ORIGINAL_ARTICLE
Cover Vol.6, No.1, Februery 2009
http://ijfs.usb.ac.ir/article_2899_64803482e5166a819fb1a57a0125543d.pdf
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10.22111/ijfs.2009.2899
ORIGINAL_ARTICLE
ROBUST $H_{\infty}$ CONTROL FOR T–S TIME-VARYING DELAY
SYSTEMS WITH NORM BOUNDED UNCERTAINTY BASED ON
LMI APPROACH
In this paper we consider the problem of delay-dependent robustH1 control for uncertain fuzzy systems with time-varying delay. The Takagi–Sugeno (T–S) fuzzy model is used to describe such systems. Time-delay isassumed to have lower and upper bounds. Based on the Lyapunov-Krasovskiifunctional method, a sufficient condition for the existence of a robust $H_{\infty}$controller is obtained. The fuzzy state feedback gains are derived by solvingpertinent LMIs. The proposed method can avoid restrictions on the derivativeof the time-varying delay assumed in previous works. The effectiveness of ourmethod is demonstrated by a numerical example.
http://ijfs.usb.ac.ir/article_214_04d0cd9efac09c8afac5f1cebbedce64.pdf
2009-02-11T11:23:20
2018-12-16T11:23:20
1
14
10.22111/ijfs.2009.214
$H_{infty}$ control
linear matrix inequality (LMI)
Delay-dependent
T–S
fuzzy systems
Uncertainty
Han-Liang
Huang
hl_huang1980.student@sina.com
true
1
Department of Mathematics, Beijing Institute of Technology,
Beijing 100081, China
Department of Mathematics, Beijing Institute of Technology,
Beijing 100081, China
Department of Mathematics, Beijing Institute of Technology,
Beijing 100081, China
LEAD_AUTHOR
Fu-Gui
Shi
f.g.shi@263.net
true
2
Department of Mathematics, Beijing Institute of Technology, Beijing
100081, China
Department of Mathematics, Beijing Institute of Technology, Beijing
100081, China
Department of Mathematics, Beijing Institute of Technology, Beijing
100081, China
AUTHOR
[1] Y. Y. Cao and P. M. Frank, Stability analysis and synthesis of nonlinear time-delay systems
1
via linear Takagi–Sugeno fuzzy models, Fuzzy Sets and Systems, 124 (2001), 213-219.
2
2] P. Gahinet, A. Nemirovski, A. J. Laub and M. Chilali, LMI control toolbox, MathWorks Inc,
3
Natick, MA, 1995.
4
[3] H. Gao, P. Shi and J. Wang, Parameter-dependent robust stability of uncertain time-delay
5
systems, J. Comput. Appl. Math., 206 (2007), 366-373.
6
[4] T. M. Guerra and L. Vermeiren, LMI-based relaxed nonquadratic stabilization conditions for
7
nonlinear systems in the Takagi–Sugeno’s form, Automatica, 40 (2004), 823–829.
8
[5] A. T. Han, G. D. Chen, M. Y. Yang and L. Yu, Stabilizing fuzzy controller design for uncertain
9
time-delay systems, Proceedings of the 3rd World Congress on Intelligent Control and
10
Automation, 2000, 1540-1543.
11
[6] Q. L. Han and K. Gu, Stability of linear systems with time-varying delay: A generalized
12
discretized Lyapunov functional approach, Asian J. Contr., 3 (2001), 170-180.
13
[7] S. K. Hong and R. Langari, An LMI-based H1 fuzzy control system design with TS framework,
14
Inform. Sci., 123 (2000), 163-179.
15
[8] X. F. Jiang, Q. L. Han and X. H. Yu, Robust H1 control for uncertain Takagi–Sugeno fuzzy
16
systems with interval time-varying delay, 2005 American Control Conference June 8-10, 2005,
17
Portland, OR, USA, 2005, 1114-1119.
18
[9] M. Li and H. G. Zhang, Fuzzy H1 robust control for nonlinear time-delay system via fuzzy
19
performance evaluator, IEEE International Conference on Fuzzy Systerms, 2003, 555-560.
20
[10] C. H. Lien, Stabilization for uncertain Takagi–Sugeno fuzzy systems with time-varying delays
21
and bounded uncertainties, Chaos Solitons Fractals, 32 (2007), 645-652.
22
[11] C. Lin, Q. G. Wang and T. H. Lee, Delay-dependent LMI conditions for stability and stabilization
23
of T–S fuzzy systems with bounded time-delay, Fuzzy Sets and Systems, 157 (2006),
24
1229-1247.
