ORIGINAL_ARTICLE
Cover Special Issue vol. 9, no. 4, October 2012--
http://ijfs.usb.ac.ir/article_2810_95ecbd1c9f5abcf931d13082bb1c90b7.pdf
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ORIGINAL_ARTICLE
CONVERGENCE APPROACH SPACES AND APPROACH
SPACES AS LATTICE-VALUED CONVERGENCE SPACES
We show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. Further we study the preservation of diagonal conditions, which characterize approach spaces. It is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued pretopological spaces and that the category of approach spaces is a coreective subcategory of a category of lattice-valued topological convergence spaces
http://ijfs.usb.ac.ir/article_129_bd3ed7750b453af4c9a20fe2aa85c8eb.pdf
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10.22111/ijfs.2012.129
L-fuzzy convergence
L-topology
L-filter
L-limit space
Approach
space
Convergence approach space
Pre-approach space
Gunther
Jager
g.jager@ru.ac.za
true
1
Department of Statistics, Rhodes University, 6140 Grahamstown,
South Africa
Department of Statistics, Rhodes University, 6140 Grahamstown,
South Africa
Department of Statistics, Rhodes University, 6140 Grahamstown,
South Africa
LEAD_AUTHOR
[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, Wiley, New
1
York, 1989.
2
[2] P. Brock and D. C. Kent, Approach spaces, limit tower spaces, and probabilistic convergence
3
spaces, Applied Categorical Structures, 5 (1997), 99-110.
4
[3] P. V. Flores, R. N. Mohapatra and G. Richardson, Lattice-valued spaces: fuzzy convergence,
5
Fuzzy Sets and Systems, 157 (2006), 2706- 2714.
6
[4] W. Gahler, Monadic convergence structures, In S. E. Rodabaugh and E. P. Klement, Editors,
7
Topological and Algebraic Structures in Fuzzy Sets. Kluwer Academic Publishers, Dordrecht,
8
[5] J. Gutierrez Garca, I. Mardones Perez and M. H. Burton, The relationship between various
9
lter notions on a GL-monoid, J. Math. Anal. Appl., 230 (1999), 291-302.
10
[6] U. Hohle, Commutative, residuated l-monoids, In: Non-classical Logics and Their Application
11
to Fuzzy Subsets (U. Hohle, S. E. Rodabaugh and eds.), Kluwer, Dordrecht, (1995), 53-106.
12
[7] U. Hohle, Many valued topology and its applications, Kluwer, Boston/Dordrecht/London,
13
[8] U. Hohle and A. P. Sostak, Axiomatic foundations of xed-basis fuzzy topology, In: Mathematics
14
of Fuzzy Sets. Logic, Topology and Measure Theory (U. Hohle, S. E. Rodabaugh and
15
eds.), Kluwer, Boston/Dordrecht/London, (1999), 123-272.
16
[9] G. Jager, A category of L-fuzzy convergence spaces, Quaest. Math., 24 (2001), 501-517.
17
[10] G. Jager, Subcategories of lattice-valued convergence spaces, Fuzzy Sets and Systems, 156
18
(2005), 1-24.
19
[11] G. Jager, Pretopological and topological lattice-valued convergence spaces, Fuzzy Sets and
20
Systems, 158 (2007), 424-435.
21
[12] G. Jager, Fischer's diagonal condition for lattice-valued convergence spaces, Quaest. Math.,
22
31 (2008), 11-25.
23
[13] G. Jager, Lattice-valued convergence spaces and regularity, Fuzzy Sets and Systems, 159
24
(2008), 2488-2502.
25
[14] G. Jager, Lattice-valued categories of lattice-valued convergence spaces, Iranian Journal of
26
Fuzzy Systems, 8 (2011), 67-89.
27
[15] E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Dordrecht, 2000.
28
[16] H. J. Kowalsky, Limesraume und Komplettierung, Math. Nachrichten, 12 (1954), 301-340.
29
[17] L. Li and Q. Jin, On adjunctions between Lim, SL-Top, and SL-Lim, Fuzzy Sets and Systems,
30
doi:10.1016/j.fss.2010.10.002, to appear.
31
[18] E. Lowen and R. Lowen, A quasitopos containing CONV and MET as full subcategories,
32
Internat. J. Math. and Math. Sci., 11 (1988), 417- 438.
33
[19] R. Lowen, Approach spaces: a common supercategory of TOP and MET, Math. Nachr., 141
34
(1989), 183-226.
35
[20] R. Lowen, Approach spaces: the missing link in the topology-uniformity-metric triad, Claredon
36
Press, Oxford, 1997.
37
[21] D. L. Orpen and G. Jager, Lattice-valued convergence spaces: extending the lattice context,
38
Fuzzy Sets and Systems, 190 (2012), 1-20.
