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SYSTEM MODELING WITH FUZZY MODELS: FUNDAMENTAL DEVELOPMENTS AND PERSPECTIVES
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2
In this study, we offer a general view at the area of fuzzy modeling and fuzzymodels, identify the visible development phases and elaborate on a new and promisingdirections of system modeling by introducing a concept of granular models. Granularmodels, especially granular fuzzy models constitute an important generalization of existingfuzzy models and, in contrast to the existing models, generate results in the form ofinformation granules (such as intervals, fuzzy sets, rough sets and others). We present arationale and deliver some key motivating arguments behind the emergence of granularmodels and discuss their underlying design process. Central to the development of granularmodels are granular spaces, namely a granular space of parameters of the models and agranular input space. The development of the granular model is completed through anoptimal allocation of information granularity, which optimizes criteria of coverage andspecificity of granular information. The emergence of granular models of type2 and typen,in general, is discussed along with an elaboration on their formation. It is shown thatachieving a sound coveragespecificity tradeoff (compromise) is of paramount relevance inthe realization of the granular models.
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14


WITOLD
PEDRYCZ
DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING
UNIVERSITY OF ALBERTA EDMONTON T6R 2V4 AB CANADA, DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERING FACULTY OF ENGINEERING KING ABDULAZIZ
UNIVERSITY JEDDAH, 21589 SAUDI ARABIA AND SYSTEMS
DEPARTMENT OF ELECTRICAL & COMPUTER ENGINEERIN
Poland
pedrycz@ee.ualberta.ca
Fuzzy models
Granular computing
information granules of higher type
Granular spaces
[[1] R. Alcala, M. J. Gacto and F. Herrera, A fast and scalable multiobjective genetic fuzzy system for##linguistic fuzzy modeling in highdimensional regression problems, IEEE Trans. Fuzzy Systems 19 (2011),##666–681.##[2] J. M. Alonso, L. Magdalena and S. Guillaume, Linguistic knowledge base simplification regarding##accuracy and interpretability, Mathware Soft Comput., 13 (2006), 203–216.##[3] J. C. Bezdek, Pattern recognition with fuzzy objective function algorithms plenum press, N. York, 1981.##[4] C. Hwang and F. C. H Rhee, Uncertain fuzzy clustering: Interval Type2 fuzzy approach to CMeans,##IEEE Trans. on Fuzzy Systems, 15 (12) (2007), 107120. ##[5] Y. Jin, Fuzzy modeling of highdimensional systems: complexity reduction and interpretability##improvement, IEEE Trans. Fuzzy Systems, 8 (2000), 212–221.##[6] T. A. Johansen and R. Babuska, Multiobjective identification of TakagiSugeno fuzzy models, IEEE##Trans. Fuzzy Systems, 11 (2003), 847–860.##[7] R. Mikut, J. Jäkel and L. Gröll, Interpretability issues in databased learning of fuzzy systems, Fuzzy##Sets & Systems, 150 (2005), 179–197.##[8] W. Pedrycz, Granular computing  The emerging paradigm, Journal of Uncertain Systems 1(1) (2007),##[9] W. Pedrycz, Granular computing: analysis and design of intelligent systems CRC press/francis taylor,##Boca Raton, 2013.##[10] W. Pedrycz and A. Bargiela, An optimization of allocation of information granularity in the##interpretation of data structures: toward granular fuzzy clustering, IEEE Trans on Systems, Man, and##Cybernetics, Part B, 42 (2012), 582590.##[11] W. Pedrycz and W. Homenda, Building the fundamentals of granular computing: A principle of##justifiable granularity, Applied Soft Computing, 13 (2013), 42094218.##[12] W. Pedrycz, KnowledgeBased Fuzzy Clustering John Wiley, N. York, 2005.##[13] R. R. Yager, Ordinal measures of specificity, Int. J. of General Systems, 17 (1990), 5772.##[14] J. T. Yao, A. V. Vasilakos and W. Pedrycz, Granular computing: perspectives and challenges, IEEE##Transactions on Cybernetics, 43(6) (2013), 1977 – 1989.##[15] L. A. Zadeh, Towards a theory of fuzzy information granulation and its centrality in human reasoning##and fuzzy logic, Fuzzy Sets and Systems, 90 (1997), 111117.##[16] L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)––an outline, Information Sciences,##172 (2005), 1 40.##[17] L. A. Zadeh, A note on Znumbers, Information Sciences, 181 (2011), 29232932.##[18] S. M. Zhou and J. Q. Gan, Lowlevel interpretability and highlevel interpretability: a unified view of##datadriven interpretable fuzzy system modelling, Fuzzy Sets and Systems, 159(23) (2008), 3091–3131.##[19] B. Zhu, C. Z. He, P. Liatsis and X. Y. Li, A GMDHbased fuzzy modeling approach for constructing TS##model, Fuzzy Sets and Systems, 189 (2012), 19–29.##]
ON THE COMPATIBILITY OF A CRISP RELATION WITH A FUZZY EQUIVALENCE RELATION
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2
In a recent paper, De Baets et al. have characterized the fuzzytolerance and fuzzy equivalence relations that a given strict order relation iscompatible with. In this paper, we generalize this characterization by consideringan arbitrary (crisp) relation instead of a strict order relation, while payingattention to the particular cases of a reflexive or irreflexive relation. The reasoninglargely draws upon the notion of the clone relation of a (crisp) relation,introduced recently by Bouremel et al., and the partition of this clone relationin terms of three different types of pairs of clones. More specifically, reflexive related clones and irreflexive unrelated clones turn out to play a key role in thecharacterization of the fuzzy tolerance and fuzzy equivalence relations that agiven (crisp) relation is compatible with.
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31


B. De
Baets
KERMIT, Department of Mathematical Modelling, Statistics and
Bioinformatics, Ghent University, Coupure links 653, B9000, Gent, Belgium
KERMIT, Department of Mathematical Modelling,
Belgium