25
[12] T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling
26
and control, IEEE Trans. Systems Man Cybernet., 15 (1985), 116-163.
27
[13] R. J. Wang, W. W. Lin and W. J. Wang, Stabilizability of linear quardratic state feedback
28
for uncertain fuzzy time-delay systems, IEEE Trans. Systems Man Cybernet., (Part B), 34
29
(2004), 1288-1292.
30
[14] W. J. Wang, K. Tanaka and M. F. Griffin, Stabilization, estimation and robustness for largescale
31
time-delay systems, Control-Theory Adv. Technol., 7 (1991), 569-585.
32
[15] H. O. Wang, K. Tanaka and M. F. Griffin, An approach to fuzzy control of nonlinear systems:
33
Stability and design issues, IEEE Trans. Fuzzy Syst., 4 (1996), 14-23.
34
[16] J. Yoneyama, Robust control analysis and synthesis for uncertain fuzzy systems with timedelay,
35
The IEEE International Conference on Fuzzy Systerms, 2003, 396-401.
36
[17] K. W. Yu and C. H. Lien, Robust H1 control for uncertain T–S fuzzy systems with state
37
and input delays, Chaos Solitons Fractals, 37 (2008), 150-156.
38
[18] L. Yu, Robust control- An LMI method, Tsinghua University Press, Beijing, China, 2002.
39
[19] D. Yue and J. Lam, Reliable memory feedback design for a class of non-linear time delay
40
systems, Internat. J. Robust and Nonlinear Control, 14 (2004), 39-60.
41
[20] Y. Zhang and A. H. Pheng, Stability of fuzzy control systems with bounded uncertain delays,
42
IEEE Trans. Fuzzy Syst., 10 (2002), 92-97.
43
ORIGINAL_ARTICLE
COMBINING FUZZY QUANTIFIERS AND NEAT OPERATORS
FOR SOFT COMPUTING
This paper will introduce a new method to obtain the order weightsof the Ordered Weighted Averaging (OWA) operator. We will first show therelation between fuzzy quantifiers and neat OWA operators and then offer anew combination of them. Fuzzy quantifiers are applied for soft computingin modeling the optimism degree of the decision maker. In using neat operators,the ordering of the inputs is not needed resulting in better computationefficiency. The theoretical results will be illustrated in a water resources managementproblem. This case study shows that more sensitive decisions areobtained by using the new method.
http://ijfs.usb.ac.ir/article_216_718ace55bcfe8d8ebb8889beaac78deb.pdf
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10.22111/ijfs.2009.216
OWA operator
Fuzzy quantifiers
Neat operator
Multi criteria decision
making
Watershed management
Ferenc
szidarovszky
szidar@sie.arizona.edu
true
1
Systems and Industrial Engineering Department, University of
Arizona, Tucson, Az 85721-0020, USA
Systems and Industrial Engineering Department, University of
Arizona, Tucson, Az 85721-0020, USA
Systems and Industrial Engineering Department, University of
Arizona, Tucson, Az 85721-0020, USA
AUTHOR
Mahdi
Zarghami
mzarghami@tabrizu.ac.ir
true
2
Faculty of Civil Engineering, University of Tabriz, Tabriz 51664,
Iran
Faculty of Civil Engineering, University of Tabriz, Tabriz 51664,
Iran
Faculty of Civil Engineering, University of Tabriz, Tabriz 51664,
Iran
LEAD_AUTHOR
[1] D. Filev and R. R. Yager, On the issue of obtaining OWA operator weights, Fuzzy Sets and
1
Systems, 94 (1988), 157-169.
2
[2] R. Fullr and P. Majlender, An analytic approach for obtaining maximal entropy OWA operator
3
weights, Fuzzy Sets and Systems, 124 (2001), 53-57.
4
[3] X. W. Liu, On the methods of decision making under uncertainty with probability information,
5
Int. J. Intell. Syst., 19 (2004), 1217-1238.
6
[4] X. W. Liu and H. Lou, Parameterized additive neat OWA operators with different orness
7
levels, Int. J. Intell. Syst., 21 (2006), 1045-1072.
8
[5] M. Marimin, M. Umano, I. Hatono and H. Tamura, Linguistic labels for expressing fuzzy
9
preference relations in fuzzy group decision making, IEEE Trans. Syst. Man. Cybern. B, 28
10
(1998), 205-218.
