Software and algorithms with
indistinct logic
Atanov S.K., the senior lecturer of
chair computer systems
The Kazakh agrotechnical university
of S.Sejfullina
The resume
In
article the review of the software products using the indistinct logic is made.
Also algorithms of decision-making of existing packages with indistinct logic
are investigated, the analysis and a scope program by a product, their
advantages and lacks is carried out. At the moment there is no one conventional
method of training of indistinct models, therefore an actual problem is working
out and search of new, effective methods. Thus, probably, the most perspective
direction of researches lays in use of genetic algorithms for training of
indistinct models.
Now the world is actively formed the
market of commercial software products for work with indistinct logic. On it
it is presented more than 100 packages of applied programs which to some extent
use the indistinct logic. Leaders in the given area are some companies-software
developers. Their tool means are focused on application of indistinct logic
in a maximum quantity of areas and appendices. It is package CubiCalc of firm Hyper
Logic, FuzzyTECH (Inform Software), FIDE (Ap-tronix), expansion packages to MatLab:
Fuzzy Logic Toolbox (it is delivered with MatLab) and FlexTool for MATLAB
companies Cynap Sys, and also package JFS ( developer Jan Mortensen) and
others [1, 2, 3].
The full-function user interface,
the developed means of import/export of data have the majority of the listed
software packages. To classify packages of indistinct logic by their
possibilities it is possible on following groups.
1.
The
software for generation of a code for the microcontrollers working on
indistinct algorithms. As a rule, the code is generated in language C or
assembler language.
2.
The
packages, allowing to build expert systems on the basis of indistinct logic. In other words, indistinct rules and
accessory functions are set by experts of a subject domain. In all
packages possibility of a choice of a kind
of functions of an accessory (triangular, a trapeze, Gauss, etc.), the
mechanism of an indistinct conclusion (Madmani, Zukamoto, Sugeno,
Larsen), a way of a composition and reduction
to clearness is given to the researcher. Work with packages is facilitated by graphic display of schemes of
indistinct models, surfaces of the response and other dependences [3].
3.
The packages, allowing to build approximating
dependences and systems of
classification on the basis of adaptive models of an indistinct conclusion.
Tool means FuzzyTECH concern the
first group and FIDE. At modelling of
difficult systems the basic interest is represented by software
packages from two last groups.
To create expert indistinct systems
give possibility the majority from listed above applied ON. Cost of some of
programs can reach several thousand dollars in standard delivery. And only in
few of them possibility of adaptive adjustment of structure and parametres of
indistinct model is provided.
As those programs focused only for
work with adaptive indistinct systems, during the spent analysis it has not
been found. Among the considered packages the greatest universality possess FuzzyTECH
and expansion Fuzzy Logic Toolbox for MatLab. We will stop only on the
characteristic of possibilities of adaptive adjustment of the indistinct
knowledge base in these packages.
In FuzzyTECH some methods of structural
adaptation of indistinct model, or methods of generation of indistinct rules
"If" [2] are realised. One of them consists that the full base of
indistinct rules in the beginning is formed and to each of them the
importance factor, at first the casual is attributed. One of four methods of
training further gets out (RealMethod, Ran-domMethod, Batch_Learn, Batch_Random)
in which course importance factors are specified. At the importance factor,
close to zero, the rule is offered to be removed, but the definitive choice
nevertheless remains for the researcher. It is necessary to notice, that the
requirement of coincidence to rules of factors of importance contradicts
ideology of indistinct systems in which it is supposed, that all rules are
identical on weight. Such approach is closer to hybrid nejro-indistinct systems
in which the role of factors of importance of indistinct rules is played by
weight factors neirons.
The second method accessible in FuzzyTECH, uses
genetic algorithm for optimisation of number of terms for each variable
system [3], typical forms of functions of
an accessory and symmetric indistinct splitting are thus used. A lack of
the given method is the big dimension of a problem, after an exhibitor
increasing at increase in number of variables of system. Besides, the problem
of optimisation of number of terms is less important, than a problem of generation
of a set of rules from experimental data.
