ORIGINAL_ARTICLE
Cove vol.6, no.3, October 2009
http://ijfs.usb.ac.ir/article_2895_46b90c9ca9a90b578f53385ed682e689.pdf
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10.22111/ijfs.2009.2895
ORIGINAL_ARTICLE
MINIMUM TIME SWING UP AND STABILIZATION OF
ROTARY INVERTED PENDULUM USING PULSE STEP
CONTROL
This paper proposes an approach for the minimum time swing upof a rotary inverted pendulum. Our rotary inverted pendulum is supported bya pivot arm. The pivot arm rotates in a horizontal plane by means of a servomotor. The opposite end of the arm is instrumented with a joint whose axisis along the radial direction of the motor. A pendulum is suspended at thejoint. The task is to design a controller that swings up the pendulum, keepsit upright and maintains the arm position. In the general intelligent hybridcontroller, a PD controller with a positive feedback is designed for swinging upand a fuzzy balance controller is designed for stabilization. In order to achievethe swing up in a minimal time, a controller named Minimum Time IntelligentHybrid Controller is proposed which is precisely a PD controller together witha pulse step controller for swinging up along with the fuzzy balance controllerfor stabilization. The impulsive control action is tuned by trial and errorto achieve the minimum-time swing-up. An energy based switching controlmethod is proposed to switch over from swing up mode to stabilization mode.Extensive computer simulation results demonstrate that the swing up timeof the proposed minimum-time controller is significantly less than that of theexisting general hybrid nonlinear controller.
http://ijfs.usb.ac.ir/article_197_db94d0141b1671df88589cda49c3502e.pdf
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10.22111/ijfs.2009.197
Fuzzy logic control (FLC)
Rotary inverted pendulum (RIP)
Swing up
control
PD control
Energy based switching control
Hybrid control and Minimum-time control
P
Melba Mary
melbance 2k4@yahoo.co.in
true
1
Anna University, Department of Electrical and Electronics Engineering,
TamilNadu, India
Anna University, Department of Electrical and Electronics Engineering,
TamilNadu, India
Anna University, Department of Electrical and Electronics Engineering,
TamilNadu, India
LEAD_AUTHOR
N. S.
Marimuthu
drnsmphd@yahoo.co.in
true
2
Anna University, Department of Electrical and Electronics Engineering,
TamilNadu, India
Anna University, Department of Electrical and Electronics Engineering,
TamilNadu, India
Anna University, Department of Electrical and Electronics Engineering,
TamilNadu, India
AUTHOR
[1] K. J. Astrom and K. Furuta, Swinging up a pendulum by energy control, Automatica, 36
1
(2000), 287-295.
2
[2] http://people.msoe.edu/˜saadat/download/3 Inverted Pendulum Project.pdf
3
[3] H. K. Lam, F. H. Leung and P. K. S. Tam, Design and stability analysis of fuzzy model-based
4
nonlinear controller for nonlinear systems using genetic algorithm, IEEE Trans. on Systems,
5
Man and Cybernetics, Part B, 33(2) (2003), 250-257.
6
[4] Z. G. Li, C. Y. Wen and Y. C. Soh , Analysis and design of impulsive control systems, IEEE
7
Trans. on Automatic Control, 46(6) (2001), 894-897.
8
[5] C. M. Lin and Y. J. Mon, Decoupling control by hierarchical fuzzy sliding-mode controller,
9
IEEE Trans. on Control Systems Technology, 13(4) (2005), 593-598.
10
[6] N. Muskinja and B. Tovornik, Swinging up and Stabilization of a real inverted pendulum,
11
IEEE Trans. on Industry electronics, 53(2) (2006), 631-639.
12
[7] S. Nudrakwang, T. Benjanarasuth, J. Ngamwiwit and N. Komine, Hybrid PD-servo state
13
feedback control algorithm for swing up inverted pendulum system, Proceedings of the ICCAS,
14
2(5) (2005), 690-693.