11
[6] M. O’Hagan, Aggregating template or rule antecedents in real-time expert systems with fuzzy
12
set, In: Grove P, editor. Proc 22nd Annual IEEE Asilomar Conf on Signals, Systems, Computers.
13
California, 1988, 681-689.
14
[7] J. I. Pel´aez and J. M. Do˜na, Majority additive-ordered weighting averaging: A new neat
15
ordered weighting averaging operators based on the majority process, Int. J. Intell. Syst., 18
16
(2003), 469-481.
17
[8] J. I. Pel´aez and J. M. Do˜na, A majority model in group decision making using QMA-OWA
18
operators, Int. J. Intell. Syst., 21 (2006), 193-208.
19
[9] C. E. Shannon, A mathematical theory of communication, Bell System Tech., 27 (1948),
20
379-423 and 623-656.
21
[10] J. Wu, C. Y. Liang and Y. Q. Huang, An argument-dependent approach to determining OWA
22
operator weights based on the rule of maximum entropy, Int. J. of Intell. Syst., 22 (2007),
23
[11] Z. Xu, An overview of methods for determining OWA weights, Int. J. Intell. Syst., 20 (2005),
24
[12] R. R. Yager, On ordered weighted averaging aggregation operators in multicriteria decisionmaking,
25
IEEE Trans. Syst. Man. Cybern., 18 (1988), 183-190.
26
[13] R. R. Yager, Families of OWA operators, Fuzzy Sets and Systems, 59 (1993), 125-143.
27
[14] R. R. Yager and D. P. Filev, Parameterized and-like and or-like OWA operators, Int. J. Gen.
28
Sys., 22 (1994), 297-316.
29
[15] R. R. Yager, Quantifier guided aggregation using OWA operators, Int. J. Intell. Syst., 11
30
(1996), 49-73.
31
[16] R. R. Yager, On the cardinality and attituditional charactersitics of fuzzy measures, Int. J.
32
Gen. Sys., 31 (2002), 303-329.
33
[17] R. R. Yager, Centered OWA operators, Soft Comp., 11 (2007), 631-639.
34
[18] L. A. Zadeh, A computational approach to fuzzy quantifiers in natural languages, Comput.
35
and Math. with App., 9 (1983), 149-184.
36
[19] M. Zarghami, F. Szidarovszky and R. Ardakanian, Sensitivity analysis of the OWA operator,
37
IEEE Trans. Syst. Man. Cybern. B, 38(2) (2008), 547-552.
38
[20] M. Zarghami and F. Szidarovszky, Revising the OWA operator for multi criteria decision
39
making problems under uncertainty, Euro. J. Oper. Res., 2008, (Article in press: doi:
40
10.1016/j.ejor.2008.09.014).
41
ORIGINAL_ARTICLE
THE PERCENTILES OF FUZZY NUMBERS AND THEIR
APPLICATIONS
The purpose of this study is to find the percentiles of fuzzy numbersand to demonstrate their applications, which include finding weightedmeans, dispersion indices, and the percentile intervals of fuzzy numbers. Thecrisp approximations of fuzzy numbers introduced in this paper are new andinteresting for the comparison of fuzzy environments, such as a variety of economic,financial, and engineering systems control problems.
http://ijfs.usb.ac.ir/article_217_28963c5c70c04cbeae3128254ac46d54.pdf
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10.22111/ijfs.2009.217
Trimmed mean
Winsorized mean
Interquartile range
Skewness
Kurtosis
Percentile interval
Eynollah
Pasha
pasha@saba.tmu.ac.ir
true
1
Department of Mathematics, The teacher Training University,
Tehran, Iran
Department of Mathematics, The teacher Training University,
Tehran, Iran
Department of Mathematics, The teacher Training University,
Tehran, Iran
AUTHOR
Abolfazl
Saiedifar
a-saiedi@iau-arak.ac.ir or saiedifar1349@yahoo.com
true
2
Department of Statistics, Science and Research branch, Islamic
Azad University, Tehran 14515-775, Iran
Department of Statistics, Science and Research branch, Islamic
Azad University, Tehran 14515-775, Iran
Department of Statistics, Science and Research branch, Islamic
Azad University, Tehran 14515-775, Iran
LEAD_AUTHOR
Babak
Asady
babakmz2002@yahoo.com
true
3
Department of Mathematics, Islamic Azad University, Arak, Iran
Department of Mathematics, Islamic Azad University, Arak, Iran
Department of Mathematics, Islamic Azad University, Arak, Iran
AUTHOR
[1] S. Bodjanova, Median value and median interval of a fuzzy number, Information Sciencees,
1
172 (2005), 73-89.