39
[22] B. Schweizer and A. Sklar, Probabilistic metric spaces, North Holland, New York, 1983.
40
[23] W. Yao, On many-valued L-fuzzy convergence spaces, Fuzzy Sets and Systems, 159 (2008),
41
2503-2519.
42
[24] W. Yao, On L-fuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 6 (2009),
43
ORIGINAL_ARTICLE
EFFICIENCY IN FUZZY PRODUCTION POSSIBILITY SET
The existing Data Envelopment Analysis models for evaluating the relative eciency of a set of decision making units by using various inputs to produce various outputs are limited to crisp data in crisp production possibility set. In this paper, rst of all the production possibility set is extended to the fuzzy production possibility set by extension principle in constant return to scale, and then the fuzzy model of Charnes, Cooper and Rhodes in input oriented is proposed so that it satis es the initial concepts with crisp data. Finally, the fuzzy model of Charnes, Cooper and Rhodes for evaluating decision making units is illustrated by solving two numerical examples.
http://ijfs.usb.ac.ir/article_130_291d4bcb1fedf08c29c53872ef51b618.pdf
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Data Envelopment Analysis
Extension principle
Fuzzy number
T.
Allahviranloo
tofigh@allahviranloo.com
true
1
Department of Mathematics, Science and Research Branch, Is-
lamic Azad University, Tehran, Iran
Department of Mathematics, Science and Research Branch, Is-
lamic Azad University, Tehran, Iran
Department of Mathematics, Science and Research Branch, Is-
lamic Azad University, Tehran, Iran
LEAD_AUTHOR
F.
Hosseinzadeh Lotfi
hosseinzadeh lotfi@yahoo.com
true
2
Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran
Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran
Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran
AUTHOR
M.
AdabitabarFirozja
mohamadsadega@yahoo.com
true
3
Department of Mathematics, Qaemshar Branch, Islamic Azad
University, Qaemshahr, Iran
Department of Mathematics, Qaemshar Branch, Islamic Azad
University, Qaemshahr, Iran
Department of Mathematics, Qaemshar Branch, Islamic Azad
University, Qaemshahr, Iran
AUTHOR
[1] J. M. Adamo, Fuzzy decision trees, Fuzzy Sets and Systems, 4 (1980), 207-219.
1
[2] T. Allahviranloo, F. Hosseinzadeh Lot, L. Alizadeh and N. Kiani, Degenercy in fuzzy linear
2
programming problems, In Journal of the Journal of Fuzzy Mathematics (International Fuzzy
3
Mathematics Institute), 17(2) (2009).
4
[3] J. F. Baldwin and N. C. F. Guild, Comparison of fuzzy sets on the same decision space,
5
Fuzzy Sets and Systems, 2 (1979), 213-233.
6
[4] R. D. Banker, A. Charnes and W. W. Cooper, Some models for estimating teachnical and
7
scale eciencies in data envelopment analysis, Manage. Sci., 30 (1984), 1078-1092.
8
[5] R. E. Bellman and L. A. Zadeh, Decision-making in a fuzzy environment, Management Sci.,
9
17 (1970), 141-164.
10
[6] A. Charnes, W. W. Cooper and E. Rhodes, Measuring the eciency of decision making
11
units, Europian Journal of Operation Research, 2 (1978), 429-444.
12
[7] W. W. Cooper, L. M. Sieford and K. Tone, Data envelopment analysis: a comprehensive text
13
with models, applications, References and DEA Solver Software, Kluwer Academic Publishers,
14
[8] W. W. Cooper, K. S. Park and J. T. Pastor, RAM: a range adjusted measure of ineciency
15
for use with additive models, and relations to other models and measures in DEA, J. Product.
16
Anal., 11 (1999), 5-24.
17
[9] M. J. Farrell, The measurement of productive eciency, Journal of the Royal Statistical
18
Society A, 120 (1957), 253-281.
19
[10] R. Fuller, Neural fuzzy systems, Donner Visiting Professor Abo Akademi University, ISBN
20
951-650-624-0, ISSN 0358-5654, Abo, 1995.
21
[11] P. Guo and H. Tanaka, Fuzzy DEA: a perceptual evaluation method, Fuzzy Sets and Systems,
22
119 (2001), 149-160.
23
[12] P. Guo, Fuzzy data envelopment analysis and its aplication to location problems, Information
24
Sciences, 176(6,1) (2009), 820-829.
25
[13] F. Hosseinzadeh Lot, T. Allahviranloo, M. Alimardani Jondabeh and L. Alizadeh, Solving
26
a full fuzzy linear programming using lexicography method and fuzzy approximate solution,
27
Applied Mathematical Modelling, 33(7) (2009), 3151-3156.
