SISOM 2013, Acoustics and Robotics, Bucharest 21-22 May
A NEW TRANSDISCIPLINARY SCIENCE—EXTENICS
Cai WEN, Yang CHUNYAN
Research Institute of Extenics and Innovation Methods, Guangdong University of Technology, Guangzhou, Guangdong, 510006
China
People’s ideal is to solve contradictory problems with the aid of computer. In order to realize the goal,
we must study rules and methods of dealing with contradictory problems. Over 30 years’ development,
we have preliminarily established the new discipline Extenics and regarded it as the basis for
intelligentized processing of contradictory problems. This paper briefly introduces the fundamental
theories and methods of Extenics and its application.
Key words: Extenics; contradictory problem; intelligentized processing.
People’s ideal is to solve contradictory problems with the aid of computer. In order to realize the goal, we
must study rules and methods of dealing with contradictory problems. In 1983, No.1 of China’s Journal of
Scientific Exploration published the paper of “Extension Set and Incompatible Problems” [1]. Later on, with
the participation of a great number of Extenics researchers, over thirty years’ development, we have
preliminarily established the theoretical system--extension theory, studied unique method system--extension
innovation method and conducted the application of extension theory and extension method in different
fields--extension engineering. Extension theory, extension innovation method and extension engineering
form the new discipline--Extenics[2].
Extenics is a science which studies the possibility of extending things, rules and methods of developing
innovation with formalized patterns, and is used to resolve contradictory problems. Its research objects are
contradictory problems in the real world. Contradictory problems are goals that can’t be realized under
current conditions. The ultimate goal of Extenics study is to help mankind to deal with contradictory
problems with the aid of computers and network.
The logic cells of Extenics are basic elements including matter-element, affair-element and relation element.
Basic elements are used to express all things, all matters, different relations, problems and the process of
solving contradictory problems.
1.
EXTENDED SCIENTIFIC THEORIES BASED ON EXTENICS
Over 30 years’ study, extension theory has formed a preliminary system (Fig. 1) and extended existing
scientific theories in five aspects:
1.1 Extended the Research Scope of Mathematics
The research objects of Extenics are contradictory problems, which is the extension of non-contradictory
Cai WEN, Yang CHUNYAN
2
problems study in mathematics. In order to solve contradictory problems, Extenics extends “the study of
quantitative relation and space form” in mathematics to the study of “three-tuples--basic elements including
objects, characteristic and measure, and study on matters, affairs and relations in a formalized way”. The
establishment of the basic element concept extends mathematics models into extension models which study
both quality and quantity; with it, formalized language can be used to express contradictory problems and its
solution process. The formalized system of extension information, knowledge and strategy based on
basic-element theory provides operable tools of solving contradictory problems with computer and network.
⎧
⎧
⎧ Divergence analysis theory
⎪
⎪
⎪
⎪
⎪ Extensible analysis theory⎪⎨ Correlative analysis theory
⎪
⎪
⎪ Implication analysis theory
⎪
⎪
⎪⎩ Opening-up analysis theory
⎪
⎪
⎪
⎪
⎧ Nonmaterial and material conjugate analysis
⎪
⎪
⎪Soft and hard conjugate analysis
⎪
⎪
⎪
⎪ Basic-element theory ⎨ Conjugate analysis theory ⎨
⎪
⎪
⎪ Latent and apparent conjugate analysis
⎪
⎪
⎪⎩ Negative and positive conjugate analysis
⎪
⎪
⎪
⎧ Basic exte nsion transformations
⎪
⎪
⎪
⎪
⎪
⎪ Extension tranformation theory ⎪⎨ Conductive transformations and conjugate transformations
⎪
⎪
⎪ Calculation of extension transformations
⎪
⎪
⎪⎩ Nature of extension transformations
⎩
⎪
Extension theory ⎨
⎧
⎧ Basic-element extension set
⎪
⎪
⎪
⎪
tension
set
Ex
⎨ Compound element extension set
⎪
⎪
⎪
⎪ Extension field and stable field
⎪ Extension set theory ⎨
⎩
⎪
⎪
⎪
⎪ Depedent function ⎧⎨ Definition of dependent function and calculation formula
⎪
⎪⎩
⎩ Types of dependent fun ction and its transformations
⎪
⎪
⎪
⎧ Extension models
⎪
⎪
⎪
⎧ Basic-element extension reasoning
⎪
⎪
⎪
⎪
Extension
reasoning
⎨ Conductive reasoning
⎪ Extension logic ⎪
⎨
⎪ Conjugate reasoning
⎪
⎩
⎪
⎪
⎪ Basic-element expression and extension of propositions and reasoning sentences
⎪
⎪
⎪
⎪⎩ Reasoning of solving contradictory problems
⎩
Fig. 1 Extension Theory System
1.2 Extended System Theory
Extenics extends “the study on matters’ structure based on components and relation” in system theory into
“study on matters’ structure from four perspectives of materiality, systematicness, dynamics and
oppositeness” in conjugate analysis so as to describe structure more comprehensively. In this way, we study
the composition of matters and their mutual transformation, and form conjugate analysis theory and methods.
