reasoning. Obviously, The attribute
weights assignment in CBR system is so important that so many distance methods in different ways may
determine the similarities between cases to meet the decision needs. Considering that human cognitive
ability and information processing ability are finite for decision-making, attribute weighting is a
powerful tool to fit for real world uncertainty naturally [11,12].
2.2. Weights Acquiring
There are many methods to determine attribute weights for different domain using, where these methods
can be divided into three categories according to the original sources data: subjective weighting method,
IMMAEE 2018
IOP Conf. Series: Materials Science and Engineering452 (2018) 042110 IOP Publishing
doi:10.1088/1757-899X/452/4/042110
3
objective weighting method and combination weighting method. Subjective weighting method is a
mature method to determine the weights of attributes given by domain experts, which the original data
are obtained just by their subjective judgment based on experience. The commonly used subjective
weighting methods include Delphi method, AHP, binomial coefficient method, minimum square method,
etc. The advantage of which is that domain experts can reasonably determine the attribute weights
through their long-term empirical learning according to actual decision-making problems, and the
shortcoming is that evaluation results deeply relies on domain experts which each has a different weight
so its application has great limitations.
Objective weighting method is proposed for its original data which should come directly from the
objective environments according to the degree of relationship and influence on their attributes. The
commonly used objective weighting methods include principal component analysis, entropy method,
deviation and mean square deviation method, multi-objective programming method and so on. Objective
weighting method has a strong mathematical theoretical basis, and mainly determines the weight
according to the relationship between the original data no need with domain experts, which becomes a
shortcoming especially in decision-making full of uncertainty, for the weights this method determined
may be inconsistent with our subjective wishes or actual conditions. Because the most important
attributes do not necessarily make the maximum difference with other attributes theoretically, the least
important attribute may have large differences and then the weight determined only by the objective
weighting method may have the greatest weight; and the calculation methods are mostly complicated.
Moreover this method of weighting relies on actual data from the problem domain without the
participation of decision-maker.
Therefore a reasonable method - combination weighting method, which combines subjective
weighting method and objective weighting method in some criteria, emerges to reach the balance of
empirical knowledge and original source data themselves. For it can be seen that the first has an
advantage in determining the weight according to the meaning of the attribute itself without objectivity,
while the latter relies on domain experts without considering the actual meaning of the attribute,
integration method can reduce the subjective randomness within subjective and objective unity, and then
achieve the reliable result.
2.3. Synthesis Reasoning
RBR (rule-based reasoning) is human learning ability from complicated data to induct the knowledge
represented as a set of rules, like decision table which the IF (condition) THEN (action) structure
specifies a relation, directive, and strategy. RBR systems such as Expert System are designed to imitate
thought processes of an expert doing a particular task, and constructed using automatic rule inference,
while the condition part of a rule is matched, the conclusion should be naturally drawn out. RBR
generally uses specialized knowledge to solve well-defined problems, but for complex tasks the
inference chains are so complicated that how a conclusion is reached and why a specific fact is needed
have been bothering experts and users, and reasonable explanation for the users are difficult. Naturally
the combination of RBR and CBR is expected to construct our case-intelligent system, to give their full
advantages to guarantee the good performance of the system for problem-solving with the uncertain and
incomplete knowledge. There are many methods to combine them in our system:
(1) parallel reasoning and choosing the better result. RBR is very suitable for regular environments,
and relies on structured prior knowledge, which is the formal expression with the most efficient
knowledge in intelligent systems. On the contrary, CBR system is more effective on special
circumstances, individual case corrections, convenience and accumulated experience. The different
focuses of the two reliable reasoning model make the two work together and coordinate with each other
in parallel technology to provide better models for such parallel computing systems.