28
[14] G. R. Jahanshahloo, M. Soleimani-Damaneh and E. Nasrabadi, Measure of eciency in DEA
29
with fuzzy input-output levels: a methodology for assessing, ranking and imposing of weights
30
restrictions, Applied Mathematics and Computation, 156 (2004), 175-187.
31
[15] N. Javadian, Y. Maali and N. Mahdavi-Amiri, Fuzzy linear programing with grades of satis-
32
faction in constraints, Iranian Journal of Fuzzy Systems, 6(3) (2009), 17-35.
33
[16] C. Kao and Shiang-Tai Liu, Fuzzy eciency measures in data envelopment analysis, Fuzzy
34
Sets and Systems, 113 (2000), 427-437.
35
[17] C. Kao and S. T. Liu, A mathematical programming approach to fuzzy eciency ranking,
36
Internat. J. Production Econom, 86 (2003), 45-154.
37
[18] S. Lertworasirikul, S. C. Fang, J. A. Joines and H. L. W. Nuttle, Fuzzy data envelopment
38
analysis(DEA):a possibility approach, Fuzzy Sets and Systems, 139 (2003), 379-394.
39
[19] T. Leon, V. Lierm, J. L. Ruiz and I. Sirvent, A fuzzy mathematical programing approach to
40
the assessment eciency with DEA models, Fuzzy Sets and Systems, 139 (2003), 407-419.
41
[20] S. Lertworasirikul, S. C. Fang, J. A. Joines and H. L. W. Nuttle, Fuzzy data envelopment
42
analysis(DEA): a possibility aporoach, Fuzzy Sets and Systems, 139(2) (2003), 379-394.
43
[21] S. T. Liu and M. Chuang, Fuzzy eciency measures in fuzzy DEA/AR with application to
44
university libraries, Expert Systems with Applications, 36(2) (2009), 1105-1113.
45
[22] S. Ramezanzadeh, M. Memariani and S. Saati, data envelopment analisis with fuzzy random
46
inputs and outputs: a chance- constrained programing approach, Iranian Journal of Fuzzy
47
Systems, 2(2) (2005), 21-29.
48
[23] M. R. Sa, H. R. Maleki and E. Zaeimazad, A note on the zimmermann method for solving
49
fuzzy linear programing problems, Iranian Journal of Fuzzy Systems, 4(2) (2007), 31-45.
50
[24] Y. M. Wang, R. Greatbanks and J. B. Yang, Interval eciency assessment using data en-
51
velopment analysis, Fuzzy Sets and Systems, 153 (2005), 347-370.
52
[25] Y. M. Wang, Y. Luo and L. Liang, Fuzzy data envelopment analysis based upon fuzzy arith-
53
metic with an aplication to performance assessment of manufacturing enterprises, Expert
54
Systems with Applications, 363 (2009), 5205-5211.
55
[26] M. Wen and H. Li, Fuzzy data envelopment analysis(DEA): model and ranking method,
56
Journal of Computational and Applied Mathematics, 223(2,15) (2009), 872-878.
57
[27] H. J. Zimmermann, Fuzzy set theory and its applications, Second ed., Kluwer-Nijho, Boston,
58
ORIGINAL_ARTICLE
CLASSIFYING FUZZY SUBGROUPS OF FINITE NONABELIAN
GROUPS
In this paper a rst step in classifying the fuzzy subgroups of a nite nonabelian group is made. We develop a general method to count the number of distinct fuzzy subgroups of such groups. Explicit formulas are obtained in the particular case of dihedral groups.
http://ijfs.usb.ac.ir/article_131_a85ac48a21fd8e1c3315ef08068da1fe.pdf
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10.22111/ijfs.2012.131
Fuzzy subgroups
Chains of subgroups
Maximal chains of subgroups
Dihedral groups
Recurrence relations
Marius
Tarnauceanu
tarnauc@uaic.ro
true
1
Faculty of Mathematics, Al.I. Cuza" University, Iasi, Romania
Faculty of Mathematics, Al.I. Cuza" University, Iasi, Romania
Faculty of Mathematics, Al.I. Cuza" University, Iasi, Romania
LEAD_AUTHOR
[1] Y. Alkhamees, Fuzzy cyclic subgroups and fuzzy cyclic p-subgroups, J. Fuzzy Math., 3 (1995),
1
[2] G. Gratzer, General lattice theory, Academic Press, New York, 1978.
2
[3] T. Head, A metatheorem for deriving fuzzy theorems from crisp versions, Fuzzy Sets and
3
Systems, 73 (1995), 349-358.
4
[4] T. Head, A metatheorem for deriving fuzzy theorems from crisp versions, Fuzzy Sets and
5
Systems, 79 (1996), 277-278.
6
[5] A. Jain, Fuzzy subgroups and certain equivalence relations, Iranian Journal of Fuzzy Systems,
7
3 (2006), 75-91.