Conjugate analysis, based on holism and reductionism, provides a new perspective for people to fully
analyze matters’ structure and another source for people to generate strategies of solving contradictory
problems.
1.3 Extended Set Theory
Extension set extends Cantor set and fuzzy set studying static classification into extension set studying the
classification under transformation.
In 1874, Cantor proposed set theory as the basis for mathematics with a history of thousands of years. In
1965, American Zadeh put forward fuzzy set, described fuzzy matters and served as the basis for fuzzy
3
A new transdisciplinary science—Extenics
mathematics. Cantor set was the categorization of certain matters. The nature of matters expressed by Cantor
set and fuzzy set is fixed. We must consider the change in the nature of matters while solving contradictory
problems. Relevant matters need to be assigned with certain nature; problems need to be transferred into
reconcilable ones from contradictory ones. Cantor set and fuzzy set don’t describe the transformation of
matters’ nature under certain conditions so they can’t be the set theory basis for solving contradictory
problems. This leads to the study on the set theory which conducts convertible classification of matters.
The concept of extension set is put forward in the reference [1]. With over twenty years’ development,
extension set has been gradually improved and introduced conversion into set theory. Hence, it’s able to
describe classification under transformation and study changes of classification. The basic-element extension
set with basic elements as elements combines quality and quantity, studies how can convert basic elements
transform contradictory problems into reconcilable ones, and describe qualitative change and quantitative
change of matters with qualitative change field and quantitative change field, thus providing solid set theory
basis for transforming contradictory problems into reconcilable problems. The establishment of extension set
also lays a foundation for extension data mining which mines the knowledge under transformation.
1.4 Extended Function Theory
In order to quantify the calculation of changes in the nature of matters, Extenics studies dependent function
and quantitative formula and expresses the degree of a matter’s nature with dependent function value. The
formula of dependent function allows people to calculate objectively according to professional knowledge
and historical data, and break away from excessive intervention of subjective factors.
We introduce the concept of “extension distance” in dependent function, accordingly, extend the concept of
“distance” in the function of real variable in mathematics and stipulate that the distance between a point in
the interval and the interval is not zero in the function of real variable but a negative number. Different
locations in the interval lead to different value numbers. In this way, real number can be used to express
“differences in the category”. Therefore, the qualitative description of “same in the category” in Cantor set is
developed into quantitative description of “differences in the category”.
1.5 The Establishment of Extension Logic Combines Formal Logic and Dialectical Logic
In mathematical logic, 0 and 1 are used to qualitatively describe true or false statements and right or wrong
reasoning. However, in real world, true or false statements and right or wrong reasoning have different
degrees. Usually we must quantitatively study the degree of being false or true and right or wrong as well as
their changes. Dependent function in extension set can be used as a quantitative tool of describing the degree.
On the other hand, in real world, the true or false statements are based on conditions. When the conditions
change, the degree of truth or falseness also changes. Likewise, the right or wrong reasoning is also based on
conditions. When the condition changes, wrong statement may become right ones while wrong reasoning
may become right one; vice versa. Therefore, we should not only study true or false nature of statements and
right or wrong nature of reasoning but also study under what transformation the false can be true and the
wrong can be right so as to establish feasible reasoning tools for solving contradictory problems.
Extension logic is the basis for the computer implementation of Extenics theories and methods. The formal
logic doesn’t take into consideration the connotation and extension of statements and reasoning. However,
connotation, extension and changes of matters must be considered while solving contradictory problems. The
Cai WEN, Yang CHUNYAN
4
dialectical logic describing them is expressed by natural language. To make it operable on computer, we must
use formalized language. Hence, Extenics integrates the formalized advantage of formal logic and the feature
of studying matters’ connotation, extension and changes by dialectical logic, combines the form of formal
logic and the description of matters’ connotation, extension and change by dialectical logic, and studies
extension logic centering on extension statement, extension reasoning and extension transformation which
are regarded as the logic tools for solving contradictory problems.
2.
EXTENSION INNOVATION METHOD SYSTEM
Extenics proposes a new methodology which studies the rules of methods of solving contradictory problems.
The method system based on this is called extension innovation method which provides operable tools for
solving contradictory problems and also method system for conducting intelligentized processing of
contradictory problems with computer and network. Over thirty years’ study, a relatively complete system
has been formed (Fig 2).