15
[8] S. Nudrakwang, T. Benjanarasuth, J. Ngamwiwit and N. Komine, Hybrid controller for
16
Swinging up Inverted Pendulum System, Proceedings of the IEEE, ICICS (2005), 488-492.
17
[9] G. N. Silva and R. B. Vinter, Necessary conditions for optimal impulsive control problems,
18
SIAM Journal on Control and Optimization, 35(6) (1997), 1829-1846.
19
[10] W. Torres-Pomales and O. R. Gonzalez, Nonlinear control of swing-up inverted pendulum,
20
Proceedings of the IEEE International Conference on Control Application, (1996), 259-264.
21
[11] A. Wallen and K. J. Astrom, Pulse -step control, Proceedings of the 15th IFAC Triennial
22
World Congress, Barcelona, Spain, 2002.
23
[12] C. H. Wang, T. C. Lin, T. T. Lee and H. L. Liu, Adaptive hybrid intelligent control for
24
uncertain nonlinear dynamical systems, IEEE Trans. on Systems, Man and Cybernetics,
25
Part B, 32 (5) (2002), 583-597.
26
[13] S. Weibel, G. W. Howell and J. Baillieul, Control of single-degree-of-freedom Hamiltonian
27
systems with impulsive inputs, Proceedings of the 35th IEEE Conference on Decision and
28
Control, Kobe, Japan, (1996), 4661-4666.
29
[14] M. Yamakita, et.al., Robust swing up control of double pendulum, Proceedings of the American
30
Control Conference, 1 (1995), 290-295.
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[15] T. Yang, Impulsive control, IEEE Trans. Autom. Contr, 44 (1999), 1081-1083.
32
[16] S. Yasunobu and M. Mori, Swing up fuzzy controller for inverted pendulum based on a human
33
control strategy, Proceedings of the Sixth IEEE International Conference on Fuzzy Systems,
34
3 (1997), 1621-1625.
35
[17] J. Yi, N. Yubazaki and K. Hirota, A new fuzzy controller for stabilization of parallel-type
36
double inverted pendulum system, Fuzzy Sets and Systems, 126(1) (2002), 105-119.
37
[18] J. Yi, N. Yubazaki and K. Hirota, Upswing and stabilization control of inverted pendulum
38
system based on the SIRMs dynamically connected fuzzy inference model, Fuzzy Sets and
39
Systems, 122 (2001), 139-152.
40
[19] K. Yoshida, Swing up control of an inverted pendulum by energy based methods, Proceedings
41
of the American Control Conference, 6 (1999), 4045- 4047.
42
ORIGINAL_ARTICLE
FUZZY LINEAR PROGRAMMING WITH GRADES OF
SATISFACTION IN CONSTRAINTS
We present a new model and a new approach for solving fuzzylinear programming (FLP) problems with various utilities for the satisfactionof the fuzzy constraints. The model, constructed as a multi-objective linearprogramming problem, provides flexibility for the decision maker (DM), andallows for the assignment of distinct weights to the constraints and the objectivefunction. The desired solution is obtained by solving a crisp problemcontrolled by a parameter. We establish the validity of the proposed modeland study the effect of the control parameter on the solution. We also illustratethe efficiency of the model and present three algorithms for solving theFLP problem, the first of which obtains a desired solution by solving a singlecrisp problem. The other two algorithms, interact with the decision maker,and compute a solution which achieves a given satisfaction level. Finally, wepresent an illustrative example showing that the solutions obtained are ofteneven more satisfactory than asked for.
