2006
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Cover Vol.3 No.2, October 2006
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Fuzzy sets form A metasystemtheoretic point of view
Fuzzy sets form A metasystemtheoretic point of view
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Amir
Daneshgar
Amir
Daneshgar
Iran
daneshgar@sharif.ir
Amir
Hashemi
Amir
Hashemi
France
Lfuzzu sets
Enriched category
I/O system theory
Morphological filtering
Translation invariant system
FUZZY OBSERVER DESIGN WITH nSHIFT MULTIPLE KEY FOR CRYPTOGRAPHY BASED ON 3D HYPERCHAOTIC OSCILLATOR
FUZZY OBSERVER DESIGN WITH nSHIFT MULTIPLE KEY FOR
CRYPTOGRAPHY BASED ON 3D HYPERCHAOTIC OSCILLATOR
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A fuzzy observer based scheme for synchronizing two hyperchaoticoscillators via a scalar transmitted signal for cryptographic application isproposed. The TakagiSugeno fuzzy model exactly represents chaotic systems.Based on the general fuzzy model, the fuzzy observer of a chaotic system isdesigned on the basis of the nshift multiple state based key encryption algorithm.The scalar transmitted signal is designed in such a way that the hyperchaoticcarrier masks the encrypted signal, which in turn hides the message signal.Simulation results show that the proposed scheme gives a better performanceeven when a small additive stochastic noise is present in the channel.
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A fuzzy observer based scheme for synchronizing two hyperchaoticoscillators via a scalar transmitted signal for cryptographic application isproposed. The TakagiSugeno fuzzy model exactly represents chaotic systems.Based on the general fuzzy model, the fuzzy observer of a chaotic system isdesigned on the basis of the nshift multiple state based key encryption algorithm.The scalar transmitted signal is designed in such a way that the hyperchaoticcarrier masks the encrypted signal, which in turn hides the message signal.Simulation results show that the proposed scheme gives a better performanceeven when a small additive stochastic noise is present in the channel.
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32
V.
NATARAJAN
V.
NATARAJAN
DEPARTMENT OF INSTRUMENTATION ENGINEERING, MIT CAMPUS, ANNA UNIVERSITY,
CHROMEPET, CHENNAL600044, INDIA
DEPARTMENT OF INSTRUMENTATION ENGINEERING,
India
natraj@mitindia.edu
P.
KANAGASABAPATHY
P.
KANAGASABAPATHY
DEPARTMENT OF INSTRUMENTATION ENGINEERING, MIT CAMPUS, ANNA
UNIVERSITY, CHROMEPET, CHENNAL600044, INDIA
DEPARTMENT OF INSTRUMENTATION ENGINEERING,
India
pks@mail.mitindia.edu
N.
SELVAGANESAN
N.
SELVAGANESAN
DEPARTMENT OF EEE, PONDICHERRY ENGINEERING COLLEGE, PONDICHERRY
605014, INDIA
DEPARTMENT OF EEE, PONDICHERRY ENGINEERING
India
n_selvag@rediffmail.com
P.
NATARAJAN
P.
NATARAJAN
DEPARTMENT OF INSTRUMENTATION ENGINEERING, MIT CAMPUS, ANNA UNIVERSITY,
CHROMEPET, CHENNAL600044, INDIA
DEPARTMENT OF INSTRUMENTATION ENGINEERING,
India
