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SISOM 2013, Annual Symposium of the Institute of Solid Mechanicsand Session of the Commission of Acoustics, Bucharest 21-22 May204Victor VLADAREANU, Ovidiu Ilie SANDRU, Paul SCHIOPU, Vlad Grigore LASCU203A New Trans-Disciplinary Science Extenics

A NEW TRANSDISCIPLINARY SCIENCE EXTENICSVictor VLADAREANU1, Radu Ioan MUNTEANU2, Ovidiu Ilie SANDRU1, Paul SCHIOPU1 and Vlad Grigore LASCU31 University Politehnica of Bucharest, ROMANIA2Technical University of Cluj-Napoca, ROMANIA3Institute of Solid Mechanics of the Romanian Academy, ROMANIA

This paper endeavours to present a general outlook on the new scientific discipline of Extenics, its main concepts and mathematical apparatus, as well as the main tools it introduces with regard to general or specific fields. The paper investigates the main applications to date and suggests opportunities for further research or inter-disciplinary collaboration as appropriate throughout the paper.Key Words: Extenics Theory, Artificial Intelligence, Basic-Element, Dependent Function, Extenics Control.1. INTRODUCTIONExtenics is a science whose stated aim is to deal with unsolvable problems. With applications in artificial intelligence, business, marketing, planning, design, control theory and image processing, to name just a few, it is one of the fastest developing new fields of study today. In his 1983 paper, Extension Set and Non Compatible Problems, Cai Wen put down some of the earlier concepts and established the foundation of what would later become Extenics Theory, a wide spanning inter-disciplinary science [1](the reference is the 1990 translation). Early papers were few and far between, before the framework of Extenics was established and it became recognized as a field of scientific research in its own right. A further milestone is the 1988 paper by the same Prof. Cai, Rule of Processing the Problem of Contradictory Conflict in Decision Systems[2], which brings important updates both in the formal expressions and the tools used in Extenics. Thus was developed a formalism which would facilitate working within the latest trends of technical processing and whose improvement is still on-going as an important direction in Extenics. One of the first papers to discuss an involved engineering application was published in 1994 by Prof. Wang and entitled Extenics control [3]. It provides a blueprint for the first Extenics controller, which has subsequently undergone numerous modifications and opens up the field of Extenics control proper (this is discussed further in Chapter 4). Since the beginning of the new millennium, an expanded research group combined with the years of existing built-up expertise to produce new directions of research in the field. Papers such as [4][5][6] outline the beginning of their respective specialized work, making Extenics applications wide-spread in the academic and business world, especially in the Asian continent. In 2012 a monograph work entitled Extenics Engineering was published in English [2] (the previous Chinese version had come out in 2007), marking a very important step to promoting Extenics world-wide.Extenics is said to be a science combining Mathematics, Engineering and Philosophy [2]. With respect to its application and use it is a trans-disciplinary science, classified as belonging to the wider field of Artificial Intelligence. Extension Logic is purported by the authors to extend fuzzy logic, much in the same way that fuzzy logic extends the classical Cantor logic [1]. This is necessary for work with Extension Sets in contradictory problems and for Extension Strategy Generation Systems (ESGSs)[7].The main goal of Extenics, as set forth in almost every paper that deals with the issue, as well as throughout its theoretical mainframe, is the generation of solutions to contradictory problems [1]. This is of course very important in and of itself, however in Extenics the process by which this goal is to be achievedisalso of great scientific relevance. Contradictory problems, or seemingly impossible problems, have been solved throughout history by using human ingenuity. Extenics studies the creation of such innovative ideas and seeks to develop procedures for understanding and creating new, original thought with the help of modern day advances in computer science. It is partly for this reason that Extenics is classified as part of Artificial Intelligence and is one of the fastest developing new fields of study in the world today.Aside from Extension Sets and Logic, Extension Transformation is one of the