⎧
⎧ Divergence analysis method
⎪ Extensible analysis methods ⎪⎨ Correlative analysis method
Implication analysis method
⎪
⎪⎩ Opening-up analysis method
⎪
⎪
⎧ Nonmaterial and material conjugate analysis method
⎪ Conjugate analysis methods ⎪⎨ Soft and hard conjugate analysis method
Latent and apparen conjugate analysis method
⎪
⎪⎩ Negative and positive conjugate analysis methods
⎪
⎪
⎧ Basic transformation method ⎫ ⎧ Universe of discourse transformation method
⎪ Extension transformation methods ⎨ Conductive transformation method ⎬ ⎨ Dependent criteria transformation method
Extension innovation methods ⎨
⎩ Conjugate transformation method ⎭ ⎩ Element transformation method
⎪
⎧ Extension classification method
⎪
⎪ Extension clustering method
⎪ Extension set methods ⎨ Extension identification method
⎪
⎪⎩ ......
⎪ Superiority evaluation methods
⎪
⎧ Rhom bus thinking mode
⎪
⎪
⎪ Extension thinking modes ⎨ Rerversed thinking mode
Conjugate thinking mode
⎪
⎪
⎩
⎩ Conductive thinking mode
Fig. 2. Extension Innovation Method System
Extension innovation method stylizes the process of solving contradictory problems by mankind, analyzes,
extends, converts and evaluates contradictory problems, and finally generates better strategies of solving
contradictory problems. It provides operable methods for people to complete the process of “discover
problems→establish models of problems→analyze problems→generate strategies for solving problems”
with formalized models.
A new transdisciplinary science—Extenics
5
3. APPLICATION OF EXTENSION THEORY AND EXTENSION INNOVATION
METHOD--EXTENSION ENGINEERING
The value of Extenics is not only to provide programmed methods and technology for different industries to
solve contradictory problems but also offer new thinking and theoretical basis for people to deal with
problems.
The combination of fundamental theories and methods in Extenics with knowledge in different fields extends
the theory and methods of the fields and also generates the extension engineering method that solves
contradictory problems in the fields. Some main application fields will be briefly introduced as follows:
3.1 Application in Information Field
Extenics studies the application of extension model in the information field. At present, most of studies focus
on extension strategy generation system and extension data mining methods.
3.2 Application in Engineering Field
Plenty of contradictory problems exist in the control and detection field such as the oppositeness between
precision, stability and speed in the control field, the contradiction of detectors’ inability of detecting some
parameters in the detection field and the contradiction of the detector’s requirement and detection
environment, etc. The problems of being unable to control and detect affect the level of automation.
Extension control and extension detection provide methods to solve these contradictory problems. At present,
extension control theory and method, extension detection theory and method, and extension robot are major
branches; in future, it will be gradually extended to other fields of the engineering science.
3.3 Application in Design Field
Extension design is a kind of design theory and method which studies the solution for contradictory
problems in the design process based on extension theory and extension methods. At present, extension
design method is frequently applied in the mechanics field and building field.
Extension method treats the process of designing new products as the process of solving contradictory
problems. It is a topic of great value to design new product with the aid of computer and network.
Further development of Extenics inevitably leads to the study on computer-aided innovative thinking. The
study will be the integration of thinking science, computer science and extension theory. Established theory
and methods will promote the development of intelligent machines which imitate human brain to conduct
innovative thinking and extend human brain.
3.4 Application in Management Field
To solve contradictory problems, management extension engineering reviews the process of management
and establishes a new set of management engineering theory and methods including extension
decision-making, extension planning, extension marketing and other theories and methods which are
generally called management extension engineering. The maturity of management extension engineering
theory and methods will strengthen the integration of extension theory with management science.
Cai WEN, Yang CHUNYAN
6
4. FUTURE DEVELOPMENT OF EXTENICS
The scientific goal of Extenics study is to form a relatively complete theoretical system by exploring the
rules of solving contradictory problems with formalized models, study the basic theory and methods of
solving contradictory problems through computer as well as reasoning technology that can be operated on
computer, research corresponding intelligent systems to solve contradictory problems in numerous fields and
finally develop Extenics into a relatively mature science with multiple branches.
Acknowledgments: This paper is sponsored by National Natural Science Foundation project (70671031,
61273306).
REFERENCES
1. WEN, Cai, Extension set and non-compatible problems [J]. Journal of Scientific Exploration,1983,（1）3:83-97
2. CHUNYAN , Yang, WEN, Cai, Extenics:Theory, Method and Application [M].Beijing: Published by Science Press, 2013.