2
[2] G. K. Bhattacharyya and R. A. Johnson, Statistical concepts and methods, John Wiley and
3
Sons, 1977.
4
[3] C. Carlsson and R. Full´er, On possibilistic mean value and variance of fuzzy numbers, Fuzzy
5
Sets and Systems, 122 (2001), 315-326.
6
[4] D. Dubois and H. Prade, Fuzzy sets and systems, theory and applications, Academikc press,
7
New York, 1980.
8
[5] D. Dubois and H. Prade, The mean value of a fuzzy number, Fuzzy Sets and Systems, 24
9
(1987), 279-300.
10
[6] D. Dubois and H. Prade, Fundamentals of fuzzy sets, The Handbooks of Fuzzy Sets Series,
11
Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000.
12
[7] A. Galvan, Univariate equtions, Internet, 2005.
13
[8] M. Ma, A. Kandel and M. Friedman, A new approach for defuzzification, Fuzzy Sets and
14
Systems, 111 (2000), 351-356.
15
[9] C. R. Marques, P. D. Neves and L. M. Sarmento, Evaluating core inflation indicator, Economic
16
Modelling, 20 (2003), 765-775.
17
[10] P. McAdam and P. McNelis, Forecasting inflation with thick model and neural networks,
18
Economic Modelling, 22 (2005), 848-867.
19
[11] A. V. Patel and B. M. Mohan, Some numerical aspects of center of area defuzzification
20
method, Fuzzy Sets and Systems, 132 (2002), 401-409.
21
[12] A. K. Rose, A stable internatinal monetary systems emerges: Inflation targeting is Bretton
22
Woods, reversed, Journal of International Money and Finance, 26 (2007), 663-681.
23
[13] A. Saiedifar and E. Pasha, The percentiles of trapezoidal fuzzy numbers and their applications,
24
ICREM3, Kuala Lumpur, Malaysia, Proceedings of Pure Mathemathics Statistics, 2007, 61-
25
[14] A. Stuart, J. K. Ord and Kendall’s, Advanced theory of statistics, Distribution Theory 6th
26
ed. New York, Oxford University Press, 1 (1998).
27
[15] L. A. Zadeh, A fuzzy set-theoritic interpretation of linguistic hedges, Journal of Cybernetics,
28
2 (1972), 4-34.
29
ORIGINAL_ARTICLE
ABSORBENT ORDERED FILTERS AND THEIR
FUZZIFICATIONS IN IMPLICATIVE SEMIGROUPS
The notion of absorbent ordered filters in implicative semigroupsis introduced, and its fuzzification is considered. Relations among (fuzzy) orderedfilters, (fuzzy) absorbent ordered filters, and (fuzzy) positive implicativeordered filters are stated. The extensionproperty for (fuzzy) absorbent orderedfilters is established. Conditions for (fuzzy) ordered filters to be (fuzzy)absorbent ordered filters are provided. The notions of normal/maximal fuzzyabsorbent ordered filters and complete absorbent ordered filters are introducedand their properties are investigated.
http://ijfs.usb.ac.ir/article_219_2b5d899b27b4fb5bad6f5035658c89f7.pdf
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61
10.22111/ijfs.2009.219
Implicative semigroup
(fuzzy) positive implicative ordered filter
(fuzzy) absorbent ordered filter
Normal fuzzy absorbent ordered filter
Maximal fuzzy absorbent
ordered filter
Complete fuzzy absorbent ordered filter
Young Bae
Jun
skywine@gmail.com
true
1
Department of Mathematics Education and (RINS), Gyeongsang National
University, Chinju 660-701, Korea
Department of Mathematics Education and (RINS), Gyeongsang National
University, Chinju 660-701, Korea
Department of Mathematics Education and (RINS), Gyeongsang National
University, Chinju 660-701, Korea
AUTHOR
Chul Hwan
Park
skyrosemary@gmail.com
true
2
Department of Mathematics, University of Ulsan, Ulsan 680-749,
Korea
Department of Mathematics, University of Ulsan, Ulsan 680-749,
Korea
Department of Mathematics, University of Ulsan, Ulsan 680-749,
Korea
LEAD_AUTHOR
D. R.
Prince Williams
princeshree1@gmail.com
true
3
Department of Information Technology, Salalah College of
Technology, Post Box: 608, Salalah-211, Sultanate of Oman
Department of Information Technology, Salalah College of
Technology, Post Box: 608, Salalah-211, Sultanate of Oman
Department of Information Technology, Salalah College of
Technology, Post Box: 608, Salalah-211, Sultanate of Oman
AUTHOR
[1] G. Birkhoff, Lattice theory, Amer. Math. Soc. Coll. Publ. Vol. XXV, Providence, 1967.