core concepts in the theory [2]. It is said that the only constant in life is change, and Extenics emphasizes the need to adapt problem specifications to ever-evolving contexts. Transformation is at the basis of solutions to contradictory problems, both from a theoretical and a practical standpoint. Basic element representations are designed to support dynamic modelling (as a type of parametric modelling) and solution algorithms consist, for the most part, of iterations of transforms and compound transforms. The paper is organized as follows: the concepts of Extenics Theory will be further elaborated in Chapter 2. Chapter 3 illustrates the key theory of contradictory problems, their definition and classification, and their solution algorithms. Chapter 4 discusses the main application areas of Extenics and attempts to give the reader a short introduction into the state of the art of each. Chapter 5 assists the work done in the previous chapter by outlining a few of the most important works in recent Extenics Theory research and provides a more in-depth discussion for each paper. The final chapter shows the main conclusions relating to this field at the time of publication.2. CONCEPTS OF EXTENICS THEORYTo be able to manipulate the outcomes of situations which represent contradictory problems, we need to have in place a representation, as well as a set of tools and an environment model in which to do so. This Chapter will briefly explain the theoretical basis of Extenics and describe the general model of thought in an Extenics problem. The three pillars of Extenics Theory are Basic Element, Extension Set and Extension Logic.Extenics Theory maps all components of a given problem into elements, which provides the basis for a working model of the problem. These are called Basic Elements and consist of the triplet formed by an object, action or relation, a possibly infinite number of characteristics and their corresponding value relating to the object. In mathematical form, we call a basic element in Extenics Theory. The m means this particular triplet defines a matter-element (although all basic elements are similar from a construction standpoint) [2].As mentioned above, there are three types of Basic Elements (BEs): matter-element (ME), action-element (AE) and relation-element (RE). These can also be parametric or dynamic, as is required by the problem being modelled. It is worth noting that the values are not necessarily numerical: in another similarity to fuzzy logic, linguistic variables are also permitted. Practical examples for each of these possibilities are given below:(1) (2)(3)One or more basic elements can be combined to form compound elements (CEs) for brevity of expression in complex models, such as:(4)Each basic or compound element can be further expanded with one of four conjugate extensions: real imaginary, hard soft, apparent latent and positive negative.Elements are organized together with the help of Extension Sets. These provide a means of classification for the initial problem, as well as the outcomes. Extension Sets are further processed using any number of transformations to achieve a desired result and new norms are introduced for work on them, such as Extenics Distances. Working with Extension Sets and the different classes of transformations to solve contradictory problems is at the very core of practical Extenics Theory applications. Extension Sets are defined as follows [2]: let U be an universe of discourse, u is any one element in U, k is a mapping of U to the real field I and T=(TU,Tk,Tu) is a given transformation, we call (5)an extension set on the universe of discourse U, the dependent function and the extension function, wherein TU, Tkand Tu are the respective transformations of the universe of discourse U, the dependent function k and the element u. The Extension Set, then, is defined in relation to a transformation and an existing function mapped onto the universe of discourse. Following the transformation, the Extension Set is divided into the positive and negative fields with regard to the dependent function value. Four subsets are therefore defined: the positive stable, the positive transitive, the negative stable and the negative transitive field. The stable fields are those for which the polarity of the dependent function is unaltered by the transformation, whereas transitive (also named extensible) fields are those affected by the change. This provides a useful classification and investigation tool for contradictory problem models. Figure 1 illustrates the four fields of the Extension Set.