[[1] G. Álvarez and S. Li , Breaking network security based on synchronized chaos, Computer##Communications, Elsevier , 27 (2004), 16791681.##[2] G. Álvarez, S. Li, F. Montoya, M. Romera and G. Pastor, Breaking projective chaos##synchronization secure communication using filtering and generalized synchronization,##Chaos, Solitons & Fractuals, Elsevier, 24 (2005), 775783.##[3] G. Álvarez, F. Montoya, M. Romera and G. Pastor, Breaking two secure communication##systems based on chaotic masking, IEEE Transactions on Circuits and SystemsII,##51 (2004), 505506.##[4] T.S. Chiang and P. Liu, Fuzzy modelbased discretetime Chiang type chaotic cryptosystem,##IEEE Int. Fuzzy Systems Conference, 2001.##[5] G. Grassi and S. Mascolo, Observer design for cryptography based on hyperchaotic##oscillators, Electronics Letters, 34 (1998), 1844 1846.##[6] K. Halle, C. W. Wu, M. Itoh and L. O. Chua, Spread spectrum communication through##modulation of chaos, Int. Journal of Bifurcations and Chaos, 3 (1992), 469477.##[7] K.Y. Lian, C.S. Chiu, T.S. Chiang, and P. Liu, Secure communications of chaotic systems##with robust performance via fuzzy observerbased design, IEEE Transactions on Fuzzy##Systems, 9 (2001), 212220.##[8] K.Y. Lian, P. Liu and C.S. Chiu, Fuzzy modelbased approach to chaotic encryption##using synchronization, Int. Journal of Bifurcation and Chaos, 13 (2003), 215225.##[9] K.M. Ma, Observer design for a class of fuzzy systems, Proceedings of First International##Conference on Machine Learning and Cybernetics, Beijing, (2002), 4649.##[10] K. M. Short, Steps towards unmasking secure communication, Int. Journal of Bifurcation##and Chaos, 4 (1994), 959977.##[11] K. M. Short, Unmasking a modulated chaotic communications scheme, Int. Journal of##Bifurcation and Chaos, 6 (1996), 367375.##[12] A. Tamasevicius, G. Mykolaitis, A. Cenys and A. Namajunas, Synchronisation of 4D##hyperchaotic oscillators, Electronics Letters, 32 (1996), 15361538.##[13] A. Tamasevicius, A. Namajunas and A. Cenys, Simple 4D chaotic oscillator, Electronics##Letters, 32 (1996), 957958.##[14] T. Yang, C. Wah Wu and L. O. Chua, Cryptography based on chaotic systems, IEEE##Transactions on Circuits and SystemsI, 44 (1997), 469472.##]
DIRECT ADAPTIVE FUZZY PI SLIDING MODE CONTROL OF SYSTEMS
WITH UNKNOWN BUT BOUNDED DISTURBANCES
DIRECT ADAPTIVE FUZZY PI SLIDING MODE CONTROL OF SYSTEMS
WITH UNKNOWN BUT BOUNDED DISTURBANCES
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An asymptotically stable direct adaptive fuzzy PI sliding modecontroller is proposed for a class of nonlinear uncertain systems. In contrast toother existing approaches of handling disturbances, the proposed approachdoes not require this bound to be known, only requiring that it exists.Moreover, a PI control structure is used to attenuate chattering. The approachis applied to stabilize an openloop unstable nonlinear system as well asthe Duffing forcedoscillation chaotic nonlinear system amid significantdisturbances. Analysis of simulations reveals the effectiveness of the proposedmethod in terms of a significant reduction in chattering while maintainingasymptotic convergence.
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An asymptotically stable direct adaptive fuzzy PI sliding modecontroller is proposed for a class of nonlinear uncertain systems. In contrast toother existing approaches of handling disturbances, the proposed approachdoes not require this bound to be known, only requiring that it exists.Moreover, a PI control structure is used to attenuate chattering. The approachis applied to stabilize an openloop unstable nonlinear system as well asthe Duffing forcedoscillation chaotic nonlinear system amid significantdisturbances. Analysis of simulations reveals the effectiveness of the proposedmethod in terms of a significant reduction in chattering while maintainingasymptotic convergence.
