=Paper=
{{Paper
|id=Vol-2571/CSP2019_paper_11
|storemode=property
|title=A Fuzzy Set Tool in the Classification and Prediction Software System (CLAPSS) (short paper)
|pdfUrl=https://ceur-ws.org/Vol-2571/CSP2019_paper_11.pdf
|volume=Vol-2571
|authors=Krzysztof Pancerz,Jaromir Sarzyński
|dblpUrl=https://dblp.org/rec/conf/csp/PancerzS19
}}
==A Fuzzy Set Tool in the Classification and Prediction Software System (CLAPSS) (short paper)==
https://ceur-ws.org/Vol-2571/CSP2019_paper_11.pdf
A Fuzzy Set Tool in the Classification and
Prediction Software System (CLAPSS)
Extended Abstract?
Krzysztof Pancerz and Jaromir Sarzyński
Department of Computer Science, Faculty of Mathematics and Natural Sciences
University of Rzeszów
Prof. S. Pigonia Str. 1, 35-310 Rzeszów, Poland
kpancerz@ur.edu.pl
Abstract. In the paper, we give the outline of a fuzzy set tool imple-
mented in the Classification and Prediction Software System (CLAPSS).
CLAPSS is being developed for solving different classification and predic-
tion problems using, among others, some specialized approaches based
mainly on fuzzy sets and rough sets which are not available in other
machine learning software systems. Theoretical background as well as
the module embedded in CLPASS, for fuzzification of attribute values in
information/decision systems, are described. Moreover, possible further
steps in the usage of CLAPSS (generation of fuzzy decision trees as well
as fuzzy flow graphs) are mentioned.
Key words: Fuzzy sets, Fuzzification, Software system, CLAPSS.
1 Theorethical Background
Most of the methods implemented in the CLAPSS system are applied for infor-
mation/decision tables representing information/decision systems understood as
Pawlak’s knowledge representation systems (cf. [12]).
A decision system is a tuple DS = (U, C, D, {Va }a∈C∪D , finf , fdec ), where U
is the non-empty, finite set of objects, C is the non-empty, finite set of condition
attributes, D is the non-empty, finite set of decision attributes, {Va }a∈C∪D is
the family of
S non-empty sets of condition and decision attribute values, finf :
C×U → Vc is the information function such that finf (c, u) ∈ Vc for each
c∈C S
c ∈ C and u ∈ U , fdec : D × U → Vd is the decision function such that
d∈D
fdec (d, u) ∈ Vd for each d ∈ D and u ∈ U . An information system is a specific case
of a decision system. In this case D = ∅ and the decision function is not defined.
Further, only information systems, in the form IS = (U, A, {Va }a∈A , finf ), will
be considered.
?
Copyright c 2019 for this paper by its authors. Use permitted under Creative
Commons License Attribution 4.0 International (CC BY 4.0).
Fuzzification is the process that transforms the real value variables into lin-
guistic variables whose domains contain linguistic values which can be described
by fuzzy sets (their membership functions). Let IS = (U, A, {Va }a∈A , finf ) be
an information system such that Va ⊆ R for each a ∈ A. For each attribute
a ∈ A, we can define a linguistic variable λa . With each linguistic variable λa ,
a set Lλa = {l1λa , l2λa , . . . , lkλaa } of linguistic values is associated. Each linguis-
tic value liλa , where i = 1, 2, . . . , ka , is described by a membership function
µlλa : R → [0, 1]. In CLAPSS, the user has a broad set of membership functions
i
which can be used to make a fuzzification process. This set consists of:
– a triangular shaped membership function,
– a trapezoidal shaped membership function,
– a Gaussian shaped membership function,
– a generalized bell shaped membership function,
– an S shaped membership function,
– a π shaped membership function,
– a sigmoidal shaped membership function,
– a fuzzy singleton membership function,
– a sinusoidal shaped membership function,
– a Z shaped membership function,
– a pseudo-exponential shaped membership function,
– an L-R shaped membership function,
– a two Gaussian shaped membership function,
– a D-sigmoidal shaped membership function,
– a P-sigmoidal shaped membership function.
Let:
– IS = (U, A, {Va }a∈A , finf ) be an information system, where card(U ) = n
and card(A) = m, such that Va ⊆ R for each a ∈ A,
– {Lλa }a∈A be the family of sets of linguistic values associated with linguistic
variables from the family {λa }a∈A defined for attributes from A, where Lλa =
{l1λa , l2λa , . . . , lkλaa } for each a ∈ A.
