The Compound Operations of Uncertain Cloud Concepts

Transcription

1 Journal of Computational Information Systems 11: 13 (2015) Available at The Compound Operations of Uncertain Cloud Concepts Longjun YIN 1,, Junjie XU 1, Guansheng ZHANG 2, Yanyan LI 3 1 School of Science, Chongqing University of Posts and Telecommunications, Chongqing , China 2 Research Center of Intelligent System and Robot, Chongqing University of Posts and Telecommunications, Chongqing , China 3 School of Computer Science & Technology, Chongqing University of Posts and Telecommunications, Chongqing , China Abstract Cloud model, an effective new cognitive model, is used to simulate the bidirectional cognitive computing between the intension and extension of concept from the forward cloud generator (FCG) and the backward cloud generator (BCG). In this paper, two kinds of cloud concepts, i.e., Young People and Middle-aged are used to generate the compound concepts in MATLAB. Firstly, the FCG is used for generating the extension set of a cloud concept. And the extension set of cloud concept can be obtained by the set operations, such as union operation, intersection operation, complementary operation and symmetric difference operation. And then the results are sent to FCG, the connotation of a new cloud concept can be obtained respectively by FCG algorithm of determined degree information and BCG algorithm of undetermined degree information. Through analyzing the output results, we can find that there are some degree atomization phenomenon in union operation, intersection operation, complementary operation and symmetric difference operation of cloud concept. And we find that removing the high membership of the cloud drops can reduce the hyper entropy, and the result about the certainty degree of complement is better. Keywords: Cloud Model; FCG; BCG; Set Operations; Cloud Concepts 1 Foreword Based on the probability theory and fuzzy set theory, Li puts forward cloud model [1] to uniformly describe randomness and fuzziness [8], which appears frequently in linguistic values. Taking the cloud model [1] as conversion model of the uncertainty between a certain qualitative This work is supported by the National Natural Science Foundation of China (No ), The Natural Science Foundation of Chongqing of China (No. cstc2013jcyja40063) and the Science & Technology Research Program of Chongqing Education Committee of China (No. KJ130534), The Youth Foundation of Chongqing University of Posts and Telecommunications (No. A ). Corresponding author. address: yinlj@cqupt.edu.cn (Longjun YIN) / Copyright 2015 Binary Information Press DOI: /jcis14670 July 1, 2015

2 4882 L. Yin et al. /Journal of Computational Information Systems 11: 13 (2015) concept described by linguistic values and its numerical representation. Cloud model [1] signifies the parameter in natural languagelinguistic values, and use three features, that are Expectation (Ex), Entropy (En) and Hyper entropy (He), to represent the natural language value. Entropy [3], this concept was initially used as a describing thermodynamic parameter, and was introduced in statistical physics [5] later. Information theory [4] was used to measure the uncertainty of the uncertain information. In the cloud model method, entropy represents a kind of metric particle size of the qualitative concept. The greater entropy comes, the greater granularity are. And information entropy can be used to granular computing for measuring the uncertainty degree of an uncertain concept. At the same time, entropy also represents the acceptable range of value to a qualitative concept in the information theory [4], i.e., ambiguity [4, 6], which is the measurement of uncertainty. The hyper entropy of cloud model is a kind of measurement of uncertainty change, i.e. the entropy of entropy. Cloud model [1] not only reflects randomness that a qualitative concept value appears, but also reflects membership degree of uncertainty, and reveals the relationship between fuzziness and randomness. At present the cloud model has been applied successfully in intelligent control [8, 9], prediction [10], fuzzy partition [11], data discretization [12], data mining technology [13, 14], system evaluation [15], uncertainty reasoning [16] and so on, and the advantage of the conversion between the qualitative concept and the quantitative concept is displayed gradually in uncertain artificial intelligent field. In this paper, the set operation of the concept extension, such as union, intersection, complementary, symmetric difference, is used to create many new extension of uncertain concept. And the BCG is used to create intension concept, in order to realize the synthesis of cloud concepts. In this paper Young people and Middle-aged are shown as two examples, to explain the compound operations, such as intersection operation, union operation, complement operation and symmetric difference operation, between any two uncertain cloud concepts based on the general normal cloud model. The rest of this paper is organized as follows. Section 2 gives the union operation of cloud concepts, and analyzes the rationality of union operation between any two uncertain cloud concepts. The intersection operation between any two uncertain cloud concepts is presented, and the rationality of intersection operation between any two uncertain cloud concepts will be analyzed in Section 3. Section 4 gives the complement operation between any two uncertain cloud concepts. In section 5 and in section 6 the difference operation and the symmetric difference operation between any two uncertain cloud concepts are proposed respectively. Section 7 is the conclusion part. 2 The Union Operation Between Two Uncertain Cloud Concepts 2.1 The principle of the algorithm Let Young people and Middle-aged people be two uncertain cloud concepts. The union operation between these two concepts means putting all the extension elements of two concepts into a new extension set, and generates a new uncertain concept called Middle and Young-aged people. Through importing the drops [1] of Young People and Middle-aged people which produced based on FCG, and the parameter of Middle and Young Caged people is exported based on BCG.