H.
Bouremel
Department of Mathematics, Faculty of Mathematics and Informatics,
Med Boudiaf University of Msila, P.O. Box 166 Ichbilia, Msila 28000, Algeria
Department of Mathematics, Faculty of Mathematics
Algeria


L.
Zedam
Department of Mathematics, Faculty of Mathematics and Informatics,
Med Boudiaf University of Msila, P.O. Box 166 Ichbilia, Msila 28000, Algeria
Department of Mathematics, Faculty of Mathematics
Algeria
l.zedam@yahoo.fr
Crisp relation
Fuzzy relation
Clone relation
Compatibility
Tolerance relation
Equivalence relation
[[1] R. Belohlavek, Fuzzy Relational Systems: Foundations and Principles, Kluwer Academic##Publishers/Plenum Publishers, New York, 2002.##[2] R. Belohlavek, Concept lattices and order in fuzzy logic, Ann. Pure Appl. Logic, 128(13)##(2004), 277298.##[3] U. Bodenhofer, A new approach to fuzzy orderings, Tatra Mt Math Publ, 16(1) (1999), 19.##[4] U. Bodenhofer, Representations and constructions of similaritybased fuzzy orderings, Fuzzy##Sets and Systems, 137(1) (2003), 113136.##[5] U. Bodenhofer and M. Demirci, Strict fuzzy orderings in a similaritybased setting, Proc. of##EUSFLATLFA 2005, Barcelona, Spain, (2005), 297302.##[6] U. Bodenhofer, B. De Baets and J. Fodor, A compendium of fuzzy weak orders: Representa##tions and constructions, Fuzzy Sets and Systems, 158(8) (2007), 811829.##[7] H. Bouremel, R. PerezFernandez, L. Zedam and B. De Baets, The clone relation of a binary##relation, Information Sciences, doi: 10.1016/j.ins.2016.12.008, accepted.##[8] A. Burusco and R. FuentesGonzales, The study of the Lfuzzy concept lattice, Mathware and##Soft Computing, 3 (1994), 209218.##[9] B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Second ed., Cambridge##University Press, Cambridge, 2002.##[10] B. De Baets and R. Mesiar, Triangular norms on product lattices, Fuzzy Sets and Systems,##104(1) (1999), 6175.##[11] B. De Baets, L. Zedam and A. Kheniche, A clonebased representation of the fuzzy tolerance##or equivalence relations a strict order relation is compatible with, Fuzzy Sets and Systems,##296 (2016), 3550.##[12] M. Demirci, Foundations of fuzzy functions and vague algebra based on manyvalued equiva##lence relations, Part I: fuzzy functions and their applications, Internat. J. General Systems,##32(2) (2003), 123155.##[13] M. Demirci, A theory of vague lattices based on manyvalued equivalence relationsI: general##representation results, Fuzzy Sets and Systems, 151(3) (2005), 437472.##[14] J. A. Goguen, Lfuzzy sets, Journal of Mathematical Analysis and Applications, 18(1) (1967),##[15] U. Hohle and N. Blanchard, Partial ordering in Lunderdeterminate sets, Information Sciences,##35(2) (1985), 133144.##[16] A. Kheniche, B. De Baets and L. Zedam, Compatibility of fuzzy relations, International##Journal of Intelligent Systems, 31(3) (2015), 240256.##[17] P. Martinek, Completely lattice Lordered sets with and without Lequality, Fuzzy Sets and##Systems, 166(1) (2011), 4455.##[18] I. Perlieva, Normal forms in BLalgebra and their contribution to universal approximation##of functions, Fuzzy Sets and Systems, 143(1) (2004), 111127.##[19] I. Perlieva, Fuzzy function: theoretical and practical point of view, Proc. EUSFLAT 2011,##AixlesBains, France, (2011), 480486.##[20] I. Perlieva, D. Dubois, H. Prade, F. Esteva, L. Godo and P. Hoddakova, Interpolation of##fuzzy data: Analytical approach and overview, Fuzzy Sets and Systems, 192 (2012), 134158. ##[21] B. S. Schroder, Ordered Sets, Birkhauser, Boston, 2002.##[22] H. L. Skala, Trellis theory, Algebra Universalis, 1 (1971), 218233.##[23] K. Wang and B. Zhao, Joincompletions of Lordered sets, Fuzzy Sets and Systems, 199##(2012), 92107.##[24] L. A. Zadeh, Similarity relations and fuzzy orderings, Information Sciences, 3(2) (1971),##[25] Q. Zhang, W. Xie and L. Fan, Fuzzy complete lattices, Fuzzy Sets and Systems, 160(16)##(2009), 22752291.##]
DCDC CONVERTER WITH FUZZY CONTROLLER FOR SOLAR CELL APPLICATIONS ON MOBILE ROBOTS
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2
Emerging technologies increase the needs on self efficient mobile robotic applications that bring a new concern of sustainable and continuous power supply for the robotic platforms. This paper covers the various techniques and technologies used to design a solar powered robot, exploring the currently available products, software and limitations to this application. The main aim is to integrate a fuzzy logic based charging system which allows the batteries to be charged from solar panels, wall outlet, and a deployable solar charging station. The goal of this paper is to summarize the tested methods and results to expedite future researchers in the correct direction. This paper will cover only up to the design of the DCDC converter and simulation, as further work is still pending implementation on actual hardware.Simulations results are provided to evaluate the feasibility of the paper for future implementations.
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J.
CruzLambert
Electrical and Computer Engineering Department, The University
of Texas at San Antonio, San Antonio, Texas, USA
Electrical and Computer Engineering Department,
United States


P.
Benavidez
Electrical and Computer Engineering Department, The University
of Texas at San Antonio, San Antonio, Texas, USA
Electrical and Computer Engineering Department,
United States


J.
Ortiz
Electrical and Computer Engineering Department, The University of Texas
at San Antonio, San Antonio, Texas, USA
Electrical and Computer Engineering Department,
United States


N.
Gallardo
Electrical and Computer Engineering Department, The University of
Texas at San Antonio, San Antonio, Texas, USA
Electrical and Computer Engineering Department,
United States