http://ijfs.usb.ac.ir/article_198_7226b83fe87443caa21599dac85680c6.pdf
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10.22111/ijfs.2009.198
Fuzzy linear programming
Fuzzy constraints
Multi-objective linear
programming
Nikbakhsh
Javadian
nijavadian@ustmb.ac.ir
true
1
Department of Industrial Engineering, Mazandaran University
of Science and Technology, Babol, Iran
Department of Industrial Engineering, Mazandaran University
of Science and Technology, Babol, Iran
Department of Industrial Engineering, Mazandaran University
of Science and Technology, Babol, Iran
AUTHOR
Yashar
Maali
y_maali@ustmb.ac.ir
true
2
Department of Industrial Engineering, Mazandaran University of
Science and Technology, Babol, Iran
Department of Industrial Engineering, Mazandaran University of
Science and Technology, Babol, Iran
Department of Industrial Engineering, Mazandaran University of
Science and Technology, Babol, Iran
AUTHOR
Nezam
Mahdavi-Amiri
nezamm@sharif.edu
true
3
Department of Mathematical Sciences, Sharif University of
Technology, P.O. Box 11365-9415, Tehran, Iran
Department of Mathematical Sciences, Sharif University of
Technology, P.O. Box 11365-9415, Tehran, Iran
Department of Mathematical Sciences, Sharif University of
Technology, P.O. Box 11365-9415, Tehran, Iran
LEAD_AUTHOR
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1
17 (1970), 141-164.
2
[2] V. J. Bowman, On the relationship of the Tchebycheff norm and the efficient frontier of multicriteria
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objectives, In: H. Thiriez and S. Zionts (Eds.), Multiple Criteria Decision Making,
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Springer-Verlag, Berlin, 1976, 76-86.
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[3] J. M. Cadenas and J. L. Verdegay, A primer on fuzzy optimization models and methods,
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and Mathematics with Applications, 37 (1999), 63-76.
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12
problems, Fuzzy Sets and Systems, 107 (1999), 191-195.
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[7] U. Keymak and J. M. Sousa, Weighting of constraint in fuzzy optimization, Proceedings of
14
the 10th IEEE International Conference on Fuzzy Systems, 3 (2001), 1131-1134.
15
[8] K. Kosaka, H. Nonaka, M. F. Kawaguchi and T. Datet, The application of fuzzy linear
16
programming to flow control of crossing gate network, Proceeding of the 9th Fuzzy System
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Symposium: Sapporo, (1993), 189-182.
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[9] Y. J. Lai and C. L. Hwang, Fuzzy mathematical programming, Springer, Berlin, 1992.
19
[10] F. Li, M. Liu, C. Wu and S. Lou, Fuzzy optimization problems based on inequality degree,
20
Proceedings of the First International Conference on Machine Learning and Cybernetics:
21
Beijing, (2002), 1566-1570.
22
[11] X. Q. Li, B. Zhang and H. Li, Computing efficient solutions to fuzzy multiple objective linear
23
programming problems, Fuzzy Sets and Systems, 157 (2006), 1328-1332.
24
[12] N. Mahdavi-Amiri and S. H. Nasseri, Duality results and a dual simplex method for linear
25
programming problems with trapezoidal variables, Fuzzy Sets and Systems, 158 (2007), 1961-
26
[13] H. R. Maleki, M. Tata and M. Mashinchi, Linear programming with fuzzy variables, Fuzzy
27
Sets and Systems, 109 (2000), 21-33.
28
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30
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31
with grade of satisfaction in each constraint, Proceedings of the Joint Fourth IEEE
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International Conference on Fuzzy Systems and the Second International Fuzzy Engineering
33
Symposium, (1995), 781-786.
34
[16] J. R. Ramik and H. Rommelfanger, Fuzzy mathematical programming based on some new
35
inequality relations, Fuzzy Sets and Systems, 81 (1996), 77-87.
36
[17] H. Rommelfanger, Fuzzy linear programming and applications, European Journal of Operational
37
Research, 92 (1996), 512-527.
38
[18] M. Sakawa, Fuzzy sets and interactive multiobjective optimization, Plenum Press: New York
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and London, 1993.
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3 (1974), 37-46.