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MOHAMMADREZA
AKBARZADEHTOTONCHI
MOHAMMADREZA
AKBARZADEHTOTONCHI
DEPARTMENT OF ELECTRICAL ENGINEERING, COLLEGE
OF ENGINEERING, FERDOWSI UNIVERSITY OF MASHHAD, MASHHAD, IRAN
DEPARTMENT OF ELECTRICAL ENGINEERING, COLLEGE
OF
Iran
akbarzadeh@ieee.org
REZA
SHAHNAZI
REZA
SHAHNAZI
DEPARTMENT OF ELECTRICAL ENGINEERING, COLLEGE OF ENGINEERING, FERDOWSI
UNIVERSITY OF MASHHAD, MASHHAD, IRAN
DEPARTMENT OF ELECTRICAL ENGINEERING, COLLEGE
Iran
shahnazi@ieee.org
Nonlinear control
Fuzzy logic
Sliding mode control
Uncertainty
External disturbances
Duffing forcedoscillation
Adaptive PI control
[[1] M.R. AkbarzadehT. and R. Shahnazi, Direct adaptive fuzzy PI sliding mode control for a##class of uncertain nonlinear systems, In Proceeding of IEEE International Conference on##Systems, Man and Cybernetics, (2005), 25662571.##[2] K. J. Astrom and B. Wittenmark, Adaptive control, second Edition, AddisonWesley Pub##Co, Newyork, December (1994).##[3] Y. Byungkook and H. Woonchul, Adaptive fuzzy sliding mode control of nonlinear systems,##IEEE Transaction Fuzzy systems, 6 (2) (1998).##[4] Z. M. Chen, J. G. Zhang, Z. C. Zhang and J. C. Zeng, Adaptive fuzzy sliding mode control##for uncertain nonlinear systems, In Proceeding of the Second International Conference##on Machine Learning and Cybernetics, Xian, 25 November (2003).##[5] Y. Guo and P. Y. Woo, Adaptive fuzzy sliding mode control for robotic manipulators, In##Proceeding of 42nd Conference on Decision and Control, Maui, Hawaii USA,##December (2003).##[6] H.G. Han and C. Y. Su, Further results on adaptive control of a class of nonlinear systems##with fuzzy logic, In Proceedings of IEEE Conference on Fuzzy Systems, Seoul, Korea,##(1999), 13091314.##[7] H. F. Ho, Y. K. Wong and A. B. Rad, Adaptive fuzzy sliding mode control design: Lyapunov##approach, In Proceeding of 5th Asian Control Conference, 3 (2004), 1502 1507.##[8] H. K. Khalil. Nonlinear systems, PrenticeHall Inc., second edition, (1996).##[9] Y. K. Kim and G. J. Jeon, Error reduction of sliding mode control using sigmoidtype##nonlinear interpolation in the boundary layer, International Journal of Control, and##Systems, 2 (4) (2004), 523529.##[10] C. C. Lee, Fuzzy logic in control systems: fuzzy logic controller, part I and part II, IEEE##Transactions on Systems, Man, and Cybernetics, 20 (1990), 404435.##[11] K. S. Narenda and A. M. Annaswamy, Stable adaptive systems, PrenticeHall Inc., (1989). ##[12] R. Shahnazi and M.R. AkbarzadehT., Robust PI adaptive fuzzy control for a class of##uncertain nonlinear systems, In Proceeding of IEEE International Conference on##Systems, Man and Cybernetics, (2005), 25482553.##[13] J. J. Slotine and W. Li, Applied nonlinear control, Prentice Hall, Inc.: Englewood Cliffs,##New Jersy, (1991).##[14] C. Y. Su and Y. Stepanenko, Adaptive control of a class of nonlinear systems with fuzzy##logic, IEEE Transactions on Fuzzy Systems, 2 (2) (1994), 285294.##[15] C. W. Tao, M.L. Chan and T. T. Lee, Adaptive fuzzy sliding mode controller for linear##systems with mismatched timevarying uncertainties, IEEE Transaction on Systems Man##and Cybernetics, Part B: Cybernetics, 33 (2)(2003).##[16] V. I. Utkin, Sliding modes and their application in variable structure systems, Moscow,##Russia: Mir, (1978).##[17] J. Wang, S. S. Get and T. H. Lee, Adaptive fuzzy sliding mode control of a class of nonlinear##systems, In Proceedings of the 3rd Asian Control Conference, Shanghai, July 47,##[18] L. X. Wang, A course in fuzzy systems and control, Prentice Hall., New Jersy, August##[19] L. X. Wang, Adaptive fuzzy systems and control: design and stability analysis, Prentice Hall,##Englewood Cliffs, NJ., (1994).##[20] L. X. Wang, Stable adaptive fuzzy control of nonlinear systems, IEEE Transaction on##Fuzzy systems, 1 (2) (1993).##]
SEMI $theta$COMPACTNESS IN INTUITIONISTIC FUZZY TOPOLOGICAL SPACES
SEMI $theta$COMPACTNESS IN INTUITIONISTIC FUZZY TOPOLOGICAL SPACES
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The purpose of this paper is to construct the concept of semi$theta$compactness in intuitionistic fuzzy topological spaces. We give some characterizationsof semi $theta$compactness and locally semi compactness. Also, wecompare these concepts with some other types of compactness in intuitionisticfuzzy topological spaces.
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The purpose of this paper is to construct the concept of semi$theta$compactness in intuitionistic fuzzy topological spaces. We give some characterizationsof semi $theta$compactness and locally semi compactness. Also, wecompare these concepts with some other types of compactness in intuitionisticfuzzy topological spaces.