Figure 1. Extension Set FieldsExtenics Distance extends the classical mathematic distance between a point and an interval to include a non-zero value for points inside the interval itself. In normal mathematics, the distance from a point inside and interval to that interval is always null, whereas in Extenics a point inside an interval is considered to have a negative distance to the interval. Extenics distance is defined as for x a point on the real axis and an open or closed interval. From the mathematical expression, it can be seen that the norm expresses in fact the distance from any point in the space to the nearest limit of the interval. The value at the interval limits is , while the global minim of the Extenics distance is at the centre of the interval, where its value is . This norm will further allow us to work with nested interval in designing function mappings across interval [1]. The most important of these, from the point of view of Extenics, is the Dependent Function. The Dependent Function gives out a measure for the compatibility of a given incompatible problem once it has been translated into the Extenics model.The Dependent Function is measured with regard to a point and two nested intervals. To understand the Dependent Function, an intermediary metric is introduced, named the Place Value. This is defined as for a point x and two nested intervals and . The Elementary Dependent Function for nested intervals with no common endpoints is then [2].(6)Extenics Transformations provide the building blocks of contradictory problem solutions. As can be seen from the previous definitions, transformations are applied to Extension sets of potential solutions, and this is the main tool that Extenics Theory has at its disposal. There are five basic classes of recognized extension transformations: substitution, increasing / decreasing, expansion / contraction, decomposition and duplication. These (an others) can be combined, both simultaneously and iteratively, to form a virtually infinite number of compound transformations for incompatible problems. As a general rule, Extenics transformations are not unique in effect. The study of their conducive effect is a current topic of great interest among researchers in the field (see Chapter 4). There are also three types of Extenics transformations, based on the primary intended target: transformations of the basic-element, of the dependent criterion and of the universe of discourse. However, for the latter two, it must be kept in mind that their conducive effect is usually much more pronounced. The same is true for transformations used in relation to the conjugate parts of elements. Extension Logic studies the rules and effects of compatible transformations of contradictory problems and is a combination of formal and dialectic logic. A brief comparison to the two classical logic systems is outlined in Figure 2. Extension logic has many of the same advantages as fuzzy logic (i.e. the ability to define custom norms and co-norms for a particular problem or element set, etc.) and extends the range of application to the entire real numbers space. There is particular promise shown in research done using working models of fuzzy logic that it can be extended to use with Extenics systems. Also, considerable work has been done using Extenics and Dezert-Smarandache Theory, which has its own close analogies to fuzzy theory [2][8][9].

Figure 2. Comparison between Cantor, Fuzzy and Extension LogicIt should be noted that the logical value of various characteristics can change with each transformation. The study objective of the Extenics concepts and mathematical apparatus is to provide a formal expression for quantitative and qualitative change.As will be seen in the next chapter, it is sometimes helpful if the problem statement can be reformulated to a substitutable hypothesis with the use of Extenics tools and formalism. The expanded model taken into consideration also enables a description of object connotation through the four conjugate extensions. This also allows Extenics to create a logic system that is able to describe ambivalent states, which proves vital in understanding and solving contradictory problems [2].

3. CONTRADICTORY PROBLEMSAs relates to the formalism of contradictory problems, these are defined as a double of two sets: the goal or goals of the problem and the conditions under which they are to be achieved. This is noted as or . Starting from this definition, we can differentiate between two distinct types of contradictory problems: incompatible problems and antithetic problems.Incompatible problems are defined by having a single goal or a non-conflictual set of goals which contradict the particular conditions of the problem. In the case of multiple goals, it is of course sufficient for one goal to be incompatible with the conditions to make it an incompatible problem. This is noted as .