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Approximate Reasoning in Decision Analysis, North-Holland: Amsterdam, 1982, 231-236.
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[21] B. Werners, An interactive fuzzy programming system, Fuzzy Sets and Systems, 23 (1987),
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[22] B. Werners, Interactive multiple objective programming subject to flexible constraints, European
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47
[23] B. Werners, Aggregation models in mathematical programming, In: G. Mitra (Ed.), Mathematical
48
Models for Decision Support, Springer, Berlin, (1988), 295-305.
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[24] Y. K. Wu, On the manpower allocation within matrix organization: a fuzzy linear programming
50
approach, European Journal of Operational Research, 183(1) (2007), 384-393.
51
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52
Sets and Systems, 122 (2001), 263-275.
53
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54
[27] H. J. Zimmermann, Description and optimization of fuzzy systems, International Journal of
55
General Systems, 2 (1976), 209-215.
56
ORIGINAL_ARTICLE
FUZZY TRANSPOSITION HYPERGROUPS
In this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.We also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.
http://ijfs.usb.ac.ir/article_199_4d70cb34aa0aa3c138225bb4f4a84eb9.pdf
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10.22111/ijfs.2009.199
Semihypergroup
Fuzzy semihypergroup
Fuzzy hypergroup
Fuzzy
transposition hypergroup
Fuzzy subsemihypergroup
Fuzzy subhypergroup
Fuzzy closed set
Fuzzy reflexive subsemihypergroup
Fuzzy normal subsemihypergroup
Fuzzy regular relation
Fuzzy quotient hypergroup
Goutam
Chowdhury
chowdhurygoutam@yahoo.com
true
1
Department of Mathematics, Derozio Memorial College
Rajarhat Road, Kolkata-700136, India
Department of Mathematics, Derozio Memorial College
Rajarhat Road, Kolkata-700136, India
Department of Mathematics, Derozio Memorial College
Rajarhat Road, Kolkata-700136, India
LEAD_AUTHOR
[1] R. Ameri and M. M. Zahedi, Hypergroup and join spaces induced by a fuzzy subset, Pure
1
Mathematics and Applications, 8 (1997), 155-168.
2
[2] R. Ameri, Fuzzy (transposition) hypergroups, Italian Journal of Pure and Applied mathematics
3
(to appear).
4
[3] P. Corsini, Prolegomena of hypergroup theory, Aviani Editore, 1979.
5
[4] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publications,
6
ISBN 1402012225 (2003).
7
[5] P. Corsini and V. Leoreanu, Fuzzy sets and join spaces associated with rough sets, Rend.
8
Circ. Mat., Palermo, 51 (2002), 527-536.
9
[6] P. Corsini and I. Tofan, On fuzzy hypergroups, Pure Mathematics and Applications, 8 (1997),
10
[7] B. Davvaz, Fuzzy Hv-groups, Fuzzy Sets and Systems, 101 (1999), 191-195.
11
[8] J. Jantosciak, Transposition hypergroups: noncommutative join spaces, Journal of Algebra,
12
187 (1997), 97-119.
13
[9] A. Kehagias, L-fuzzy join and meet hyperoperations and the associated L-fuzzy hyperalgebras,
14
Rend. Circ. Mat., Palermo, 51 (2002), 503-526.
15
[10] V. Leoreanu, Direct limit and inverse limit of join spaces associated with fuzzy sets, Pure
16
Math. Appl., 11 (2000), 509-512.
17
[11] F. Marty, Sur une generalization de la notion de groupe, 8ieme Congres des Mathematiciens
18
Scandinaves, Stockholm, (1934), 45-49.
19
[12] V. Murali, Fuzzy equivalence relations, Fuzzy Sets and System, 30 (1989), 155-163.
20
[13] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
21
[14] M. K. Sen, R. Ameri and G. Chowdhury, Fuzzy hypersemigroups, Soft Computing, 12(9)
22
(2008), 891-900.
23
[15] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338-353.