8
[6] R. Kumar, Fuzzy algebra, I, Univ. of Delhi, Publ. Division, 1993.
9
[7] M. Mashinchi and M. Mukaidono, A classication of fuzzy subgroups, Ninth Fuzzy System
10
Symposium, Sapporo, Japan, (1992), 649-652.
11
[8] M. Mashinchi and M. Mukaidono, On fuzzy subgroups classication, Research Report of Meiji
12
Univ., 9 (1993), 31-36.
13
[9] J. N. Mordeson, Invariants of fuzzy subgroups, Fuzzy Sets and Systems, 63 (1994), 81-85.
14
[10] J. N. Mordeson, N. Kuroki and D. S. Malik, Fuzzy semigroups, Springer Verlag, Berlin, 2003.
15
[11] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups, I, Fuzzy Sets and
16
Systems, 123 (2001), 259-264.
17
[12] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups, II, Fuzzy Sets and
18
Systems, 136 (2003), 93-104.
19
[13] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups, III, Int. J. Math. Sci.,
20
36 (2003), 2303-2313.
21
[14] V. Murali and B. B. Makamba, Counting the number of fuzzy subgroups of an abelian group
22
of order pnqm, Fuzzy Sets and Systems, 144 (2004), 459-470.
23
[15] V. Murali and B. B. Makamba, Fuzzy subgroups of nite abelian groups, FJMS, 14 (2004),
24
[16] S. Ngcibi, V. Murali and B. B. Makamba, Fuzzy subgroups of rank two abelian p-group,
25
Iranian Journal of Fuzzy Systems, 7 (2010), 149-153.
26
[17] R. Schmidt, Subgroup lattices of groups, de Gruyter Expositions in Mathematics, de Gruyter,
27
Berlin, 14 (1994).
28
[18] R. P. Stanley, Enumerative combinatorics, II, Cambridge University Press, Cambridge, 1999.
29
[19] M. Suzuki, Group theory, I, II, Springer Verlag, Berlin, (1982, 1986).
30
[20] M. Stefanescu and M. Tarnauceanu, Counting maximal chains of subgroups of nite nilpotent
31
groups, Carpathian J. Math., 25 (2009), 119-127.
32
[21] M. Tarnauceanu, Groups determined by posets of subgroups, Ed. Matrix Rom, Bucuresti,
33
[22] M. Tarnauceanu, The number of fuzzy subgroups of nite cyclic groups and Delannoy num-
34
bers, European J. Combin., doi: 10.1016/j.ejc.2007.12.005, 30 (2009), 283-287.
35
[23] M. Tarnauceanu, Distributivity in lattices of fuzzy subgroups, Information Sciences, doi:
36
10.1016/j.ins.2008.12.003, 179 (2009), 1163-1168.
37
[24] M. Tarnauceanu and L. Bentea, On the number of fuzzy subgroups of nite abelian groups,
38
Fuzzy Sets and Systems, doi: 10.1016/j.fss.2007.11.014, 159 (2008), 1084-1096.
39
[25] M. Tarnauceanu and L. Bentea, A note on the number of fuzzy subgroups of nite groups,
40
Sci. An. Univ. "Al.I. Cuza" Iasi, Math., 54 (2008), 209-220.
41
[26] I. Tomescu, Introduction to combinatorics, Collet's Publishers Ltd., London, 1975.
42
[27] A. C. Volf, Counting fuzzy subgroups and chains of subgroups, Fuzzy Systems & Articial
43
Intelligence, 10 (2004), 191-200.
44
[28] A. Weinberger, Reducing fuzzy algebra to classical algebra, New Math. Natur. Comput., 1
45
(2005), 27-64.
46
[29] Y. Zhang and K. Zou, A note on an equivalence relation on fuzzy subgroups, Fuzzy Sets and
47
Systems, 95 (1998), 243-247.
48
ORIGINAL_ARTICLE
SOME FIXED POINT THEOREMS IN LOCALLY CONVEX
TOPOLOGY GENERATED BY FUZZY N-NORMED SPACES
The main purpose of this paper is to study the existence of afixed point in locally convex topology generated by fuzzy n-normed spaces.We prove our main results, a fixed point theorem for a self mapping and acommon xed point theorem for a pair of weakly compatible mappings inlocally convex topology generated by fuzzy n-normed spaces. Also we givesome remarks in locally convex topology generated by fuzzy n-normed spaces.