3 L. Yin et al. /Journal of Computational Information Systems 11: 13 (2015) This algorithm is shown as follows, (1) Importing Ex1, En1, He1 into FCG, the membership coordinates Y(x, y) of Young peoples are obtained. Then Importing Ex2, En2, He2 into FCG, the membership coordinates M(x, y) of Middle-aged peoples are obtained; (2) Importing Y and M into BCG. 2.2 Analysis of the results The results of reverse the normal cloud generator algorithm are shown as follows, Ex= , En = and He= (Fig. 1(a)). From Fig. 1(a), we find that the dispersion degree of these drops is very high. If we replace the condition remove the cloud drops with more than [3] membership to remove the drops membership which greater than 0.9, then He= (Fig. 1(b)); if amended as reject the drops membership which greater than 0.6, then He= (Fig. 1(c)). The union operation between any two uncertain cloud concepts means that the two extensions set merge into a new extension set in order to generate a new uncertain concept. From above algorithm we can know that the new concept is greatly influenced by those cloud drops which have high membership, and the atomization of the cloud drops is obvious. (a) The result of the union operation, n=5000 (b) The result of He= Fig. 1: The union operation of two cloud concepts (c) The result of He= The Intersection Operation Between Cloud Concepts 3.1 The principle of the algorithm The intersection set of Young People and Middle-aged people, As young people gradually become the process of young people. So the intersection set take the common elements of two sets into a new set. The idea of the algorithm is to find out those drops among maximum age in Young People and the minimum age in Middle-aged people, then send those drops into BCG. Algorithm is shown as follows, (1) Importing Ex1, En1, He1 into FCG, the membership coordinates Y(x, y) of Young People are obtained of; then importing Ex2, En2, He2 into FCG, the membership coordinates M(x, y) of

4 4884 L. Yin et al. /Journal of Computational Information Systems 11: 13 (2015) middle-aged people are obtained; (2) Do the intersection operation: take the abscissa maximum of Y(x, y) remember to x max, and remove the abscissa values greater than x max from Y(x, y), The remaining part is denoted as M similarly, take the abscissa minimum of Y(x, y), remember to x min, and remove the abscissa values less than x min from Y(x, y), The remaining part is denoted as Y ; (3) Send Y and M into BCG. 3.2 Analysis of the results The results of reverse the normal cloud generator algorithm are shown as follows, Ex = , En =4.1520, He = (Fig. 2(a)). If we replace the condition remove the cloud drops with more than membership to remove the drops membership which greater than 0.9, then He= (Fig. 2(b)); if amended as reject the drops membership which greater than 0.6, then He= (Fig. 2(c)). (a) The results of reverse the normal cloud generator, n=5000 (b) The result of He= Fig. 2: The intersection operation between cloud concepts (c) The result of He= The Complementary Operation Between Cloud Concepts 4.1 The principle of the algorithm Suppose the universal set is human longevity which between zero and one hundred, With the Young People, as an example, the Complementary set of Young People are between 0 and 100, developing the new concept by removing the value greater than maximum and less than minimum of Young People, then send this set into BCG. This algorithm is shown as follows, (1) Find out the maximum abscissa max and the minimum abscissa min from the Young People drops FCG; (2) Generating N uniformly distributed random numbers in [0,100], remove which belongs to [min,max];