24
[16] M. M. Zahedi, M. Bolurian and A. Hasankhani, On polygroups and fuzzy subpolygroups, J.
25
of Fuzzy Mathematics, 1 (1995), 1-15.
26
[17] M. M. Zahedi and R. Ameri, On the prime, primary and maximal subhypermodules, Italian
27
Journal of Pure and Applied Mathematics, 5 (1999), 61-80.
28
ORIGINAL_ARTICLE
Some types of $(\in,\ivq)$-interval-valued fuzzy
ideals of BCI algebras
In this paper, we introduce the notions of interval-valued and $(\in,\ivq)$-interval-valued fuzzy ($p$-,$q$- and $a$-) ideals of BCI algebras and investigate some of their properties. We then derive characterization theorems for these generalized interval-valued fuzzy ideals and discuss their relationship.
http://ijfs.usb.ac.ir/article_200_da5a23de010339b6dc1ec0f1cf5a965c.pdf
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63
10.22111/ijfs.2009.200
Xueling.
Ma
true
1
Department of Mathematics, Hubei Institute for Nationalities,
Enshi, Hubei Province,445000, P. R. China
Department of Mathematics, Hubei Institute for Nationalities,
Enshi, Hubei Province,445000, P. R. China
Department of Mathematics, Hubei Institute for Nationalities,
Enshi, Hubei Province,445000, P. R. China
AUTHOR
Jianming.
Zhan
zhanjianming@hotmail.com
true
2
Department of Mathematics, Hubei Institute for Nationalities,
Enshi, Hubei Province,445000, P. R. China
Department of Mathematics, Hubei Institute for Nationalities,
Enshi, Hubei Province,445000, P. R. China
Department of Mathematics, Hubei Institute for Nationalities,
Enshi, Hubei Province,445000, P. R. China
AUTHOR
Young Bea
Jun
skywine@gmail.com
true
3
Department of Mathematics Education, Gyeongsang National University,
Chinju 660-701, Korea
Department of Mathematics Education, Gyeongsang National University,
Chinju 660-701, Korea
Department of Mathematics Education, Gyeongsang National University,
Chinju 660-701, Korea
LEAD_AUTHOR
[1] S. K. Bhakat, (2, 2_ q)-fuzzy normal, quasinormal and maximal subgroups, Fuzzy Sets and
1
Systems, 112 (2000), 299-312.
2
[2] S. K. Bhakat and P. Das, (2, 2 _ q)-fuzzy subgroups, Fuzzy Sets and Systems, 80 (1996),
3
[3] R. Biswas, Rosenfeld’s fuzzy subgroups with interval- valued membership functions, Fuzzy
4
Sets and Systems, 63 (1994), 87-90.
5
[4] B. Davvaz, (2, 2 _q)-fuzzy subnear-rings and ideals, Soft Computing, 10 (2006), 206-211.
6
[5] B. Davvaz and P. Corsini, Redefined fuzzy Hv-submodules and many valued implications,
7
Inform. Sci., 177 (2007), 865-875.
8
[6] B. Davvaz and P. Corsini, On (, )-fuzzy Hv-ideals of Hv-rings, Iranian J. Fuzzy Systems,
9
5(2) (2008), 35-48.
10
[7] W. A. Dudek, On group-like BCI-algebras, Demonstratio Math., 21 (1998), 369-376.
11
[8] W. A. Dudek and J. Thomys, On decompositions of BCH-algebras, Math. Japon., 35 (1990),
12
1131-1138.
13
[9] G. Deschrijver, Arithmetric operators in interval-valued fuzzy theory, Inform. Sci., 177
14
(2007), 2906-2924.
15
[10] F. Esteva and L. Godo, Monoidal t-norm based logic: towards a logic for left-continuous
16
t-norms, Fuzzy Sets and Systems, 124 (2001), 271- 288.