Package Fuzzy Logic Toolbox for MatLab
possesses more ample opportunities in comparison with FuzzyTECH for
approximation of nonlinear dependences by adaptive indistinct models [4].
Important plus is that fact, that mathematical MatLab environment is popular in
the CIS and there is enough of the documentation and information sources on
its application. The basic functions and algorithms in expansion Fuzzy Logic Toolbox
are realised for the conclusion mechanism on Sugeno (TSK). Possibility of
work both with descriptive, and with rules in the form of TSK is given.
Training of indistinct model is spent to two stages. At the first stage
generation of rules and a finding of borders of terms is spent on the basis of
a method active êëàñòåðîâ.
At the second stage technology AN-FIS (Adaptive Network-based Fuzzy Inference System)
- iterative procedure for adjustment of functions of an accessory by a method
of return distribution of an error is used. Training of models Madmani in the
given package is not provided, work with àïïðîêñèìàòèâíûìè rules in the form of Madmani is not
supported also. With application of additional package Optimization Toolbox it
is possible to spend adaptive adjustment of functions of an accessory on
Madmani, but indistinct rules are necessary for setting independently.
Possibility of application of evolutionary calculations and genetic
algorithms in methods of adjustment of adaptive indistinct models in Fuzzy Logic
Toolbox also is absent. This possibility is accessible in other package of
expansion for MatLab - package FlexTool of company CynapSys. It is unique of
widely known commercial packages in which there is a possibility of full
genetic adjustment of all parts of indistinct model. On a choice it is offered
to the researcher three types of functions of an accessory (triangular, a
trapeze and ãàóññà), 10
ways of indistinct implication (after Back,
Madmani, Lukazevich, the Maple-dienesu, etc.) 19 ways of superposition
of indistinct sets (including such rare, as Dubo, Dombi, Jagera, etc.), 8
methods äåôàçèôèêàöèè
and two mechanisms of a conclusion - Mums-tributes and Ñóãåíî. Such variety of indistinct models
for an adaptive indistinct conclusion more than sufficient as in practice
use, as a rule, implication in the form of
a minimum and superposition by maximum or product operation. The
adaptive indistinct model is capable to be adjusted under a concrete way äåôàçèôèêàöèè, therefore as criterion of a choice of this or that
way its least computing
complexity should serve. For model training on experimental data there is a
possibility of a choice from three types of genetic algorithm - standard
HECTARE, Micro-hectares (Micro-GA) and steady HECTARE (Steady State GA). Last two
represent updatings of standard HECTARE and are in detail described, for
example in [4].
It is necessary to carry to lacks of package FlexTool:
1.
The
high price to which it is necessary to add MATLAB environment price and then full cost of a package will make from
2,5 to 4,5 thousand dollars depending on a delivery variant.
2.
Absence of the documentation in Russian to package FlexTool.
3.
The
methods used in package FlexTool for training of indistinct model by genetic
algorithm, are undescribed in the system directory.
The spent review of known software packages for
indistinct modelling
has shown, that the majority of them are focused on construction of
indistinct expert systems when parametres of functions of an accessory and a
rule are set by the expert, just in one package genetic algorithms for
formation of indistinct model are used. Methods of construction (training) of
adaptive indistinct models are more difficult and labour-consuming, than
methods of other intellectual models. The basic difficulties are connected with
generation of base of indistinct rules and updating of the form of functions of
an accessory. At the moment there is no one conventional method of training of
indistinct models, therefore an actual problem is working out and search of
new, effective methods. Thus, probably, the most perspective direction of
researches lays in use of genetic algorithms for training of indistinct models.
The literature
1. <http://www.mathworks.com>
2. John E. Dickerson and Julie A.
Dickerson "Fuzzy Network Profiling for Intrusion Detection", Iowa
State University. September, 2001
3. Zamboni D, "An Architecture
for Intrusion Detection using Autonomous Agents," COAST Technical Report
98/05, COAST Laboratory. Purdue University. June 11, 1998
4. Malyshev N.G., Bershtein L.S.,
Bogenuk A.V. Indistinct models for expert systems in SAPR. Ì:
Energoatomizdat, 1991.