B. A.
Erol
Electrical and Computer Engineering Department, The University of
Texas at San Antonio, San Antonio, Texas, USA
Electrical and Computer Engineering Department,
United States


J.
Richey
Electrical and Computer Engineering Department, The University of
Texas at San Antonio, San Antonio, Texas, USA
Electrical and Computer Engineering Department,
United States


S.
Morris
Electrical and Computer Engineering Department, The University of
Texas at San Antonio, San Antonio, Texas, USA
Electrical and Computer Engineering Department,
United States


M.
Jamshidi
Electrical and Computer Engineering Department, The University of
Texas at San Antonio, San Antonio, Texas, USA
Electrical and Computer Engineering Department,
United States
Solar
Renewable
LiPo
Lithium Polymer
MPPT
Robotics
Fuzzy controller
Energy
[[1] AVR451: BC100 Hardware User's Guidedoc8088.pdf., Available: http://www.atmel.com/##images/doc8088.pdf, 2016.##[2] AVR458: Charging LithiumIon Batteries with ATAVRBC100  doc8080.pdf., Available:##http://www.atmel.com/images/doc8080.pdf, 2016.##[3] Avr microcontrollers forums topicmegaavr and tinyavr bc100., Available:##http://www.avrfreaks.net/forum/bc100, 2016.##[4] S. Bidyadhar and P. Raseswari, A comparative study on maximum power point tracking##techniques for photovoltaic power systems, Sustainable Energy, IEEE Transactions on, 4(1)##(2013), 89{98.##[5] J. Fattal and P. B. D. N. Karami, Review on dierent charging techniques of a lithium poly##mer battery, In Technological Advances in Electrical, Electronics and Computer Engineering##(TAEECE), 2015 Third International Conference on, IEEE, (2015), 33{38.##[6] Y. Fei and H. Lv, Design of the solardriven module on modular mobile robot, Mechatronics##and Machine Vision in Practice (M2VIP), 2012 19th International Conference, (2012), 470{##[7] HobbyKing ZIPPY Flightmax 5000mah 3s1p 30c, Available: http://www.hobbyking.com/##hobbyking/store/uh viewitem.asp?idproduct=8587, 2016. ##52 J.CruzLambert, P.Benavidez, J.Ortiz,N.Gallardo, B.A.Erol,J.Richey, S.Morris and M.Jamshidi##[8] A. Kaplan and P. Uhing and N. Kingry and R. D. Adam, Integrated path planning and##power management for solarpowered unmanned ground vehicles, 2015 IEEE International##Conference on Robotics and Automation (ICRA), (2015), 982987.##[9] J. Leitner and W. Chamberlain and D. G. Dansereau and M. Dunbabin and M. Eich and##T. Peynot and J. Roberts and R. Russell and N. Snderhauf, LunaRoo: Designing a hopping##lunar science payload, 2016 IEEE Aerospace Conference, (2016), 112.##[10] J. H. Lever, A. Streeter and LR. Ray, Performance of a solarpowered robot for polar in##strument networks, Proceedings of the 2006 IEEE International Conference on Robotics and##Automation, 2006, ICRA 2006, (2006), 4252{4257.##[11] Ned Mohan, Power Electronics: A First Course, Wiley, 2012.##[12] Projects/avr bc100.git., Available: http://git.kpe.io/?p=avr bc100.git, 2016.##[13] L. Ray, A. Adolph, A. Morlock and B. Walker and M. Albert and J. H. Lever and J. Dibb,##Autonomous rover for polar science support and remote sensing, 2014 IEEE Geoscience and##Remote Sensing Symposium, (2014), 4101{4104.##]
A NOTE TO INTERPRETABLE FUZZY MODELS AND THEIR LEARNING
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2
In this paper we turn the attention to a well developed theory of fuzzy/linguistic models that are interpretable and, moreover, can be learned from the data.We present four different situations demonstrating both interpretability as well as learning abilities of these models.
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65