(2) Mutual conversion. transforms case knowledge and rule knowledge into one another, and uses a
form of knowledge reasoning in the system. The first is that each case implies an analogy corresponding
to a rule, so the case is converted into a rule, thereby forming two knowledge bases that can be used by
the intelligent system, and then refining and integrating. The second is to convert the rules into cases, to
IMMAEE 2018
IOP Conf. Series: Materials Science and Engineering452 (2018) 042110 IOP Publishing
doi:10.1088/1757-899X/452/4/042110
4
ensure that the converted case library coverage can not be less than that of the original rule base, and
integrate the two case libraries through induction technology.
(3) Master-slave auxiliary reasoning. one method is dominant with the other method is auxiliary. For
example, RBR is the main with CBR as the auxiliary, for which the function of the RBR system is
mainly improved by CBR technology. A key question is how much coverage of the problem CBR
technology can increase, and increase the functionality of the RBR system; if a similar case is found,
the correction rule can also be used to find the solution; otherwise, use the rule base to infer the solution,
such as deriving the solution to the problem, or return to the CBR master module, solved by human-
machine dialogue or expert.
Well known as the 4R- Retrieve, Reuse, Revise, and Retain are the four main CBR processes for a
new problem solving, each of them is involving in attributes weight for similarity measurement is the
key to CBR system reasoning ability. CBR process as experts can also make case adoption that is much
faster and more accurate with RBR assistant, for they have excellent flexibility; especially CBR can
make case good explanation to users for each case is a true action.
3. Experimental results with outlook
3.1. Improved Weighting Algorithm
Rough Sets is a useful KDD tool for information processing, which can decrease the system complexity
from the suitable granularity; for the traditional RS only can deal with the discrete attribute, we use
Similarity Rough Sets for our Case Intelligent system to discretize the real continuous value easily and
can greatly decrease the time cost for they having the same similarity measurement. According to the
similarity Rough sets theory, the measurement of similarity between objects i and j in attribute a∈A is :
max min
, 1 | | / | |
a i j i j
S v v v v a a , with the definition the threshold of similarity in attribute a is t(a)∈
0,1. Assume a attribute subset B, BA, then SIMB is the similarity relation, x SIMB y while
Ba
aa tyaxaSW ,, t∈0,1 and wa is the weight of attribute a; so SIMB_(X)={x∈U: SIMBx X},
Xx
BB xSIMXSIM
)( ,
dUX
BSIMB XSIMdPOS
/
_
.
The importance of an attribute can be objectively computed by the rSIMB(d), which represents the
classification ability of attribute subset B, for different subsets have their different classification ability.
Ucard
dPOScard
dr SIMB
SIMB
))((
)( )()()( }){( drdraK aBSIMSIMBSIMB
( 1)()(0 draK SIMBSIM B ). Source data,
attribute discretization and decision table are omitted for the paper limited, from the table 1, we can
compute the importance of attribute with POS(A), core(A), etc, but they are complex with time
consuming, our weighting algorithm directly computes each attribute from the discernibility matrix.
Table 1. Discernibility Matrix and Attribute Grade
X0
X2
X4
X6
X9
a
b
c
d
e
grade
X1
b,c,d,e
b,c,d
a
a,b,c,d
a,b,c
M1
1
0
1
0
1
5
X3
a,b,c,d,e
c
b,c,d
a,b
a,d,e
M2
2
3
1
2
0
4
X5
a,c,e
b,c,d,e
b,c,d,e
a,d,e
a,b,d,e
M3
4
4
5
6
5
3
X7
a,b,c,e
a,b,d,e
c,d,e
b,d,e
a,b,d,e
M4
5
8
5
7
7
2
X8
a,b,c,d,e
a,d
b,c
b,d
e
M5
2
2
2
2
2
1
Classifying each attribute from the discernibility matrix, marked each the attribute as M1, M2…
Mm, which reflects the grade m, m-1… 1, and M1 is the highest grade.
Counting for each property item in the collection of each class, and calculating the number of
occurrences of each item.
IMMAEE 2018
IOP Conf. Series: Materials Science and Engineering452 (2018) 042110 IOP Publishing
doi:10.1088/1757-899X/452/4/042110
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Comparison of their counts for each attribute from M1 to Mm, if the counts are the same, the
comparison of their number in the M2 must be done, and so on.