5 L. Yin et al. /Journal of Computational Information Systems 11: 13 (2015) (3) Importing the surplus random numbers into BCG. 4.2 Analysis of the results (i) The results of reverse the normal cloud generator algorithm of determined degree information are shown as follows, Ex = , En = INF, He =NAN; In this algorithm, the cloud droplet information degree is determined, so the complement information degree is a Constant. Therefore the entropy of complementary set is infinite and hyper entropy of complementary set does not exist. (ii) The results of reverse the normal cloud generator algorithm of undetermined degree information are shown as follows, Ex = , En = , He = (Fig. 3). The complementary set of cloud is a great concept Remove all the young people, this concept is very extensive, so the hyper entropy has a large value. Fig. 3: The result of Ex = , En = , He =4.1285, the number of drops is n= The Difference Operation Between Cloud Concepts 5.1 The principle of the algorithm Young People minus Middle-aged means remove lager value from Young People, then importing the remaining elements into BCG. This algorithm is shown as follows, (1) Importing Ex1, En1, He1 into FCG, the membership coordinates Y(x, y) of Young Peoples are obtained; The importing Ex2, En2, He2 into FCG, the membership coordinates M(x, y) of Middle-aged s are obtained; (2) Do complement operation: take the abscissa minimum of M(x, y), remember to x min, and remove the abscissa values less than x min from Y(x, y), The remaining part is denoted as Y ; (3) Importing Y into BCG.

6 4886 L. Yin et al. /Journal of Computational Information Systems 11: 13 (2015) Analysis of the results (i) The result of reverse the normal cloud generator algorithm of determined degree are shown as follows, Ex = , En =3.3451, He = (Fig. 4(a)). (ii) The result of reverse the normal cloud generator algorithm of undetermined degree are shown follows, Ex = , En =3.5663, He = (Fig. 4(b)). Because the hyper entropy of arithmetic (i) approximately equal to the hyper entropy of Young People, so it is not necessary to deleting the high point of the membership. The difference set concept means narrowing the range of this conceptremove the older parts of Young People, equivalent to the concept of adolescent, the Hyper entropy is less different between the new concept and the original concept, and data results in line with the fact as well. (a) The result of Ex = , En =3.3451, He =0.5334, the number of drops is n=5000 (b) The result of Ex = , En =3.5663, He =0.4436, the number of drops is n=5000 Fig. 4: The difference operation between cloud concepts 6 The Symmetric Difference Operation Between Cloud Concepts 6.1 The principle of the algorithm The symmetric difference operation is opposite to the intersection operation, removing the age group which both belongs Young People and Middle-aged from Young and Middle-aged. It means finding out the drops which have maximum age in Young People and have minimum age in Middle-aged, sending those drops which except the two above into BCG. This algorithm is shown as follows, (1) Importing Ex1, En1, He1 into FCG, the membership coordinates Y(x, y) of Young People s are obtained; Then Importing Ex2, En2, He2 into FCG, the membership coordinates M(x, y) of Middle-aged s are obtained; (2) Do symmetric difference operation, take the abscissa maximum of Y(x, y), remember to x max, and remove the abscissa values less than x max from M(x, y), The remaining part is denoted