Vilem
Novak
University of Ostrava, Institute for Research and Applications of
Fuzzy Modeling, NSC IT4Innovations, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
University of Ostrava, Institute for Research
Czech Republic
Fuzzy Natural Logic
Perceptionbased logical deduction
Learning. } newlineindent{footnotesize {The paper has been supported by the project IT4I XS (LQ1602)
[[1] A. Dvorak, H. Habiballa, V. Novak and V. Pavliska, The software package LFLC 2000  its##specicity, recent and perspective applications, Computers in Industry, 51 (2003), 269{280.##[2] A. Dvorak, M. Stepnicka and L. Stepnickova, On Redundancies in Systems of##Fuzzy/Linguistic IFTHEN Rules under Perceptionbased Logical Deduction Inference, Fuzzy##Sets and Systems.##[3] E. Hullermeier, Does machine learning need fuzzy logic?, Fuzzy Sets and Systems, 281 (2015),##[4] V. Novak, Linguistically oriented fuzzy logic controller, in: Proc. of the 2nd Int. Conf. On##Fuzzy Logic and Neural Networks IIZUKA'92, Fuzzy Logic Systems Institute, Iizuka, (1992),##[5] V. Novak, Fuzzy relation equations with words, in: M. Nikravesh, L. Zadeh, V. Korotkikh##(Eds.), Fuzzy Partial Dierential Equations and Relational Equations, Springer, Berlin,##(2004), 167{185.##[6] V. Novak, Perceptionbased logical deduction, in: B. Reusch (Ed.), Computational Intelligence,##Theory and Applications, Springer, Berlin, (2005), 237{250.##[7] V. Novak, Mathematical fuzzy logic in modeling of natural language semantics, in: P. Wang,##D. Ruan, E. Kerre (Eds.), Fuzzy Logic { A Spectrum of Theoretical & Practical Issues,##Elsevier, Berlin, (2007), 145{182.##[8] V. Novak, A comprehensive theory of trichotomous evaluative linguistic expressions, Fuzzy##Sets and Systems, 159 (22) (2008), 2939{2969.##[9] V. Novak, On modelling with words, Int. J. of General Systems, 42 (2013), 21{40. ##[10] V. Novak, Evaluative linguistic expressions vs. fuzzy categories?, Fuzzy Sets and Systems,##281 (2015), 81{87.##[11] V. Novak, Fuzzy Natural Logic: Towards Mathematical Logic of Human Reasoning, in:##E. Seising, R.and Trillas, J. Kacprzyk (Eds.), Fuzzy Logic: Towards the Future, Springer,##(2015), 137{165.##[12] V. Novak, Linguistic characterization of time series, Fuzzy Sets and Systems, 285 (2016),##[13] V. Novak and J. Kova, Linguistic IFTHEN rules in large scale application of fuzzy control,##in: R. Da, E. Kerre (Eds.), Fuzzy IfThen Rules in Computational Intelligence: Theory and##Applications, Kluwer Academic Publishers, Boston, (2000), 223{241.##[14] V. Novak and S. Lehmke, Logical structure of fuzzy IFTHEN rules, Fuzzy Sets and Systems,##157 (2006), 2003{2029.##[15] V. Novak, V. Pavliska and Valasek, Specialized software for fuzzy natural logic and fuzzy##transform applications, in: Proc. Int. Conference FUZZIEEE'2014, Beijing, China, (2014),##2337{2344.##[16] V. Novak, V. Pavliska, M. Stepnicka and L. Stepnickova, Time series trend extraction and##its linguistic evaluation using Ftransform and fuzzy natural logic, in: L. Zadeh, A. Abbasov,##R. Yager, S. Shahbazova (Eds.), Recent Developments and New Directions in Soft Computing,##Springer, Berlin, (2014), 429{442.##[17] V. Novak and I. Perlieva, Smooth fuzzy logic deduction with words, in: Proc. Int. Conf.##Fuzzy Information Processing: Theories and Applications, Vol. II, Tsinghua University##Press/Springer, Beijing, (2003), 599{604.##[18] V. Novak and I. Perlieva, On the semantics of perceptionbased fuzzy logic deduction, International##Journal of Intelligent Systems, 19 (2004), 1007{1031.##[19] V. Novak, I. Perlieva and A. Dvorak, Insight into Fuzzy Modeling, Wiley & Sons, Hoboken,##New Jersey, 2016.##[20] V. Novak, I. Perlieva and N. G. Jarushkina, A general methodology for managerial decision##making using intelligent techniques, in: E. RakusAnderson, R. Yager, N. Ichalkaranje, L. Jain##(Eds.), Recent Advances in Fuzzy DecisionMaking, Springer, Heidelberg, (2009), 103{120.##[21] V. Novak, I. Perlieva, A. Romanov and N. Yarushkina, Time series grouping and trend##forecast using F1transform and fuzzy natural logic, in: R. Marco se Moraes, E. E. Kerre,##L. dos Santos Machado, J. Lu (Eds.), Decision Making and Soft Computing, World Scientic,##(2014), 143{148.##[22] I. Perlieva, Fuzzy transforms: theory and applications, Fuzzy Sets and Systems, 157 (2006),##[23] L. Zadeh, Toward a logic of perceptions based on fuzzy logic, in: V. Novak, I. Perlieva##(Eds.), Discovering the World With Fuzzy Logic, Studies in Fuzziness and Soft Computing,##SpringerVerlag, Heidelberg, (2000), 4{28.##[24] L. A. Zadeh, A rationale for fuzzy control, Trans. ASME, Ser. G, J. Dynamic. Systems,##Measurement and Control, 94 (1972), 3{4.##[25] L. A. Zadeh, Outline of a new approach to the analysis of complex systems and decision##processes, IEEE Trans. on Systems, Man, and Cybernetics SMC3, (1973), 28{44.##[26] L. A. Zadeh, Quantitative fuzzy semantics, Information Sciences, 3 (1973), 159{176.##[27] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning##I, II, III, Information Sciences, 89 (1975), 199{257, 301{357, 43{80.##[28] L. A. Zadeh, Fuzzy logic = computing with words, IEEE Trans. Fuzzy Systems, 4 (1996),##[29] L. A. Zadeh, From computing with numbers to computing with words & from manipulation##of measurements to manipulation of perceptions, Int. J. of Applied Math and Comp. Sci., 12##(2002), 307{324.##[30] L. A. Zadeh, Precisiated natural language, AI Magazine, 25 (2004), 74{91.##]
MINING FUZZY TEMPORAL ITEMSETS WITHIN VARIOUS TIME INTERVALS IN QUANTITATIVE DATASETS
2
2
This research aims at proposing a new method for discovering frequent temporal itemsets in continuous subsets of a dataset with quantitative transactions. It is important to note that although these temporal itemsets may have relatively high textit{support} or occurrence within particular time intervals, they do not necessarily get similar textit{support} across the whole dataset, which makes it almost impossible to extract them using the existing traditional algorithms. This paper directly addresses this problem and introduces a new algorithm called Fuzzy Solid Linguistic Itemset Mining (FSLIM) to discover Solid Linguistic Itemsets (SLIs) within a quantitative dataset. SLI is a new concept introduced here as an essential part of the solution presented in this paper. The proposed method consists of two phases. In the first phase, fuzzy set theory is used to transform each quantitative value to a linguistic item; and in the second phase, all SLIs are extracted. Finally, the efficiency of FSLIM is compared in terms of execution time, scalability and the number of frequent patterns with those of two classic approaches on synthetic datasets. The proposed approach is also applied to an actual Mashhad Urban Traffic dataset in order to illustrate FSLIM's ability in discovering the hidden knowledge that could not be extracted by traditional methods.
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67
89


Mahnaz
Kadkhoda
Department of Computer Engineering, Center of Excellence
on Soft Computing and Intelligent Information Processing, Ferdowsi University of
Mashhad, Mashhad, Iran
Department of Computer Engineering, Center
Iran


MohammadR.
AkbarzadehT
Department of Computer Engineering, Center of Excellence on Soft Computing and Intelligent Information Processing, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Computer Engineering, Center
Iran