http://ijfs.usb.ac.ir/article_132_837208a7dd5fddbb57bd0b81a873f2a3.pdf
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10.22111/ijfs.2012.132
Fuzzy n-normed spaces
n-seminorm
Fixed points
S. K.
Elagan
sayed khalil2000@yahoo.com
true
1
Mathematics and statistics Department, Faculty of Science, Taif Uni-
versity (P.O.888), Zip Code 21974, Kingdom of Saudi Arabia (KSA) and Department of
Mathematics, Faculty of Science, Menofiya University, Shebin Elkom, Egypt
Mathematics and statistics Department, Faculty of Science, Taif Uni-
versity (P.O.888), Zip Code 21974, Kingdom of Saudi Arabia (KSA) and Department of
Mathematics, Faculty of Science, Menofiya University, Shebin Elkom, Egypt
Mathematics and statistics Department, Faculty of Science, Taif Uni-
versity (P.O.888), Zip Code 21974, Kingdom of Saudi Arabia (KSA) and Department of
Mathematics, Faculty of Science, Menofiya University, Shebin Elkom, Egypt
LEAD_AUTHOR
M. R.
Segi Rahmat
Mohd.Rafi@nottingham.edu.my
true
2
School of Applied Mathematics, University of Nottingham Malaysia
Campus, Jalan Broga, 43500, Semenyih, Selangor D.E, Malaysia
School of Applied Mathematics, University of Nottingham Malaysia
Campus, Jalan Broga, 43500, Semenyih, Selangor D.E, Malaysia
School of Applied Mathematics, University of Nottingham Malaysia
Campus, Jalan Broga, 43500, Semenyih, Selangor D.E, Malaysia
AUTHOR
[1] C. Alaca, A new perspective to the mazur-ulamproblem in 2-fuzzy 2-normed linear spaces,
1
Iranian Journal of Fuzzy Systems, in press.
2
[2] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math.,
3
11(3) (2003), 687-705.
4
[3] S. Berberian, Lectures in functional analsysis and operator theory, Springer-Verlag, New
5
York, 1974.
6
[4] S. C. Chang and J. N. Mordesen, Fuzzy linear operators and fuzzy normed linear spaces,
7
Bull. Calcutta Math. Soc., 86(5) (1994), 429-436.
8
[5] C. Felbin, Finite- dimensional fuzzy normed linear space, Fuzzy Sets and systems, 48(2)
9
(1992), 239-248.
10
[6] C. Felbin, The completion of a fuzzy normed linear space, J. Math. Anal. Appl., 174(2)
11
(1993), 428-440.
12
[7] C. Felbin, Finite dimensional fuzzy normed linear space. II., J. Anal., 7 (1999), 117-131.
13
[8] S. Gahler, Untersuchungen uber verallgemeinerte m-metrische Raume, I, II, III., Math.
14
Nachr., 40 (1969), 165-189.
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[9] H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27(10) (2001),
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[10] A. K. Katsaras, Fuzzy topological vector spaces. II., Fuzzy Sets and Systems, 12(2) (1984),
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[11] S. S. Kim and Y. J. Cho, Strict convexity in linear n- normed spaces, Demonstratio Math.,
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29(4) (1996), 739-744.
19
[12] S. V. Krish and K. K. M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets and
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Systems, 63(2) (1994), 207-217.
21
[13] R. Malceski, Strong n-convex n-normed spaces, Math. Bilten No., 21 (1997), 81-102.
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[14] A. Misiak, n-inner product spaces, Math. Nachr., 140 (1989), 299-319.
23
[15] A. Narayanan and S. Vijayabalaji, Fuzzy n normed linear spaces, Int. J. Math. Math. Sci.,
24
27(24) (2005), 3963-3977.
25
[16] R. Rado, A theorem on innite series, J. Lond. Math. Soc., 35 (1960), 273-276.
26
[17] M. R. S. Rahmat, Fixed point theorems on fuzzy inner product spaces, Mohu Xitong yu
27
Shuxue, Fuzzy Systems and Mathematics. Nat. Univ. Defense Tech., Changsha, 22(3) (2008),
28
[18] G. S. Rhie, B. M. Choi and D. S. Kim, On the completeness of fuzzy normed linear spaces,
29
Math. Japon., 45(1) (1997), 33-37.
30
[19] A. Smith, Convergence preserving function: an alternative discussion, Amer. Math. Monthly,
31
96 (1991), 831-833.
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[20] S. Vijayabalaji and N. Thilligovindan, Complete fuzzy n-normed space, J. Fund. Sciences,
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Available Online at www.ibnusina.utm.my/jfs, 3 (2007), 119-126.
34
[21] G. Wildenberg, Convergence preserving functions, Amer. Math. Monthly, 95 (1988), 542-544.