1
[2] T. S. Blyth, Pseudo-residuals in semigroups, J. London Math. Soc., 40 (1965), 441-454.
2
[3] M. W. Chan and K. P. Shum, Homomorphisms of implicative semigroups, Semigroup Forum,
3
46 (1993), 7-15.
4
[4] H. B. Curry, Foundations of mathematics logic, McGrow-Hill, New York, 1963.
5
[5] Y. B. Jun, Implicative ordered filters of implicative semigroups, Comm. Korean Math. Soc.,
6
14(1) (1999), 47-55.
7
[6] Y. B. Jun, Fuzzy implicative ordered filters in implicative semigroups, Southeast Asian. Bull.
8
Math., 26 (2003), 935-943.
9
[7] Y. B. Jun, Folding theory applied to implicative ordered filters of implicative semigroups,
10
Southeast Asian. Bull. Math., 31 (2007), 893-901.
11
[8] Y. B. Jun and K. H. Kim, Positive implicative ordered filters of implicative semigroups,
12
Internat. J. Math. Math. Sci., 23(12) (2000), 801-806.
13
[9] Y. B. Jun, Y. H. Kim and H. S. Kim, Fuzzy positive implicative ordered filters of implicative
14
semigroups, Internat. J. Math. Math. Sci., 32(5) (2002), 263-270.
15
[10] Y. B. Jun, J. Meng and X. L. Xin, On ordered filters of implicative semigroups, Semigroup
16
Forum, 54 (1997), 75-82.
17
[11] S. W. Kuresh, Y. B. Jun and W. P. Huang, Fuzzy ordered filters in implicative semigroups,
18
Chinese Quartely J. Math., 13(2) (1998), 53-57.
19
[12] J. Meng, Implicative commutative semigroups are equivalent to a class of BCK-algebras,
20
Semigroup Forum, 50 (1995), 89-96.
21
[13] W. C. Nemitz, Implicative semilattices, Trans. Amer. Math. Soc., 117 (1965), 128-142.
22
ORIGINAL_ARTICLE
ON ($\epsilon, \epsilon \vee q$)-FUZZY IDEALS OF BCI-ALGEBRAS
The aim of this paper is to introduce the notions of ($\epsilon, \epsilon \vee q$)-fuzzy p-ideals, ($\epsilon, \epsilon \vee q$)-fuzzy q-ideals and ($\epsilon, \epsilon \vee q$)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterizationtheorems for these generalized fuzzy ideals are proved and the relationshipamong these generalized fuzzy ideals of BCI-algebras is discussed. It is shownthat a fuzzy set of a BCI-algebra is an ($\epsilon, \epsilon \vee q$)-fuzzy a-ideal if and only if itis both an ($\epsilon, \epsilon \vee q$)-fuzzy p-ideal and an ($\epsilon, \epsilon \vee q$)-fuzzy q-ideal. Finally, the concept of implication-based fuzzy a-ideals in BCI-algebras is introduced and,in particular, the implication operators in Lukasiewicz system of continuousvaluedlogic are discussed.
http://ijfs.usb.ac.ir/article_222_5803dad8f3359c0150f261e18f2d8330.pdf
2009-02-11T11:23:20
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81
94
10.22111/ijfs.2009.222
BCI-algebra
($epsilon
epsilon vee q$)-fuzzy (p-
q- and a-) ideal
fuzzy logic
Implication
operator
Jianming
Zhan
zhanjianming@hotmail.com
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
LEAD_AUTHOR
Young Bae
Jun
skywine@gmail.com
true
2
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
AUTHOR
Bijan
Davvaz
davvaz@yazduni.ac.ir
true
3
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
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] C. C. Chang, Algebraic analysis of many valued logic, Trans. Amer. Math. Soc., 88 (1958),
4
[4] B. Davvaz, (2, 2 _q)-fuzzy subnear-rings and ideals, Soft Computing, 10 (2006), 206-211.
5
[5] B. Davvaz and P. Corsini, Redefined fuzzy Hv-submodules and many valued implications,
6
Inform. Sci., 177 (2007), 865-875.
7
[6] F. Esteva and L. Godo, Monoidal t-norm based logic: towards a logic for left-continuous
8
t-norms, Fuzzy Sets and Systems, 124 (2001), 271-288.