S. Mahmoud
Taheri
Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran
Faculty of Engineering Science, College of
Iran
taher@cc.iut.ac.ir;sm_taheri@ut.ac.ir
Fuzzy data mining
Temporal data mining
Frequent itemset
Temporal quantitative dataset
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Eng. ICSSE 2011 Int. Conf. On, IEEE, (2011), 405{409.##[7] J. Han, J. Pei, Y. Yin and R. Mao, Mining frequent patterns without candidate generation:##A frequentpattern tree approach, Data Min. Knowl. Discov., 8 (2004), 53{87.##[8] T. P. Hong, Y. Y. Wu and S. L. Wang,An eective mining approach for uptodate patterns,##Expert Syst. Appl., 36 (2009), 9747{9752.##[9] T. P. Hong, C. S. Kuo and S. C. Chi, Tradeo between computation time and number of rules##for fuzzy mining from quantitative data, Int. J. Uncertain. Fuzziness Knowl.Based Syst., 9##(2001), 587{604.##[10] J. W. Huang, B. R. Dai and M. S. Chen, Twain: Twoend association miner with precise##frequent exhibition periods, ACM Trans. Knowl. Discov. Data TKDD., 1 (2007), 8.##[11] H. Ishibuchi and T. Yamamoto, Rule weight specication in fuzzy rulebased classication##systems, Fuzzy Syst. IEEE Trans. On., 13 (2005), 428{435.##[12] G. C. Lan, C. H. Chen, T. P. Hong and S. B. Lin, A fuzzy approach for mining general##temporal association rules in a publication database, In: Hybrid Intell. Syst. HIS 2011 11th##Int. Conf. On, IEEE, (2011), 611{615.##[13] C. H. Lee, M. S. Chen and C. R. Lin, Progressive partition miner: an ecient algorithm for##mining general temporal association rules, Knowl. Data Eng. IEEE Trans. On., 15 (2003),##1004{1017.##[14] W. J. Lee and S. J. Lee, Discovery of fuzzy temporal association rules, Syst. Man Cybern.##Part B Cybern. IEEE Trans. On., 34 (2004), 2330{2342.##[15] W. J. Lee, J. Y. Jiang and S. J. Lee, Mining fuzzy periodic association rules, Data Knowl.##Eng., 65 (2008), 442{462.##[16] Y. Li, P. Ning, X. S. Wang and S. Jajodia, Discovering calendarbased temporal association##rules, Data Knowl. Eng., 44 (2003), 193{218.##[17] C. W. Lin and T. P. Hong, Temporal data mining with uptodate pattern trees, Expert Syst.##Appl., 38 (2011), 15143{15150.##[18] S. G. Matthews, M. A. Gongora and A. A. Hopgood, Evolving temporal association rules##with genetic algorithms, In: Res. Dev. Intell. Syst. XXVII, Springer, (2011), 107{120.##[19] S. G. Matthews, M. A. Gongora, A. A. Hopgood and S. Ahmadi, Web usage mining with##evolutionary extraction of temporal fuzzy association rules, Knowl.Based Syst., 54 (2013),##[20] S. G. Matthews, M. A. Gongora and A. A. Hopgood, Evolutionary algorithms and fuzzy sets##for discovering temporal rules, Int. J. Appl. Math. Comput. Sci., 23 (2013), 855{868.##[21] S. G. Matthews, M. A. Gongora and A. A. Hopgood, Evolving temporal fuzzy itemsets from##quantitative data with a multiobjective evolutionary algorithm, In: Genet. Evol. Fuzzy Syst.##GEFS 2011 IEEE 5th Int. Workshop On, IEEE, (2011), 9{16.##[22] J. S. Park, M. S. Chen and P. S. Yu, Using a hashbased method with transaction trimming##for mining association rules, Knowl. Data Eng. IEEE Trans. On., 9 (1997), 813{825.##[23] J. Pei, J. Han, H. Lu, S. Nishio, S. Tang and D. Yang, Hmine: Hyperstructure mining of##frequent patterns in large databases, In: Data Min. 2001 ICDM 2001 Proc. IEEE Int. Conf.##On, IEEE, (2001), 441{448.##[24] B. Saleh and F. Masseglia, Discovering frequent behaviors: time is an essential element of##the context, Knowl. Inf. Syst., 28 (2011), 311{331.##[25] S. Suvvari and R. B. V. Subramanyam, An efficient approach for significant time intervals##of frequent itemsets, Int. J. Intell. Syst. Technol. Appl., 13 (2014), 222{243.##[26] Y. Xiao, R. Zhang and I. Kaku, A new framework of mining association rules with time##windows on realtime transaction database, Int. J. Innov. Comput. Inf. Control., 7 (2011),##3239{3253. ##[27] Y. Xiao, Y. Tian and Q. Zhao, Optimizing frequent timewindow selection for association##rules mining in a temporal database using a variable neighbourhood search, Comput. Oper.##Res., 52 (2014), 241{250.##[28] J. S. Yoo and S. Shekhar, Similarityproled temporal association mining, Knowl. Data Eng.##IEEE Trans. On., 21 (2009), 1147{1161.##[29] L. A. Zadeh, Fuzzy sets, Inf. Control., 8 (1965), 338{353.##[30] C. Zhuo, L. Jiahui and L. Chen, A fuzzy calendarbased algorithm for mining temporal as##sociation rules and its application, In: Fuzzy Syst. Knowl. Discov. 2009 FSKD09 Sixth Int.##Conf. On, IEEE, (2009), 28{33.##]
SOLUTIONSET INVARIANT MATRICES AND VECTORS IN FUZZY RELATION INEQUALITIES BASED ON MAXAGGREGATION FUNCTION COMPOSITION
2
2
Fuzzy relation inequalities based on maxF composition are discussed, where F is a binary aggregation on [0,1]. For a fixed fuzzy relation inequalities system $ A circ^{F}textbf{x}leqtextbf{b}$, we characterize all matrices $ A^{'} $ For which the solution set of the system $ A^{' } circ^{F}textbf{x}leqtextbf{b}$ is the same as the original solution set. Similarly, for a fixed matrix $ A $, the possible perturbations $ b^{'} $ of the righthand side vector $ b $ not modifying the original solution set are determined. Several illustrative examples are included to clarify the results of the paper.
1