17
[11] P. H´ajek, Metamathematics of fuzzy logic, Kluwer Academic Press, Dordrecht, 1998.
18
[12] Y. Imai and K. Is´eki, On axiom system of propositional calculus, Proc. Japan Acad., 42
19
(1966), 19-22.
20
[13] A. Iorgulescu, Some direct ascendents of Wajsberg and MV algebras, Sci. Math. Japon., 57
21
(2003), 583-647.
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[14] A. Iorgulescu, Iseki algebras, connection with BL algebras, Soft Computing, 8 (2004), 449-
23
[15] K. Is´eki, An algebra related with a propositional calculus, Proc. Japan Acad., 42 (1966),
24
[16] K. Is´eki, On BCI-algebras, Math. Seminar Notes (now Kobe Math J.), 8 (1980), 125-130.
25
[17] K. Is´eki and S. Tanaka, Ideal theory of BCK-algebras, Math. Japon., 21 (1966), 351-366.
26
[18] K. Is´eki and S. Tanaka, An introduction to the theory of BCK- algebras, Math. Japon., 23
27
(1978), 1-26.
28
[19] Y. B. Jun, Interval-valued fuzzy subalgebras/ideals in BCK-algebras, Sci. Math., 3 (2000),
29
[20] Y. B. Jun, Interval-valued fuzzy ideals in BCI- algebras, J. Fuzzy Math., 9 (2001), 807-814.
30
[21] Y. B. Jun, On (, )-fuzzy ideals of BCK/BCI- algebras, Sci. Math. Japon., 60 (2004),
31
[22] Y. B. Jun, On (, )-fuzzy subalgebras of BCK/BCI-algebras, Bull. Korean Math. Soc., 42
32
(2005), 703-711.
33
[23] Y. B. Jun and J. Meng, Fuzzy p-ideals in BCI-algebras, Math. Japon, 40 (1994), 271-282.
34
[24] Y. B. Jun and J. Meng, Fuzzy commutative ideals in BCI-algebras, Comm. Korean Math.
35
Soc., 9 (1994), 19-25.
36
[25] Y. L. Liu and J. Meng, Fuzzy q-ideals of BCI-algebras, J. Fuzzy Math., 8 (2000), 873-881.
37
[26] Y. L. Liu and J. Meng, Fuzzy ideals in BCI-algebras, Fuzzy Sets and Systems, 123 (2001),
38
[27] Y. L. Liu, J. Meng, X. H. Zhang and Z. C. Yue, q-ideals and a-ideals in BCI-algebras, SEA
39
Bull. Math., 24 (2000), 243-253.
40
[28] Y. L. Liu, Y. Xu and J. Meng, BCI-implicative ideals of BCI-algebras, Inform. Sci., 177
41
(2007), 4987-4996.
42
[29] Y. L. Liu and X. H. Zhang, Fuzzy a-ideals in BCI-algebras, Adv. in Math. (China), 31 (2002),
43
[30] X. Ma, J. Zhan, B. Davvaz and Y. B. Jun, Some kinds of (2, 2 _ q)-interval-valued fuzzy
44
ideals of BCI-algebras, Inform. Sci., 178 (2008), 3738-3754.
45
[31] P. M. Pu and Y. M. Liu, Fuzzy topology I: Neighourhood structure of a fuzzy point and
46
Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571-599.
47
[32] A. B. Saeid and Y. B. Jun, Redefined fuzzy subalgebras of BCK/BCI-algebras, Iranian J.
48
Fuzzy Systems, 5(2) (2008), 63-70.
49
[33] L. Torkzadeh, M. Abbasi and M. M. Zahedi, Some results of intuitionistic fuzzy weak dual
50
hyper K-ideals, Iranian J. Fuzzy Systems, 5(1) (2008), 65-78.
51
[34] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.
52
[35] J. Zhan and Z. Tan, Intuitionistic fuzzy a-ideals in BCI- algebras, Soochow Math. J., 30
53
(2004), 207-216.