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I. M.
Hanafy
I. M.
Hanafy
Department of Mathematics,
AlArish Faculty of Education, AlArish, Egypt.
Department of Mathematics,
AlArish Faculty
Egypt
ihanafy@hotmail.com
A. M.
Abd ElAziz
A. M.
Abd ElAziz
Department of Mathematics,
AlArish Faculty of Education, AlArish, Egypt.
Department of Mathematics,
AlArish Faculty
Egypt
T. M.
Salman
T. M.
Salman
Department of Mathematics,
AlArish Faculty of Education, AlArish, Egypt.
Department of Mathematics,
AlArish Faculty
Egypt
tarek00−salman@hotmail.com,tarek69salman@yahoo.com
[[1] K. Atanassov, Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, (1983)(in Bulgarian).##[2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 8796.##[3] D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems,##88(1997), 8189.##[4] D. Coker, An introduction to fuzzy subspaces in intuitionistic fuzzy topological spaces, Journal##of Fuzzy Math., 4(2)(1996), 749764.##[5] D. Coker and A. H. Es, On fuzzy compactness in intuitionistic fuzzy topological spaces,##Journal of Fuzzy Math., 3(4) (1995), 899909.##[6] D. Coker and M. Demirci, On intuitionistic fuzzy points, NIFS, 1(1995), 7984.##[7] H. Gurcay, D. Coker and A. H. Es, On fuzzy continuity in intuitionistic fuzzy topological##spaces, Journal of Fuzzy Math., 5(2) (1997), 365378.##[8] I. M. Hanafy, Completely continuous functions in intuitionistic fuzzy topological spaces,##Czechoslovak Math. Journal, 53(4)(2003), 793803.##[9] I. M. Hanafy, A. M. Abd El Aziz and T. M. Salman, Intuitionistic fuzzy − closure operator,##to appear in Bulletin of the Venezuelan Mathematical Society.##[10] I. M. Hanafy, A. M. Abd El Aziz and T. M. Salman, Semi − continuity in intuitionistic##fuzzy topological spaces, Bull. Malays. Math. Sci. Soc., (2) 29(1) (2006), 110.##[11] L. A. Zadeh, Fuzzy sets, Infor. and Control, 9(1965), 338353.##]
INTERVALVALUED FUZZY BALGEBRAS
INTERVALVALUED FUZZY BALGEBRAS
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In this note the notion of intervalvalued fuzzy Balgebras (briefly,iv fuzzy Balgebras), the level and strong level Bsubalgebra is introduced.Then we state and prove some theorems which determine the relationshipbetween these notions and Bsubalgebras. The images and inverse images ofiv fuzzy Bsubalgebras are defined, and how the homomorphic images andinverse images of iv fuzzy Bsubalgebra becomes iv fuzzy Balgebras arestudied.
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In this note the notion of intervalvalued fuzzy Balgebras (briefly,iv fuzzy Balgebras), the level and strong level Bsubalgebra is introduced.Then we state and prove some theorems which determine the relationshipbetween these notions and Bsubalgebras. The images and inverse images ofiv fuzzy Bsubalgebras are defined, and how the homomorphic images andinverse images of iv fuzzy Bsubalgebra becomes iv fuzzy Balgebras arestudied.
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Arsham
Borumand Saeid
Arsham
Borumand Saeid
Dept. of Mathematics, Islamic Azad University, Kerman
Branch, Kerman, Iran
Dept. of Mathematics, Islamic Azad University,
Iran
arsham@iauk.ac.ir
[[1] R. Biswas, Rosenfeld’s fuzzy subgroups with interval valued membership function, Fuzzy Sets##and Systems, 63 , 1(1994), 8790.##[2] A. Borumand Saeid, Fuzzy topological Balgebras, (Submitted ).##[3] S. M. Hong, Y. B. Jun, S. J. Kim and G. I. Kim, Fuzzy BCIsubalgebras with intervalvalued##membership functions, IJMMS., 25, 2 (2001), 135143.##[4] Y. Imai and K. Iseki, On axiom systems of propositional calculi, XIV Proc. Japan Academy,##42 (1966), 1922.##[5] Y. B. Jun, E. H. Roh, Chinju and H. S. Kim, On Fuzzy Balgebras, Czechoslovak Math.##Journal, 52 (2002), 375384.##[6] J. Meng and Y.B. Jun, BCKalgebras, Kyung Moonsa, Seoul, Korea, (1994).##[7] J. Neggers and H. S. Kim, On Balgebras, Math. Vensik, 54 (2002), 2129.##[8] , On dalgebras, Math. Slovaca, 49 (1999), 1926.##[9] A. Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl., 35 (1971), 512517.##[10] L. A. Zadeh, Fuzzy Sets, Inform. Control, 8 (1965), 338353.##[11] , The concept of a linguistic variable and its application to approximate reasoning. I,##Information Sci., 8 (1975), 199249.##]
FUZZY SUBGROUPS AND CERTAIN EQUIVALENCE RELATIONS
FUZZY SUBGROUPS AND CERTAIN EQUIVALENCE RELATIONS
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In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a group homomorphism.