Figure 3. Extension Strategy Generation AlgorithmWhereas incompatible problems have coherent goals, which are not accomplishable, antithetic problems are defined by having a conflictual set of goals under current conditions. An antithetic problem is noted as . Each goal in itself may or may not be incompatible with the conditions. If one of them is, the problem is reduced to multiple incompatible problems instead. Obviously, no single-goal problem can be an antithetic problem. This is an important distinction to make because the two types of problems are solved slightly differently in Extenics [2]. Generally speaking, there are three ways in which to solve an incompatible problem: (1) transformations of conditions, keeping the same goal; (2) transformation of one or more goals, with the same conditions; (3) solve the contradictory problem with both goals and conditions changed. Figure 3 shows the general algorithm for extension strategy generation [2][7][10].4. APPLICATION AREASThere are a number of noteworthy applications areas that have to do with both practical achievements in different fields, on the one hand, and with improving and growing the concepts of Extenics itself, on another. It is of course paramount for such a young scientific field that the framework itself is developing, at an almost equal rate to that of practical applications, and work is undertaken to perfect understanding of the science itself. This chapter will give a look at the various directions of study under the current state of the art in Extenics.While with most scientific fields today the main mathematical and practical apparatus is finalized to a great degree, this is not necessarily the case with Extenics. This is, in fact, one of the reasons for which Extenics is one of the most exciting current fields of study. Work is still being carried out on achieving formalization systems that can encompass greater and greater representations of the extended system of Information Knowledge - Strategy for any given problem [2]. This is seen as an intermediary step to the end goal of processing populations of potential solutions with the aid of a computer, which naturally requires a coherent, unitary and preferably somewhat simpler representation. A slightly different and more practice-oriented approach to involving the use of computers is the Extension Strategy Generation System [7]. Work in any of these directions directly benefits both approaches. This led to the actual implementation of data warehouse-type applications into various recommender systems. This may or may not be, of course, coupled with other techniques for recommender systems which are already a mainstay of artificial intelligence implementations.Another field using data bases and Extenics is Extension Data Mining, which has seen quite a number of practical implementations [4][11]. Extension Data Mining comprises a number of methods for extended classification using data bases, extended clustering and conducive information. Extended clustering is of great use in applications which require the manipulation of a great number of elements and also provides insight into the most likely successful transformations. Data mining for conducive information refers to investigating the conducive effect of transformations or combinations of transformations on the population of solutions. This is also attempted with various other methods native to the field of Artificial Intelligence (such as Neural Networks), as formalizing the standard effect of transformations would represent an important breakthrough in computer implementations of Extenics algorithms.Extension Marketing is one of the most straightforward applications of the current Extenics formalism. Populations of solutions consisting of basic and compound elements are used for product and business innovation and contradictory problem algorithms for market and resource extension. Especially helpful in this field are the evaluation algorithms used for extended solutions [12].Extension Planning is a somewhat related field which applies Extenics methods and algorithms for the requirements of the business world. On a theoretical level, it is mostly concerned with the theory and methods needed to reduce any problem to a known type of incompatible or antithetical problem [5]. With regards to practical operations, extended planning is used for resource integration, project management, crisis prevention and control and market development.Extension Design applies Extenics theory and methods to product and (most importantly) concept development [13][14]. Whereas Extension Marketing is mainly used from the viewpoint of product marketability, Extension Design usually relates to a radical revision of a given concept, encompassing anything from complex engineering applications to fast-moving consumer goods. The main difference, as opposed to regular design concepts, is in the quantitative and qualitative formulations of the process. There is an increasing trend in Extension Design towards using bionic models, thereby finding inspiration and confirmation in nature. Extension Control applies Extenics concepts, norms and algorithms to the study of control theory. While classical control study deals with improving well-known indicators such as stability, rise time, overshoot, etc., most applications are geared towards improving controller quality by extending the range of the controller [3][15]. This is effect means increasing the possible universe of control. A number of papers have dealt with the topic and there exist working models for practical controllers using Extenics: the upper extended controller and an improved version, the basic extended controller. Newer research, however, is considering Extenics controllers for improving control action in the classical sense, as well as using fuzzy