54
ORIGINAL_ARTICLE
EMBEDDING OF THE LATTICE OF IDEALS OF A RING INTO
ITS LATTICE OF FUZZY IDEALS
We show that the lattice of all ideals of a ring $R$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. For this purpose, we introduce the concept of the generalizedcharacteristic function $\chi _{s}^{r} (A)$ of a subset $A$ of a ring $R$ forfixed $r , s\in [0,1] $ and show that $A$ is an ideal of $R$ if, and only if, its generalizedcharacteristic function $\chi _{s}^{r} (A)$ is a fuzzy ideal of $R$. We alsoshow that the set of all generalized characteristic functions $C_{s}^{r}(I(R))$ of the members of $I(R)$ for fixed $r , s\in [0,1] $ is acomplete sublattice of the lattice of all fuzzy ideals of $R$ and establishthat this latter lattice is generated by the union of allits complete sublattices $C_{s}^{r} (I(R))$.
http://ijfs.usb.ac.ir/article_201_bd470dfb2a74278bd4d77763cb364c23.pdf
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71
10.22111/ijfs.2009.201
Algebra
Ideal of a ring
Morphism
Embedding
Lattice
Iffat
Jahan
ij.umar@yahoo.com
true
1
Department of Mathematics, Ramjas College, University Of Delhi,
Delhi, India
Department of Mathematics, Ramjas College, University Of Delhi,
Delhi, India
Department of Mathematics, Ramjas College, University Of Delhi,
Delhi, India
LEAD_AUTHOR
[1] N. Ajmal and K. V. K. Thomas, The lattice of fuzzy subgroups and fuzzy normal subgroups,
1
Information Sci., 76 (1994), 1-11.
2
[2] T. Head, A metatheorem for deriving fuzzy theorems from crisp versions, Fuzzy Sets and
3
Systems, 73 (1995), 349-358.
4
[3] L. Wangjin, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982),
5
[4] D. S. Malik and J. N. Mordeson, Radicals of fuzzy ideals, Information Sci., 65 (1992) 23,
6
[5] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
7
[6] A. Weinberger, Embedding lattices of fuzzy subalgebras into lattices of crisp sub-algebras,
8
Information Sci., 108 (1998), 51-70.
9
ORIGINAL_ARTICLE
FUZZY BOUNDED SETS AND TOTALLY FUZZY BOUNDED
SETS IN I-TOPOLOGICAL VECTOR SPACES
In this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. Thena relation between totally fuzzy bounded sets and N-compactness is discussed.Finally, a geometric characterization for fuzzy totally bounded sets in I- topologicalvector spaces is derived.
http://ijfs.usb.ac.ir/article_202_64a93cd049b93f2b635f02575c9de600.pdf
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73
90
10.22111/ijfs.2009.202
I-topological vector space
Fuzzy bounded set
Totally fuzzy bounded
set
N-compact set
Shen-Qing
Jiang
jsq288@163.com
true
1
Institute of Math., school of Math. and Computer Sciences, Nanjing
Normal University, Nanjing Jiangsu 210046, People0 s Republic of China
Institute of Math., school of Math. and Computer Sciences, Nanjing
Normal University, Nanjing Jiangsu 210046, People0 s Republic of China
Institute of Math., school of Math. and Computer Sciences, Nanjing
Normal University, Nanjing Jiangsu 210046, People0 s Republic of China
AUTHOR
Cong-hua
Yan
chyan@njnu.edu.cn
true
2
Institute of Math., school of Math. and Computer Sciences, Nanjing
Normal University, Nanjing Jiangsu 210046, People0 s Republic of China
Institute of Math., school of Math. and Computer Sciences, Nanjing
Normal University, Nanjing Jiangsu 210046, People0 s Republic of China
Institute of Math., school of Math. and Computer Sciences, Nanjing
Normal University, Nanjing Jiangsu 210046, People0 s Republic of China
LEAD_AUTHOR
[1] S. Z. Bai, Some properties of near SR -compactness, Iranian Journal of Fuzzy Systems, 4(2)
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(2007), 83-87.