1
In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a group homomorphism.
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91
APARNA
JAIN
APARNA
JAIN
DEPARTMENT OF MATHEMATICS, SHIVAJI COLLEGE, UNIVERSITY OF DELHI, NEW DELHI,
INDIA
DEPARTMENT OF MATHEMATICS, SHIVAJI COLLEGE,
India
jainaparna@yahoo.com
Fuzzy subgroup
Equivalence relation
Lattice
$alpha$– cut
Strong $alpha$– cut
Homomorphism
[[1] N. Ajmal, Homomorphism of fuzzy groups, correspondence theorem and fuzzy quotient##groups, Fuzzy Sets and Systems, 61 (1994), 329339.##[2] N. Ajmal, Fuzzy group theory : A comparison of different notions of product of fuzzy sets,##Fuzzy Sets and Systems, 110 (2000), 437446.##[3] N. Ajmal and K. V. Thomas, The lattices of fuzzy subgroups and fuzzy normal subgroups,##Inform. Sci., 76 (1994), 111.##[4] N. Ajmal, The lattice of fuzzy normal subgroups is modular, Inform. Sci., 83 (1995), 199##[5] N. Ajmal and K. V. Thomas, The lattices of fuzzy ideals of a ring, Fuzzy Sets and##Systems, 74 (1995), 371379.##[6] P. S. Das, Fuzzy groups and level subgroups, Journal of Math. Anal. Appl., 84 (1981),##[7] C. Degang, J. Jiashang, W. Congxin and E. C. C. Tsang, Some notes on equivalent fuzzy##sets and fuzzy subgroups, Fuzzy Sets and Systems, 152 (2005), 403409.##[8] V. N. Dixit, R. Kumar and N. Ajmal, Level subgroups and union of fuzzy subgroups, Fuzzy##Sets and Systems, 37 (1990), 359371.##[9] A. Jain and N. Ajmal, A new approach to the theory of fuzzy groups, Journal of Fuzzy##Math., 12 (2) (2004), 341355.##[10] A. Jain, Tom Head’s join structure of fuzzy subgroups, Fuzzy Sets and Systems, 125 (2002),##[11] J. G. Kim and S. J. Cho, Structure of a lattice of fuzzy subgroups, Fuzzy Sets and Systems,##89 (1997), 263266.##[12] M. Mashinchi and M. Mukaidono, A classification of fuzzy subgroups, Ninth Fuzzy##System Symposium, Sapporo, Japan, (1992), 649652.##[13] M. Mashinchi and M. Mukaidono, On fuzzy subgroups classification, Research report of##Meiji University, Japan, 9 (65) (1993), 3136.##[14] M. Mashinchi and M. M. Zahedi, A counter example of P. S. Das’s paper, Journal of##Math. Anal. & Appl., 153 (2) (1990), 591592.##[15] J. N. Mordeson, Lecture notes in fuzzy mathematics and computer science, LSubspaces##and LSubfields, Creighton University, Omaha, Nebraska 68178 USA, 1996.##[16] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups I, Fuzzy Sets and##Systems, 123 (2001), 259264.##[17] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups II, Fuzzy Sets and##Systems, 136 (2003), 93104. ##[18] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups III, The International##Journal of Math. And Math. Sciences, 36 (2003), 23032313.##[19] S. Ray, Isomorphic fuzzy groups, Fuzzy Sets and Systems, 50 (1992), 201207.##[20] A. Rosenfeld, Fuzzy groups, Journal of Math. Anal. Appl., 35 (1971), 512517.##[21] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##]
Persiantranslation Vol.3 No.2, October 2006
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