91
100


F.
Kouchakinejad
Department of Mathematics, Graduate University of Advanced
Technology, Kerman, Iran
Department of Mathematics, Graduate University
Iran


M.
Mashinchi
Department of Statistics, Faculty of Mathematics and Computer Sciences, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Statistics, Faculty of Mathematics
Iran
ijfseditor@usb.ac.ir


R.
Mesiar
Slovak University of Technology in Bratislava, Faculty of Civil Engineering, Radlinskeho 11, 810 05 Bratislava, Slovak Republic
Slovak University of Technology in Bratislava,
Slovakia (Slovak Rep)
Aggregation function
Maxaggregation function composition
Solutionset invariant matrices
Solutionset invariant vectors
System of fuzzy relation inequalities
[[1] M. Baczynski and B. Jayaram, Fuzzy implications, Studies in Fuzziness and Soft Computing,##[2] G. Beliakov, A. Pradera and T. Calvo, Aggregation functions: A guide for practitioners,##Springer, Berlin: Heidelberg, 2007.##[3] J. Drewniak and Z. Matusiewicz, Properties of maxfuzzy relation equations, Soft Computing,##14 (2010), 10371041.##[4] F. Durante, J. J. QuesadaMolina and C. Sempi, Semicopulas: characterizations and appli##cability, Kybernetika, 42 (2006), 287302.##[5] M. J. Fernandez and P. Gil, Some specific types of fuzzy relation equations, Inform. Science,##164 (2004), 189195.##[6] M. Grabisch, J. L. Marichal, R. Mesiar and E. Pap, Aggregation functions, Cambridge: Cam##bridge University press, 2009.##[7] E. P. Klement, R. Mesiar and E. Pap, Triangular norms, Kluwer, Dordrecht, 2000.##[8] K. Peeva and Y. Kyosev, Fuzzy relational calculus  theory, applications and software, Ad##vances in Fuzzy SystemsApplications and Theory, World Scientific, 2005.##[9] E. Sanchez, Resolution of composite fuzzy relation equations, Inform. and Control, 30 (1976),##[10] B. S. Shieh, Solutions of fuzzy relation equations based on continuous Tnorms, Inform.##Science, 177 (2007), 42084215.##[11] G. B. Stamou and S. G. Tzafestas, Resolution of composite fuzzy relation equations based on##archimedean triangular norms, Fuzzy Set. Syst., 120 (2001), 395407.##[12] H. F. Wang and H. M. Hsu, Sensitivity analysis of fuzzy relation equations, Int. J. Gen. Syst.,##19 (1991), 155169.##]
AN OBSERVERBASED INTELLIGENT DECENTRALIZED VARIABLE STRUCTURE CONTROLLER FOR NONLINEAR NONCANONICAL NONAFFINE LARGE SCALE SYSTEMS
2
2
In this paper, an observer based fuzzy adaptive controller (FAC) is designed fora class of large scale systems with noncanonical nonaffine nonlinear subsystems. It isassumed that functions of the subsystems and the interactions among subsystems areunknown. By constructing a new class of state observer for each follower, the proposedconsensus control method solves the problem of unmeasured states of nonlinear noncanonicalnonaffine subsystems. The main characteristics of the proposed observerbasedintelligent controller are: 1) online adaptation of the controller and the observer parameters,2) ultimate boundedness of both the output and the observer errors, 3) boundedness of allsignals involved, 4) employing experts’ knowledge in the controller design procedure and 5)chattering avoidance. The simulation results are further carried out to demonstrate better theeffectiveness of the proposed fuzzy based consensus controller method.
1

101
130


REZA
GHASEMI
DEPARTMENT OF ELECTRICAL ENGINEERING, UNIVERSITY OF QOM, QOM, IRAN
DEPARTMENT OF ELECTRICAL ENGINEERING, UNIVERSITY
Iran