2
[2] J. X. Fang, On local bases of fuzzy topological vector space, Fuzzy Sets and Systems, 87
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(1997), 341-347.
4
[3] J. X. Fang, On I-topology generated by fuzzy norm, Fuzzy Sets and Systems, 157(20)
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(2006), 2739-2750.
6
[4] J. X. Fang and C. H. Yan, L-fuzzy topological vector spaces, J. Fuzzy Math., 5(1) (1997),
7
[5] U. H¨ohle and S. E. Rodabaugh(Eds.), Mathematics of fuzzy set: logic, topology and measure
8
theory, the handbook of fuzzy sets series, Kluwer Academic Publisher, Dordrecht, 3 (1999).
9
[6] A. K. Katsaras, Fuzzy topological vector spaces I, Fuzzy Sets and Systems, 6 (1981), 85-95.
10
[7] A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984),
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[8] A. K. Katsaras and D. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, J.
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Math. Anal. Appl., 58 (1997) 135-146.
13
[9] Y. M. Liu and M. K. Luo, Fuzzy topology, World Scientific Publishing, Singapore, 1997.
14
[10] A. Narayanan and S. Vijayabalaji, Intuitionistic fuzzy bounded linear operators, Iranian
15
Journal of Fuzzy Systems, 4(1) (2007), 89-101.
16
[11] P. M. Pu and Y. M. Liu, Fuzzy topology I, neighborhood structure of a fuzzy point and
17
Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571-599.
18
[12] D. W. Qiu, Fuzzifying topological linear spaces, Fuzzy Sets and Systems, 147 (2004), 249-272.
19
[13] G. J. Wang, A new compactness defined by fuzzy sets, J. Math. Anal. Appl., 94 (1983), 1-23.
20
[14] R. H. Warren, Neighborhoods bases and continuity in fuzzy topological spaces, Rocky Mountain
21
J. Math., 8 (1978), 459-470.
22
[15] C. X. Wu and J. X. Fang, A new definition of Fuzzy topological vector space, Science
23
Exploration (China), 4 (1982), 113-116.
24
[16] J. R. Wu, Fuzzy totally bounded sets, J. Suzhou Institute of Urban Construction and Environment
25
Protection (China), 11 (1998), 8-12.
26
[17] C. H. Yan, Two generating mappings !L and L in complete lattices TVS and LFTVS., J.
27
Fuzzy Math., 6(3) (1998) 745-750.
28
[18] C. H. Yan and J. X. Fang, Generalization of Kolmogoroff’s theorem to L-topological vector
29
spaces, Fuzzy Sets and Systems, 125(2) (2002), 177-183.
30
[19] C. H. Yan and J. X. Fang, Generalization of inductive topologies to L-topological vector
31
spaces, Fuzzy Sets and Systems, 131(3) (2002), 347-352.
32
[20] C. H. Yan and J. X. Fang, L-fuzzy bilinear operator and its continuity, Iranian Journal of
33
Fuzzy Systems, 4(1) (2007), 65-73.
34
[21] H. Zhang and J. X. Fang, On locally convex I-topological vector spaces, Fuzzy Sets and
35
Systems, 157(14) (2006), 1995-2002.
36
[22] H. P. Zhang and J. X. Fang, Local convexity and local boundedness of induced I(L)- topological
37
vector spaces, Fuzzy Sets and Systems, 158(13) (2007), 1496-1503.
38
ORIGINAL_ARTICLE
Persian-translation vol.6, no.3, October 2009
http://ijfs.usb.ac.ir/article_2896_330c2cb514e8384fadcc4d21c5573245.pdf
2009-10-30T11:23:20
2018-05-25T11:23:20
93
98
10.22111/ijfs.2009.2896