7 L. Yin et al. /Journal of Computational Information Systems 11: 13 (2015) as M. Then take the abscissa minimum of M(x, y), remember to x min, and remove the abscissa values greater than x min from Y(x, y), The remaining part is denoted as Y ; (3) Importing Y and M into BCG. 6.2 Analysis of the results (i) The results of reverse the normal cloud generator algorithm of determined degree are shown as follows, Ex = , En = , He = (Fig. 5(a)). If changing the condition reject the drops membership which greater than to reject the drops membership which greater than 0.9, then He= (Fig. 5(b)); if amended as reject the drops membership which greater than 0.6, then He= (Fig. 5(c)). (ii) The results of reverse the normal cloud generator algorithm of undetermined degree are shown as follows, Ex = , En = , He = (Fig. 6). Symmetric difference is a union operation of two sets which are no intersection. (a) The results of reverse the normal cloud generator,n=5000 (b) The result of He= (c) The result of He= Fig. 5: The results of reverse the normal cloud generator algorithm of determined degree Fig. 6: The result of Ex = , En = , He = , the number of drops is n= Conclusion In this paper, many certain concepts are developed by FCG, and these new concepts are outputted by FCG based on the set operations. The theoretical foundation of the improvement of the cloud

8 4888 L. Yin et al. /Journal of Computational Information Systems 11: 13 (2015) model is enhanced, and a new idea for knowledge representation with cloud model is presented. Many new methods for transformation between the quantitative concepts and qualitative concepts are proposed, and the rationality of uncertain concept in cloud model is revealed. These results are beneficial to the deeper and wider development of cloud model. From the above results, we can know that intersection, complement and complementary operations are conforming to human cognition model, and the effect of the rest operations be not in accord with the human cognitive habits. Discrete degree of these new concepts is different due to the different algorithm of FCG. Therefore, in the future work, the method for choosing cloud drops and the algorithm of BCG may determine the disadvantage and advantage of the new concept generated by set operations of could model. References [1] Li De-Yi, Du Yi. Artificial intelligence with uncertainty [M]. Beijing: National Defense Industry Press, [2] Liu Gui-hua, Song Cheng-xiang, Liu Hong Software Implementation of Cloud Generators [J]. Application Research of Computers, 2007, 24(1): [3] Ashley H. Carter, Classical and Statistical Thermodynamics [M]. Beijing University Press, [4] Wang S L, Li D R, Shi W Z, et al. Cloud model-based spatial data mining [J]. Geographical Information Science, 2003, 9(2): [5] Liu Jie, Chen Xiao-ping, Cai Qing-sheng, Fan Yan, Recognition Structure of Uncertainty: a Unified Framework for Representation, Reasoning and Learning [J]. Journal of Software, 2002, 13(4): [6] Zadeh L A. Fuzzy sets, Information and Control, 1965, 8: [7] Russell S, Norvig P. Artificial Intelligence: a Modem Approach. New Jersey: Prentice Hall, [8] Li De-Yi. The cloud control method and balancing patterns of triple link inverted pendulum systems. Engineering Science, 1999, 1(2): [9] Zhang Fei-Zhou, Fan Yue-Zu, Shen Cheng-Zhi, Li De-Yi. Intelligent control based on membership cloud generators. Acta Aeronautics ET Astronautica Sinica, 1999, 20(1): [10] Yu Shao-Wei, Cai Kai, Zhao Mo. Traffic information forecast algorithm based on the one-dimension cloud model. Journal of Shandong University (Engineering Science), 2007, 37(2): [11] Jiang Rong, Li De-Yi, Fan Jian-Hua. Automatic Generation of Pan-Concept-Tree on numerical data. Chinese Journal of Computers, 2000, 23(5): 1-7. [12] Li Xing-Sheng, Li De-Yi. A new method based on cloud model for discretization of continuous attributes in rough sets. Pattern Recognition and Artificial Intelligence, 2003, 16(1): [13] Du Yi, Li De-Yi. Concept partition based on cloud and its application to mining association rules. Journal of Software, 2001, 12(2): [14] Wang S L, Li D R, Shi W Z, et al. Cloud model-based spatial data mining. Geographical Information Science, 2003, 9(2): [15] Li De-Yi, Yu Quan, Jiang Guang-Jie. A unified assessment of reliability, invulnerability and anticounterm easurement for C3I Systems. Systems Engineering Theory and practice, 1997, 17(3): [16] Yu Shao-Wei. A new approach to reasoning about uncertainty based on cloud theory. Journal of Shandong University (Natural Science), 2009, 44(3):