MOHAMMAD BAGHER
MENHAJ
DEPARTMENT OF ELECTRICAL ENGINEERING, AMIRKABIR UNIVERSITY
OF TECHNOLOGY, TEHRAN, IRAN, AND QIAU’S INCUBATOR CENTER OF TECHNOLOGY UNITS (CENTER
OF COGNITIVE SYSTEMS), QAZVIN, IRAN
DEPARTMENT OF ELECTRICAL ENGINEERING, AMIRKABIR
Iran
Lyapunov stability
Adaptive control
Nonaffine nonlinear system
large scale systems
Fuzzy systems
Nonlinear observer
[[1] C.C. Cheng, S.H. Chien, Adaptive Sliding Mode Controller Design Based On T–S Fuzzy System Models,##Elsevier Science, Automatica, 42 (2006), 10051010.##[2] L. Chen, G. Chen, Y.W. Lee, Fuzzy Modeling And Adaptive Control Of Uncertain Chaotic Systems,##Elsevier Science, Information Sciences, 121 (1999), 2737.##[3] C.C. Chiang, Adaptive Fuzzy Sliding Mode Control For TimeDelay Uncertain LargeScale Systems,##Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control##Conference, pp. 40774082,Seville, Spain, December, (2005), 1215.##[4] C. L. P. Chen, G. X. Wen, Y. J. Liu, Adaptive Consensus Control for a Class of Nonlinear Multiagent##TimeDelay Systems Using Neural Networks, IEEE Transaction of neural network learning systems, 25##(2014), 12171226.##[5] C. L. P. Chen, Y. J. Liu, G. X. Wen, Fuzzy neural networkbased adaptive control for a class of##uncertain nonlinear stochastic systems, IEEE Trans. Cybernetics, 44 (2014), 583593.##[6] G. Feng, S.G. Cao, N.W. Rees, Stable Adaptive Control Of Fuzzy Dynamic Systems, Elsevier Science,##Fuzzy Sets and Systems, 131 (2002), 217 – 224.##[7] G. Feng, An Approach To Adaptive Control Of Fuzzy Dynamic Systems, IEEE TRANSACTIONS ON##FUZZY SYSTEMS, 10 (2002), 268275.##[8] R. Ghasemi, M.B. Menhaj, A. Afshar, A decentralized stable fuzzy adaptive controller for large scale##nonlinear systems, Journal of Applied Science, 9 (2009), 892900.##[9] R. Ghasemi, M.B. Menhaj and A. Afshar, A New Decentralized Fuzzy Model Reference Adaptive##Controller for a Class of Largescale Nonaffine Nonlinear Systems, European Journal of Control, 5##(2009), 1–11.##[10] R Ghasemi, MB Menhaj, A variable structure observer based control design for a class of large scale##MIMO nonlinear systems, Amirkabir International Journal of Modeling, Identification, Simulation &##Control, 48 (2016), 4756. ##[11] N. Golea, A. Golea, K. Benmahammed, Stable Indirect Fuzzy Adaptive Control, Elsevier Science,##Fuzzy Sets and Systems, 137 (2003), 353366.##[12] A. Hamzaoui, N. Essounbouli, K. Benmahammed, and J. Zaytoon, State Observer Based Robust##Adaptive Fuzzy Controller for Nonlinear Uncertain and Perturbed Systems, IEEE TRANSACTIONS##ON SYSTEMS, MAN, AND CYBERNETICS—PART B, 34 (2004), 2328.##[13] H.F. Ho, Y.K. Wong, A.B. Rad, W.L. Lo, State Observer Based Indirect Adaptive Fuzzy Tracking##Control, Simulation Modeling Practice and Theory, 13 (2005), 646–663.##[14] Y.C. Hsu, G. Chen, S. Tong, H.X. Li, Integrated Fuzzy Modeling And Adaptive Control For Nonlinear##Systems, Elsevier Science, Information Sciences, 153 (2003), 217236.##[15] J. Hu, Y. Hong, Leaderfollowing coordination of multiagent systems with coupling time delays,##Physica A, 374 (2007), 853863.##[16] S. Jagannathan, Adaptive Fuzzy logic control of feedback linearization discrete time dynamical systems##under persistence of excitation, Automatica, 34 (1998), 12951310.##[17] X. Jiang,W. Xu, Q.L. Han, Observerbased fuzzy control design with adaptation to delay parameter for##timedelay systems, Elsevier Science, Fuzzy Sets and Systems, 152 (2005), 637–649.##[18] S. Labiod, M. S. Boucherit, T. M. Guerra, Adaptive fuzzy control of a class of MIMO nonlinear##systems, Elsevier Science, Fuzzy Sets and Systems, 151 (2005), 59–77.##[19] S. Labiod, T. M. Guerra, Adaptive fuzzy control of a class of SISO nonaffine nonlinear systems,##Elsevier Science, Fuzzy Sets and Systems, 158 (2007), 1126 –1137.##[20] Z. Li, X. Liu, P. Lin, W. Ren, Consensus of linear multiagent systems with reducedorder observerbased##protocols, Systems & Control Letters, 60 7 (2011), 510516.##[21] Y.J. Liu, W. Wang, Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems,##Elsevier Science, Information Sciences, 4 (2007), 117.##[22] Y. J. Liu, S. C. Tong, C. L. P. Chen, Adaptive fuzzy control via observer design for uncertain##nonlinear systems with unmodeled dynamics, IEEE Trans. Fuzzy Syst., 21 (2013), 275288.##[23] Y. J. Liu, S. C. Tong, D. Wang, T. S. Li, C. L. P. Chen, Adaptive neural output feedback controller##design with reducedorder observer for a class of uncertain nonlinear SISO systems, IEEE Trans.##Neural Netw., 22 (2011), 13281334.##[24] R. OlfatiSaber, R. M. Murray, Consensus problems in networks of agents with switching topology##and timedelays, IEEE Trans. Automatic Control, 49 (2004), 15201533.##[25] C.W. Park, M. Park, Adaptive Parameter Estimator Based On T–S Fuzzy Models And Its Applications##To indirect adaptive fuzzy control design, Elsevier science, Information Sciences, 159 (2004), 125139.##[26] K. Peng, Y. Yang, Leaderfollowing consensus problem with a varyingvelocity leader and timevarying##delays, Physica A, 388 (2009), 193208.##[27] W. Ren, K. Moore, Y. Chen, HighOrder Consensus Algorithms in Cooperative Vehicle Systems, in##Proc. ICNSC, 129 (2006), 457  462.##[28] T. Shaocheng, C. Bin, W. Yongfu, fuzzy adaptive output feedback control for MIMO nonlinear##systems, Elsevier Science, Fuzzy Sets and Systems, 156 (2005), 285–299.##[29] Y. Tang, N. Zhang, Y. Li, stable fuzzy adaptive control for a class of nonlinear systems, Elsevier##Science, Fuzzy Sets and Systems, 104 (1999), 279288.##[30] S. C. Tong, Q. Li, T. Chai, fuzzy adaptive control for a class of nonlinear systems, Elsevier Science,##Fuzzy Sets and Systems, 101 (1999), 3139.##[31] S. Tong, H.X. Li, W. Wang, ObserverBased Adaptive Fuzzy Control For SISO Nonlinear Systems,##Elsevier Science, Fuzzy Sets and Systems, 148 (2004), 355–376.##[32] S. Tong, H.X. Li, and G. Chen, adaptive fuzzy decentralized control for a class of largescale##nonlinear systems, IEEE Transactions on Systems, Man, and Cybernetics—Part B, 34 (2004), 2427.##[33] S. C. Tong, Y. Li, Y. M. Li, and Y. J. Liu, Observerbased adaptive fuzzy backstepping control for a##class of stochastic nonlinear strictfeedback systems, IEEE Trans. Syst., Man, Cybern. Part B, 41##(2011), 16931704.##[34] S. C. Tong, Y. M. Li, G. Feng, and T. S. Li, Observer based adaptive fuzzy backstepping dynamic##surface control for a class of MIMO nonlinear systems, IEEE Trans. Syst., Man, Cybern. Part B, 41##(2011), 1124 1135.##[35] S.Tong and J.Tang and T. Wang, Fuzzy Adaptive Control Of Multivariable Nonlinear Systems,##Elsevier Science, Fuzzy Sets and Systems, 111 (2000), 153167.##[36] D. VélezDíaz and Y. Tang, Adaptive robust fuzzy control of nonlinear systems, IEEE Transactions On##Systems, Man, And Cybernetics—Part B: Cybernetics, 34 (2004), 3439. ##[37] R.J. Wai, M. Kuo, and J.D. Lee, Cascade direct adaptive fuzzy control design for a nonlinear twoaxis##invertedpendulum servomechanism, IEEE Transactions On Systems, Man, and Cybernetics—Part B:##Cybernetics, 38 (2008), 6777.##[38] X. Wang, T. Li, C. L. P. Chen, Adaptive robust control based on single neural network approximation##for a class of uncertain strictfeedback discretetime nonlinear systems, Neurocomputing, 138 (2014),##[39] H. Wu, Decentralized adaptive robust control for a class of largescale systems including delayed##state perturbations in the interconnections, IEEE Transactions On Automatic Control, 47 (2002), 1745##[40] P. Yingguo, Z. Huaguang, Design of fuzzy direct adaptive controller and stability analysis for a##class of nonlinear system, Proceedings of the American Control conference, Philadelphia, Pennsylvania,##(1998), 22742275.##[41] T. Yiqian, W. Jianhui, G. Shusheng, Q. Fengying, Fuzzy Adaptive Output Feedback Control For##Nonlinear MIMO Systems Based On Observer, Proceedings of the 5th World Congress on Intelligent##Control and Automation Hangzhou, P.R. China, (2004), 506510.##[42] W.S. Yu, Model Reference Fuzzy adaptive control for uncertain dynamical systems with time delays,##IEEE International Conference on Systems, Man and Cybernetics, 5 (2004), 52465251.##[43] L. Zhang, Stable Fuzzy Adaptive Control Based On Optimal Fuzzy Reasoning, IEEE, Proceedings of##the Sixth International Conference on Intelligent Systems Design and Applications (ISDA'06), (2006),##[44] H. Zhang and Z.Bien, Adaptive fuzzy control of MIMO nonlinear systems, Fuzzy Sets and Systems,##115 (2000), 191204.##[45] H. W. Zhang and F. L. Lewis, Adaptive cooperative tracking control of higherorder nonlinear##systems with unknown dynamics, Automatica, 48 (2012), 14321439.##[46] W. Zhu and D. Cheng, Leaderfollowing consensus of secondorder agents with multiple timevarying##delays, Automatica, 46 (2010), 19941999.##]
MINIMAL AND STATEWISE MINIMAL INTUITIONISTIC GENERAL LFUZZY AUTOMATA
2
2
In this note, by considering the notions of the intuitionistic general Lfuzzy automaton and $(alpha, beta)$language, we show that for any $(alpha, beta)$language $mathcal{L}$, there exists a minimal intuitionistic general Lfuzzy automaton recognizing $mathcal{L}$.We prove that the minimal intuitionistic general Lfuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, beta)$reduced maxmin intuitionistic general Lfuzzy automaton.%Also, we prove that the minimal intuitionistic general Lfuzzy automaton is an $(alpha, beta)$reduced.Also, we show that for any strong deterministic maxmin intuitionistic general Lfuzzy automaton there exists a statewise $(alpha, beta)$minimal intuitionistic general Lfuzzy automaton.In particular, a connection between the minimal and statewise $(alpha, beta)$minimal intuitionistic general Lfuzzy automaton is presented.%We show if $tilde{F}^*$ is an $(alpha, beta)$complete $(alpha, beta)$accessible deterministic maxmin intuitionistic general Lfuzzy automaton and it is recognizing $(alpha, beta)$language $mathcal{L}$, then the minimal $tilde{F}^*_{mathcal{L}}$ is homomorphism with threshold $(alpha, beta)$ to statewise $(alpha, beta)$minimal $tilde{F}_{m}^*$, where $tilde{F}_{m}^*$ is statewise $(alpha, beta)$equivalent to $tilde{F}^*$.Also, for a given intuitionistic general Lfuzzy automaton, we present two algorithms, which determinesstates of the minimal intuitionistic general Lfuzzy automaton and the statewise $(alpha, beta)$minimal intuitionistic general Lfuzzy automaton.Finally, by giving some examples, we comparison minimal intuitionistic general Lfuzzy automaton and statewise $(alpha, beta)$minimal intuitionistic general Lfuzzy automaton.
1