35
ORIGINAL_ARTICLE
Fuzzy $h$-ideal of Matrix Hemiring $S_{2}=left(
begin{array}{cc}
R & Gamma \
S & L \
end{array}
right)$
The purpose of this paper is to study matrix hemiring $S_{2}$ via fuzzy subsets and fuzzy $h$-ideals.
http://ijfs.usb.ac.ir/article_133_ab7b86c21df96936081a587cc5bade03.pdf
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10.22111/ijfs.2012.133
$Gamma$-hemiring
Fuzzy $h$-ideal
$h$-hemiregular
Matrix hemiring
Operator hemirings
S. K.
Sardar
sksardarjumath@gmail.com
true
1
Department of Mathematics, Jadavpur University, Kolkata, India
Department of Mathematics, Jadavpur University, Kolkata, India
Department of Mathematics, Jadavpur University, Kolkata, India
AUTHOR
D.
Mandal
dmandaljumath@gmail.com
true
2
Department of Mathematics, Jadavpur University, Kolkata, India
Department of Mathematics, Jadavpur University, Kolkata, India
Department of Mathematics, Jadavpur University, Kolkata, India
AUTHOR
B.
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
LEAD_AUTHOR
bibitem{B} Y. Bingxue, {it Fuzzy semi-ideal and generalized fuzzy quotient ring}, Iranian Journal of Fuzzy Systems, {bf 5(2)} (2008), 87-92.
1
bibitem{D1} B. Davvaz and P. Corsini, {it On $(alpha,beta)$-fuzzy $Hsb v$-ideals of $Hsb v$-rings}, Iranian Journal of Fuzzy Systems, {bf5(2)} (2008), 35-47.
2
bibitem{D2} B. Davvaz, {it Fuzzy hyperideals in ternary semihyperrings}, Iranian Journal of Fuzzy Systems, {bf6(4)} (2009), 21-36.
3
bibitem{Dudek} W. A. Dudek, M. Shabir and R. Anjum, {it Characterization of hemirings by their $h$-ideals}, Computer Mathematics with Applications, {bf 59} (2010), 3167-3179.
4
bibitem{re:Dutta} T. K. Dutta and S. K. Sardar, {it On the operator semirings of a
5
$Gamma$-semiring}, Southeast Asian Bull. Math.,
6
{bf 26} (2002), 203-213.
7
bibitem{Golan} J. S. Golan, {it Semirings and their applications}, Kluwer Academic
8
Publishers, 1999.
9
bibitem{Henriksen} M. Henriksen, {it Ideals in semirings with commutative addition},
10
Am. Math. Soc. Notices, {bf6} (1958), 321.
11
bibitem{Iizuka} K. Iizuka,{it On the Jacobson radical of semiring}, Tohoku Math. J., {bf 11(2)}
12
(1959), 409-421.
13
bibitem{J} I. Jahan, {it Embedding of the lattice of ideals of a ring into its lattice of fuzzy ideals}, Iranian Journal of Fuzzy Systems, {bf 6(3)} (2009), 65-71.
14
bibitem{YBjun} Y. B. Jun, M. A. "{O}zt"{u}rk and S. Z. Song, {it On Fuzzy $h$-ideals in
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hemiring}, Information Sciences, {bf 162} (2004), 211-226.
16
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begin{array}{cc}
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R & Gamma
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S & L
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end{array}
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right)
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$ and morita context}, Int. J. Alg., {bf4} (2010), 303-315.
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Math., {bf56} (2009), 439-450.
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Information sciences, {bf 177} (2007), 876-886.
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38
ORIGINAL_ARTICLE
ATANASSOV'S INTUITIONISTIC FUZZY GRADE OF I.P.S.
HYPERGROUPS OF ORDER LESS THAN OR EQUAL TO 6
In this paper we determine the sequences of join spaces and Atanassov's intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than or equal to 6, focusing on the calculation of their lengths.
http://ijfs.usb.ac.ir/article_134_d4fa23b3ec49455af1d2d822746a7833.pdf
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10.22111/ijfs.2012.134
Fuzzy set
Atanassov's intuitionistic fuzzy set
i.p.s. hypergroup
Fuzzy grade
Join space
B.
Davvaz
davvaz@yazduni.ac.ir
true
1
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
LEAD_AUTHOR
E.
Hassani Sadrabadi
hassanipma@yahoo.com
true
2
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
AUTHOR
I.
Cristea
irinacri@yahoo.co.uk
true
3
University of Udine, Via delle Scienze 206, 33100 Udine, Italy
University of Udine, Via delle Scienze 206, 33100 Udine, Italy
University of Udine, Via delle Scienze 206, 33100 Udine, Italy
AUTHOR
[1] R. Ameri and H. Hedayati, Fuzzy isomorphism and quotient of fuzzy subpolygroups, Quasi-
1
groups and Related Systems, 13 (2005), 175-184.
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[2] R. Ameri and H. Hedayati, On fuzzy closed, invertible and re
3
exive subsets of hypergroups,
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Italian J. Pure Appl. Math., 22 (2007), 95-114.