Extenics applications in complex robot control [16].Extension Detection is based on dividing all elements within the environment into detectable and undetectable, thereby introducing a new characteristic into every element. It then uses correlations from detectable basic and compound elements to measure the characteristics of undetectable elements. The novel approach has inspired a number of papers on the subject [17].5. PAPERS OF INTERESTWhile an attempt was made to provide all possible suitable references for the directions of study discussed, some papers merit further consideration on their own for being representative of the current development of Extenics and of particular of interest to applying Extenics to a wide range of engineering problems. It must be noted that there are a number of interesting papers on the subject that are unfortunately as yet to be translated into English and, from that standpoint, do not enjoy widespread circulation in international academic circles. These were omitted from consideration for the purposes of this paper.At the top of the list for any works on Extenics Theory should be, due to considerations both of completeness and of recent publication, the monograph Extension Engineering by Profs. Cai and Yang [2]. It is by far the most detailed work on the subject available and it has been translated into English since its publication, as part of an effort to further promote the science outside of Asia. It covers most theoretical and practical concepts of Extenics at the time of publication (2012) and provides useful references for those works which are not discussed in detail due to space constraints. If, historically, Prof. Cais1983 paper is the first landmark of Extenics, from an understanding standpoint, Extension Engineering would be it. It is a point of reference in publications on Extenics Theory and, barring any completely unforeseen breakthroughs, should stand as the foremost work on the subject for years to come.As mentioned in the chapter discussing Extenics concepts, there are a number of different norms that can be used to describe the relations of the various sets and basic elements. The situation is somewhat analogous to the norms and co-norms in fuzzy logic, with which Extenics has a number of similarities. It has surely not escaped notice, however, that all those discussed or alluded to in the initial chapter are one-dimensional. In keeping with the trend of expanding the mathematical apparatus of Extenics, as well as foreseeing the need for more complex norms in the future, Prof. Smarandache has, in his 2012 paper Generalizations of the Distance and Dependent Function in Extenics to 2D, 3D, and n-D[9], laid the basis for developing Extenics in higher dimensions [18]. The work also develops Extenics deeper from a theoretical standpoint using the authors proficiency in complex mathematics and, among others, elements of Dezert-Smarandache Theory [8]. Within another year, a second type of implementation for n-dimensional dependent functions was independently developed by Prof. Sandru for use in his 2013 paper Multidimensional Extenics Theory[19], which deals with the subject. Prof Sandru also generalized the Elementary Dependent Function, the most commonly used Extenics function, to allow for a unified formal expression for all dimensions.An Extenics Based Intelligent Distance Learning Systemby Profs. Lee and Terashima provides a very good example of Extenics implementation in a classical problem for the field of Artificial Intelligence. It would probably serve as one of the best initial examples for a reader looking for a general, high grade, yet straightforward application of Extenics to an actual problem. With web-based learning becoming one of the major applications of the internet and by applying the Extenics engineering method, a model-based intelligent curriculum website is proposed. In order to recognize the learning status of students to the provided course effectively, the content of the course is divided in detail, so as to record the web page and the period that students browsed more accurately. They show that through these experiments more accurate information of students learning conditions can be obtained and analysed. Also, by applying the proposed Extenics-based mechanism, instructors can provide students more adequate learning materials in accordance with individual students aptitude [20]. A Novel Approach to Balance the Dynamic Load using Extension Theory on Heterogeneous Server Cluster is, in some ways, the opposite of the previous paper. The work is rather involved for readers unfamiliar with the subject, yet the application of Extenics is discernable even without full comprehension of the task at hand.Load balancing in distributed computer systems is the process of redistributing the work load among processors in the system to improve system performance. The paper uses the operation of matter-element theory, extension set, and dependent function in extension theory as well as the membership degree of fuzzy math to set up an extension-based dynamic load balancing model of heterogeneous server cluster [21]. Finally, papers such asExtension hybrid force-position control of mechatronics systems by Profs. Vladareanu, Sandru and Yu illustrates a new direction in the field of Extenics control [22][23]. An extension dynamic position-force control