131
152


M.
Shamsizadeh
Department of Mathematics, Graduate University of Advanced
Technology, Kerman, Iran
Department of Mathematics, Graduate University
Iran


M. M.
Zahedi
Department of Mathematics, Graduate University of Advanced Tech
nology, Kerman, Iran
Department of Mathematics, Graduate University
Iran
zahedi_mm@ mail.uk.ac.ir
Minimal automata
$(alpha
beta)$language
Statewise minimal automata
Homomorphism with threshold $(alpha
beta)$
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SOFT TOPOLOGY AND SOFT PROXIMITY AS FUZZY PREDICATES BY FORMULAE OF LUKASIEWICZ LOGIC
2
2
In this paper, based in the L ukasiewicz logic, the definition offuzzifying soft neighborhood structure and fuzzifying soft continuity areintroduced. Also, the fuzzifying soft proximity spaces which are ageneralizations of the classical soft proximity spaces are given. Severaltheorems on classical soft proximities are special cases of the theorems weprove in this paper.
1

153
168


O. R.
Sayed
Department of Mathematics, Faculty of Science, Assiut University,
Assiut, Egypt
Department of Mathematics, Faculty of Science,
Egypt


R. A.
Borzooei
Department of Mathematics, Shahid Beheshti University, Tehran,
Iran
Department of Mathematics, Shahid Beheshti
Iran
borzooei@sbu.ac.ir
Soft set
Soft topology
Fuzzifying soft topology
Fuzzifying soft proximity
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