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[3] R. Ameri and M. M. Zahedi, Hypergroup and join space induced by a fuzzy subset, Pure
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Math. App., 8 (1997), 155-168.
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[4] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
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[5] G. Chowdhury, Fuzzy transposition hypergroups, Iranian Journal of Fuzzy Systems, 6(3)
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(2009), 37-52.
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[6] P. Corsini, Prolegomena of hypergroups theory, Aviani Editore, 1993.
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di Palermo, Serie II, Tomo, XXXVI (1987), 205-219.
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II, 24 (1987), 81-104.
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Math., 27 (2003), 221-229.
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A.H.A. 1993, Iasi, Romania, Hadronic Press, (1994), 45-52.
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Math Appl., 14(4) (2003), 275-288.
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[12] P. Corsini and I. Cristea, Fuzzy grade of i:p:s: hypergroups of order 7, Iranian Journal of
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Fuzzy Systems, 1 (2004), 15-32.
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Sci., 20 (1995), 293-303.
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[14] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Advances in Mathematics,
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Kluwer Academic Publishers, Dordercht, 2003.
27
[15] P. Corsini and V. Leoreanu-Fotea, On the grade of a sequence of fuzzy sets and join spaces
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determined by a hypergraph, Southeast Asian Bull. Math., 34 (2010), 231-242.
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[16] P. Corsini, V. Leoreanu-Fotea and A. Iranmanesh, On the sequence of hypergroups and mem-
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bership functions determined by a hypergraph, J. Mult.-Valued Logic Soft Comput., 14 (2008)
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[17] I. Cristea, About the fuzzy grade of the direct product of two hypergroupoids, Iranian Journal
32
of Fuzzy Systems, 7 (2010), 95-108.
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[18] I. Cristea and B. Davvaz, Atanassov's intuitionistic fuzzy grade of hypergroups, Information
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Sciences, 180 (2010), 1506-1517.
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[19] B. Davvaz, Fuzzy hyperideals in ternary semihyperrings, Iranian Journal of Fuzzy Systems,
36
6(4) (2009), 21-36.
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[20] B. Davvaz, Fuzzy Hv-groups, Fuzzy Sets and Systems, 101 (1999), 191-195.
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Systems, 5(2) (2008), 35-47.
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[22] B. Davvaz and V. Leoreanu-Fotea, Hyperring theory and applications, Hadronic Press, Inc,
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115, Palm Harber, USA, 2007.
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[23] B. Davvaz, P. Corsini and V. Leoreanu-Fotea, Atanassov's intuitionistic (S; T)-fuzzy n-ary
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subhypergroups and their properties, Information Sciences, 179 (2009), 654-666.
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[24] M. Horry and M. M. Zahedi, Hypergroups and general fuzzy automata, Iranian Journal of
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Fuzzy Systems, 6(2) (2009), 61-74.
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[25] O. Kazanc, S. Yamak and B. Davvaz, On n-ary hypergroups and fuzzy n-ary homomorphism,
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Iranian Journal of Fuzzy Systems, 8(1) (2011), 1-17.
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[26] J. Mittas, Hypergroupes canoniques, values et hypervalues. Hypergroupes fortement et su-
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Stockholm, (1934), 45-49.
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[28] W. Prenowitz and J. Jantosciak, Geometries and join spaces, J. Reine und Angew Math.,
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257 (1972), 100-128.
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[29] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
55
[30] M. Stefanescu and I. Cristea, On the fuzzy grade of hypergroups, Fuzzy Sets and Systems,
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159 (2008), 1097-1106.
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[31] T. Vougiouklis, Hyperstructures and their Representations, Hadronic Press, Inc, 115, Palm
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Harber, USA, 1994.
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[32] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
60
ORIGINAL_ARTICLE
More General Forms of $(alpha, beta )$-fuzzy Ideals of Ordered Semigroups
This paper consider the general forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. Special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related properties are investigated. Thecharacterization of regular ordered semigroups in terms of$(in_{gamma},ivq)$-fuzzy left (right) ideals,$(in_{gamma},ivq)$-fuzzy bi-ideals and$(in_{gamma},ivq)$-fuzzy interior ideals is also investigated.