Different importance of an attribute is emerging for their different counts in different grades,
while the number of items in the count is more than any other items within each Mi, the attribute
having the higher weight is computed.
From the first step {a,c,e} can be easily realized their more importance from the discernibility matrix
in grade 5, the same with RS for their core attributes; but attribute a is more import than c or e, for their
counts are (2,1,0) in grade 4. Although the reduction {a,b,c,e} or {a,c,d,e}, attribute b is more import
than d, for their counts are (3,2) in grade 4. each attribute weight (a:0.367, b:0.078, c:0.291,d:0.063,
e:0.201) can be accurately objectively, and the complexity of our algorithm also with its time
consumption are much lower than the composing POS(X) and Core(X) in RS theory.
3.2. Experiments and Analysis
The data set of “Mushrooms” in our experiments is downloaded from UCI repository of machine
learning databases and describes hypothetical samples corresponding to 23 species, each species is
identified as definitely edible, definitely poisonous, or of unknown edibility and not recommended. Its
main information is: 8124 Instances, 22 Attributes plus the 1 decision attribute as edible (4208- 51.8%)
or poisonous (3916- 48.2%), can be all simulated as binary decision, while 5244 instances are in
complete attribute value and 2480 instances in missing attribute values. So the experiment are unfolded
in the following three states: complete decision table, incomplete decision table and the real world
decision table (that is the real decision table with attributes missing).
a
Figure 1. System Recognizing Rate with Different Weighting
We have got objective weighting method from similarity RS to decrease the influence of experts and
possible errors in subjective weighting, the combines weights of subjective weighting method and
objective weighting method are used in the following experiments with
(1 )
I aQ a P
. The 10-
fold cross validation is used in our experiments as usual corresponding with
a
=(0, 0.3, 0.5, 1).
From fig 1, we can see the first curve has little mutation, for they have the complete information on
each attribute; and the pulse curve is changed sharply with
a
for they have the so many attributes
missing for us to distinguish them and incomplete information cannot be well dealt with. As well known,
fully complete or incomplete attributes are the two extreme conditions for our world full of uncertainty,
combination weighting can performs well for it benefits from objective weighting and subjective
weighting.
Although combination weighting can approach excellent results, it should be carefully chosen for
they changes irregularly and can’t get a global rule for the weight of each attribute should be determined
according to the difference of each scheme under the features. Case-intelligent system ability depends
on its similarity computation, simulating the reasoning and learning of human ability, though the most
IMMAEE 2018
IOP Conf. Series: Materials Science and Engineering452 (2018) 042110 IOP Publishing
doi:10.1088/1757-899X/452/4/042110
6
optimal case isn’t chosen as the target sometimes, what they are mostly in candidate sets suggests us
that problem-solving process should interact with us to increase system ability. The conversational CBR
can be a good selection for the process of problem-solving especially in uncertain or incomplete
conditions, which may assistant us in real decision- making reliably.
4. Conclusion
Attributes Weighting has been attracted much greater concerns for decision-making full of uncertainty,
and how to effectively solve with such complicated or inconsistent constrains becomes a great challenge.
Synthesis-reasoning technology is proposed as a solution while the domain expertise is rich with rule
knowledge deficient to construct a flexible system. Combination weighting based on similarity Rough
Sets can be efficiently integrated in our case- intelligent system as machine learning components, and
acquires attributes preferences from the former stored cases to reduce unnecessary features and
redundant information. The experiments indicate that combination weighting is a powerful method to
conquer the scale and uncertainty of real problem, greatly decrease the complexity of our intelligent
system and time consumption for they having the consistent similarity measurement.
Acknowledgments
This research is financially supported by the China Postdoctoral Fund of HFUT, and the Natural Science
Project of Jiangsu Province YJ2017012. All the persons involved in the research projects are thanked
for their help.
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