9
[7] P. H´ajek, Metamathematics of fuzzy logic, Kluwer Academic Press, Dordrecht, 1998.
10
[8] Y. Imai and K. Iseki, On axiom system of propositional calculus, Proc. Japan Acad., 42
11
(1966), 19-22.
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[9] A. Iorgulescu, Some direct ascendents of wajsberg and MV algebras, Sci. Math. Japon., 57
13
(2003), 583-647.
14
[10] A. Iorgulescu, Pseudo-Iseki algebras. connection with pseudo-BL algebras, Multiple-Valued
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Logic and Soft Computing, 11 (2005), 263-308.
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[11] K. Iseki, An algebra related with a propositional calculus, Proc. Japan Acad., 42 (1966),
17
[12] K. Iseki and S. Tanaka, Ideal theory of BCK-algebras, Math. Japon., 21 (1966), 351-366.
18
[13] Y. B. Jun, Closed fuzzy ideals in BCI-algebras, Math. Japon., 38 (1993), 199-202.
19
[14] Y. B. Jun, On (, )-fuzzy ideals of BCK/BCI-algebras, Sci. Math. Japon., 60 (2004), 613-
20
[15] Y. B. Jun, On (, )-fuzzy subalgebras of BCK/BCI-algebras, Bull. Korean Math. Soc., 42
21
(2005), 703-711.
22
[16] Y. B. Jun and J. Meng, Fuzzy p-ideals in BCI-algebras, Math. Japon, 40 (1994), 271-282.
23
[17] Y. B. Jun and J. Meng, Fuzzy commutative ideals in BCI-algebras, Comm. Korean Math.
24
Soc., 9 (1994), 19-25.
25
[18] Y. B. Jun and W. H. Shim, Fuzzy strong implicative hyper BCK-ideals of hyper BCK-algebras,
26
Inform. Sci., 170 (2005), 351-361.
27
[19] Y. B. Jun, Y. Xu and J. Ma, Redefined fuzzy implicative filters, Inform. Sci., 177 (2007),
28
1422-1429.
29
[20] T. D. Lei and C. C. Xi, p-radical in BCI-algebras, Math. Japon., 30 (1995), 511-517.
30
[21] Y. L. Liu, Some results on p-semisimple BCI-algebras, Math. Japon, 30 (1985), 511-517.
31
[22] Y. L. Liu, S. Y. Liu and J. Meng, FSI-ideals and FSC-ideals of BCI-algebras, Bull. Korean
32
Math. Soc., 41 (2004), 167-179.
33
[23] Y. L. Liu and J. Meng, Fuzzy q-ideals of BCI-algebras, J. Fuzzy Math., 8 (2000), 873-881.
34
[24] Y. L. Liu and J. Meng, Fuzzy ideals in BCI-algebras, Fuzzy Sets and Systems, 123 (2001),
35
[25] Y. L. Liu, J. Meng, X. H. Zhang and Z. C. Yue, q-ideals and a-ideals in BCI-algebras, SEA
36
Bull. Math., 24 (2000), 243-253.
37
[26] Y. L. Liu, Y. Xu and J. Meng, BCI-implicative ideals of BCI-algebras, Inform. Sci., 177
38
(2007), 4987-4996.
39
[27] Y. L. Liu and X. H. Zhang, Fuzzy a-ideals in BCI-algebras, Adv. in Math.(China), 31 (2002),
40
[28] J. Meng and X. Guo, On fuzzy ideals in BCK-algebras, Fuzzy Sets and Systems, 149 (2005),
41
[29] J. Meng and Y. B. Jun, BCK-algebras, Kyung Moon Sa Co., Seoul, Korean, 1994.
42
[30] D. Mundici, MV algebras are categorically equivalent to bounded commutative BCK-algebras,
43
Math. Japon., 31 (1986), 889-894.
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[31] P. M. Pu and Y. M. Liu, Fuzzy topology I: Neighourhood structure of a fuzzy point and
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Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571-599.
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[32] X. H. Yuan, C. Zhang and Y. H. Ren, Generalized fuzzy groups and many valued applications,
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Fuzzy Sets and Systems, 138 (2003), 205-211.
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49
[34] L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outine, Inform. Sci., 172
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ORIGINAL_ARTICLE
Persian-translation Vol.6, No.1, Februery 2009
http://ijfs.usb.ac.ir/article_2900_7982b613498239c3a5bb8604cc60869b.pdf
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2018-12-16T11:23:20
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10.22111/ijfs.2009.2900