A fuzzified information system is a tuple F(IS) = (U F , Φ, {Vφ }φ∈Φ , finf
F
), where
F ∗ F
U is the non-empty, finite set of objects such that each u ∈ U corresponds
exactly to one u ∈ U , Φ = Φa1 ∪ Φa2 ∪ · · · ∪ Φam is the non-empty, finite set of
S {Vφ }φ∈Φ is the family of sets of fuzzifiedF attribute ∗values,
fuzzified attributes,
F
finf : Φ×U F → Vφ is the information function such that finf (φ λaj , u ) ∈ Vφ
φ∈Φ li
∗ F F
for each φ λaj ∈ Φ and u ∈ U , finf (φ λaj , u∗ ) = µ λaj (finf (aj , u)), where µ λaj
li l
i l
i l
i
λa
is a membership function describing li j .
2 CLAPSS
CLAPSS is our tool developed for solving different classification and prediction
problems using, among others, some specialized approaches based mainly on
fuzzy sets and rough sets. CLAPSS is equipped with the graphical user interface
(see Figure 1). In general, our main idea is to implement in CLAPSS those
specialized approaches which are not available in other machine learning software
systems. Selected functionalities of CLAPSS were earlier described in [7], [8], and
Fig. 1. CLAPSS (the graphical user interface).
[11].
The general usage of methods, based on fuzzy sets, implemented in CLAPSS
is shown in Figure 2. Information/decision systems (also those fuzzified) can be
imported from/exported to other machine learning software systems, RSES [1],
WEKA [4], ORANGE [2], as it was depicted in Figure 2.
For methods based on fuzzy sets, CLAPSS offers, first of all, a tool for fuzzi-
fication of attribute values in information/decision systems. The fuzzification
process can be done in three ways: graphical, scripting, and external.
For graphical fuzzification, Membership Function Creator (MFC) has been
developed (see Figure 3). MFC enables the user to:
– determine linguistic values and membership functions (their shapes and pa-
rameters) associated with them,
– manually modify membership functions created earlier (for example, char-
acteristic points or slopes can be moved),
– see calculated values of the fuzzified attribute (these values are automatically
updated if some changes in membership functions are made).
After the fuzzification process of the selected attribute, a script (a special
scripting language was designed for CLAPSS) is generated. The script, consisting
of membership function definitions for each attribute to be fuzzified, can also be
created manually, i.e., in a scripting way (see an example below).
ATTR[0]->fuzzification(lingvalues={low=(trapezoidal,0.0000,0.0000,1.0000,3.0000),
medium=(triangular,1.0000,2.5000,4.0000),high=(trapezoidal,2.0000,4.0000,5.0000,5.0000)});
Fig. 2. CLAPSS (a general scheme of the usage of the fuzzy set tool).
Fig. 3. CLAPSS (Membership Function Creator).
ATTR[1]->fuzzification(lingvalues={low=(trapezoidal,0.0000,0.0000,1.0000,3.0000),
medium=(triangular,1.0000,2.5000,4.0000),high=(trapezoidal,2.0000,4.0000,5.0000,5.0000)});
ATTR[2]->fuzzification(lingvalues={low=(trapezoidal,0.0000,0.0000,1.0000,3.0000),
medium=(triangular,1.0000,2.5000,4.0000),high=(trapezoidal,2.0000,4.0000,5.0000,5.0000)});
Fuzzification of attribute values in the external tool is also possible. Then,
the user can import a fuzzified information/decision system into CLAPSS.
Further steps which can be performed in CLAPSS for fuzzified informa-
tion/decision systems can be as follows:
– Generation of fuzzy decision trees. Fuzzy decision trees are generated using
the algorithm based on cumulative information estimations of initial data
[5].
– Generation of fuzzy flow graphs [11]. Fuzzy flow graphs are generated using
the fuzzy cardinality (power) of linguistic values (cf. [6]).
The visualization of fuzzy decision trees and fuzzy flow graphs is possible due to
the option for exporting them to the DOT format [3].
The practical usage of CLAPSS was presented in case of analysis and clas-
sification of MMPI (Minnesota Multiphasic Personality Inventory) data. Fuzzi-
fied decision systems were used among others in determining the importance
of ranges of MMPI scales [10] and classification of MMPI profiles using fuzzy
decision trees [9].
3 Conclusions
In the paper, we have briefly presented an important part of the CLAPSS system
concerning implemented methods based on fuzzy sets. CLAPSS is constantly
being developed. One of the main directions in further developing of CLAPSS,
in the considered area, is to add other types of membership functions and to add
graph algorithms for fuzzy flow graphs to extract rules, episodes, etc.
Acknowledgments
This work was partially supported by the Center for Innovation and Transfer of
Natural Sciences and Engineering Knowledge at the University of Rzeszów.
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