system integrating the multi-stage fuzzy method with solved acceleration in position-force control and dynamic control loops using Extenics theory and the ZMP method is presented. It is also noted that in addition to hybrid position-force control, three other main tasks are added, resulting from the analysis of the robot's walking cycle, conforming to movement characteristics: real time balance control, walking scheme control and predictable control of the walking robot movement. The results obtained show that this allows the robot to adapt to rough terrain through a real time control with increased stability during walking. A multi-microprocessor architecture is designed with multi-tasking control that allows a fast feedback loop for real time robot control, improving stability and flexibility performance.6. CONCLUSIONSThe paper gives a brief introduction into the world of Extenics Engineering. It attempts to summarize as best possible the works and accomplished results before it and provide a glimpse into the future directions of research. We have already seen that ideas can be generated using populations of potential solutions: in fact, the entire field of Evolutionary Algorithms is more or less based on that initial assumption. Due to this similarity, there is an increasing trend to combine the two in all manner of practical solutions in fields related or unrelated to artificial intelligence. Perhaps the most important aspect of Extenics study is the hope that it may one day provide, in part or completely, techniques for the independent creation of original thought by machines, thereby revolutionizing the world of engineering as we understand it. Until then, however, progress made every day by Extenics is used successfully in world-wide applications, making it one of the most exciting fields of study in artificial intelligence today.REFERENCES1. Cai Wen. Extension Set and Non-Compatible Problems [A]. Advances in Applied Mathematics and Mechanics in China [C]. Peking: International Academic Publishers, 1990.1-21.2. Yang Chunyan, Cai Wen, Extension Engineering, Science Press, Beijing, 2002.3. Wang Xingyu, Li Jian. Extension Control [ J]. Control theory & applications1994111125-128.4. Yang Chunyan, Li Xiaomei, Chen Wenwei, Cai Wen. Extension Data Mining Methods and Their Computer Implementation [M]. Guangzhou: Guangdong Higher Education Press, 2010.5. Yang Chunyan, Zhang Yongjun. Extension Planning [M]. Beijing: Science Press2002.6. HU Bao-qing, WANG Xiao-li, HE Juan-juan. Extension Set and the Independent Function on Intervals [J]. Journal Of Guangdong University Of Technology200017(2)101-104.7. Li Lixi, Yang Chunyan, Li Huawen. Extension Strategy Generation System [M]. Science Press2006.8. Smarandache, Florentin. Extenics in Higher Dimensions. Infinite Study, 2012.9. FlorentinSmarandache, Generalizations of the Distance and Dependent Function in Extenics to 2D, 3D, and n-D, viXra.org, http://vixra.org/pdf/1206.0014v1.pdf, 2012.10. Yang Chunyan, Li Weihua, Li Xiaomei. Recent Research Progress in Theories and Methods for the Intelligent Disposal of Contradictory Problems [J]. Journal of Guangdong University of Technology2011, 28186-93.11. Yang Chunyan, Cai Wen. The Progress of Extension Data Mining [J]. Mathematics in Practice and Theory, 2009, 39 (4): 134-141.12. Cai Wen, Yang Chunyan. Extension Marketing[M]. Beijing: Science and Technology Literature Publishing House, 2000.13. Zhao Yanwei, Sunan. Extension Design [M]. Beijing: Science Press2010.14. Yang Guowei, Wang Xianmei, TuXuyan. New Models and Principles on Computer-Oriented Innovative and Creative Design of Products (I) [J]. Computer Engineering and Applications2003, 3932:7-10.15. He Bin, Zhu Xuefeng. Hybrid Extension and Adaptive Control [J]. Control Theory & Applications2005222165-170.16. Vladareanu V., Sandru O.I., Schiopu P., Sandru A., Vladareanu L., Extension Hybrid Force-Position Control of Mechatronics Systems, accepted for publication in Communications in Cybernetics, Systems ScienceandEngineering, CRC Press, Beijing 201317. Yongquan Yu, HaixiaPeng, Weiqong Ye. The Principle of Extnesion Detecting with Extension Sets [A]. Int. Conf. Computer, Communication and Control Technologies(CCCT)[C]. Florida, USA, 2003, 7: Vol.4, 113-118.18. Smarandache, Florentin, Vladareanu, Victor. "Applications of Extenics to 2D-Space and 3D-Space."Extenics in Higher Dimensions39 (2012).19. O. I. andru, L. Vldreanu, P. chiopu, V. Vldreanu, A. andru, Multidimensional Extenics Theory, U.P.B. Sci. Bull., Series A, Vol. 75, Iss. 1, 2013, ISSN 1223-7027.20. Lee, Ying-Chen, and Nobuyoshi Terashima. "An Extenics-based intelligent distance learning system."IJCSNS: Interna-tional Journal of Computer Science and Network Security11.5 (2011): 57-63.21. K.Ramana, A.Subramanyam, T.Hari Krishna, V.Lokeswara Reddy A Novel Approach to Balance the Dynamic Load using Extension Theory on Heterogeneous Server Cluster, IJCAE, Vol.2 Issue 2, June 2012, 11-1922. Vladareanu, V., andru, O. I., chiopu, P., andru, A., & Vladareanu, L. (2013). Extension hybrid force-position control of mechatronics systems.Extenics and Innovation Methods, 167.23. andru, O. I., Vladareanu, L., chiopu, P., Vladareanu, V., &andru, A. (2013). New progress in extension theory.Extenics and Innovation Methods, 37. Cai Wen, Extension Theory and Its Application, Chinese Science Bulletin1999, 44 (17), 1538-1548.