http://ijfs.usb.ac.ir/article_135_cbe7d4b32ae35a4d34772c5395e4b648.pdf
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10.22111/ijfs.2012.135
Ordered
semigroups
$(alpha
beta)$-fuzzy left (right) ideals
$(in_{gamma}
ivq)$-fuzzy bi-ideals
ivq)$-fuzzy
interior ideals
Yunqiang
Yin
yunqiangyin@gmail.com
true
1
State Key Laboratory, Breeding Base of Nuclear Resources and
Environment, East China Institute of Technology, Nanchang, 330013, China
State Key Laboratory, Breeding Base of Nuclear Resources and
Environment, East China Institute of Technology, Nanchang, 330013, China
State Key Laboratory, Breeding Base of Nuclear Resources and
Environment, East China Institute of Technology, Nanchang, 330013, China
LEAD_AUTHOR
Young Bae
Jun
skywine@gmail.com
true
2
Department of Mathematics Education (and RINS), Gyeongsang Na-
tional University, Chinju 660-701, Korea
Department of Mathematics Education (and RINS), Gyeongsang Na-
tional University, Chinju 660-701, Korea
Department of Mathematics Education (and RINS), Gyeongsang Na-
tional University, Chinju 660-701, Korea
AUTHOR
Zhihui
Yang
zhhyang75@gmail.com
true
3
School of Mathematics and Information Sciences, East China Institute
of Technology, Fuzhou, Jiangxi 344000, China
School of Mathematics and Information Sciences, East China Institute
of Technology, Fuzhou, Jiangxi 344000, China
School of Mathematics and Information Sciences, East China Institute
of Technology, Fuzhou, Jiangxi 344000, China
AUTHOR
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1
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by their intuitionistic fuzzy bi-ideals}, Iranian Journal of Fuzzy
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Systems, textbf{7} (2010 ), 55-69.
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semigroups}, Lobachevskii J. Math., textbf{30} (2009), 30-39.
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semigroups}, Iranian Journal of Fuzzy
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fuzzy ideals}, Comput. Math. Appl., textbf{59} (2010), 539-549.
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in terms of fuzzy subsets}, Iranian Journal of Fuzzy
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Systems, textbf{7} (2010),
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41
ORIGINAL_ARTICLE
L-FUZZIFYING TOPOLOGICAL GROUPS
The main purpose of this paper is to introduce a concept of$L$-fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$-fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$-fuzzifying neighborhood structure of the unit is given. It isshown that the category of $L$-fuzzifying topological groups$L$-{\bf FYTPG} is topological over the category of groups {\bf GRP}with respect to the forgetful functor. As an application, theconclusion that the product of $L$-fuzzifying topological groups isalso an $L$-fuzzifying topological group is proved. Finally, it isproved the forgetful functor preserves the product.
http://ijfs.usb.ac.ir/article_136_5aec0b42a085eb0d15775832efc7139a.pdf
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10.22111/ijfs.2012.136
L-fuzzifying topological groups
L-fuzzifying topology
L-fuzzifying
neighborhood structure
Category
Shai-yan
Zhang
syzhang79@126.com
true
1
School of Science, Southern Yangtze University, Wuxi, Jiangsu
214122, People0 s Republic of China
School of Science, Southern Yangtze University, Wuxi, Jiangsu
214122, People0 s Republic of China
School of Science, Southern Yangtze University, Wuxi, Jiangsu
214122, People0 s Republic of China
AUTHOR
Cong-hua
Yan
chyan@njnu.edu.cn
true
2
school of Math. Sciences, Nanjing Normal Uni-
versity, Nanjing Jiangsu 210046, People0 s Republic of China
school of Math. Sciences, Nanjing Normal Uni-
versity, Nanjing Jiangsu 210046, People0 s Republic of China
school of Math. Sciences, Nanjing Normal Uni-
versity, Nanjing Jiangsu 210046, People0 s Republic of China
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[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, John Wiley &
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Sons, 1990.
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Academic Publishers, (1999), 389-432.
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Fuzzy Systems, 5(3) (2008), 31-44.
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ectivity of L-fuzzifying topological spaces in L-
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36
ORIGINAL_ARTICLE
FUZZY INTEGRAL OF MEASURABLE MULTIFUNCTIONS
We study a fuzzy type integral for measurable multifunctions with respect to a fuzzy measure. Some classical properties and convergence theorems are presented.
http://ijfs.usb.ac.ir/article_137_bae43e24655cf7f43dd488e58f3d5596.pdf
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10.22111/ijfs.2012.137
Fuzzy integral
Fuzzy measure
Measurable multifunction
Anca
Croitoru
croitoru@uaic.ro
true
1
"Al.I. Cuza" University, Faculty of Mathematics, Bd. Carol I, No.
11, Iasi, 700506, Romania
"Al.I. Cuza" University, Faculty of Mathematics, Bd. Carol I, No.
11, Iasi, 700506, Romania
"Al.I. Cuza" University, Faculty of Mathematics, Bd. Carol I, No.
11, Iasi, 700506, Romania
LEAD_AUTHOR
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set multifunctions, WSEAS Transactions on Mathematics, 8 (2009), 246-257.
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(2008), 1-20.
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60(3) (2010), 289-318.
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Sets and Systems, 160 (2009), 2106-2116.
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and null sets, Fuzzy Sets and Systems, 112 (2000), 233-239.
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Journal of Fuzzy Systems, 7(3) (2010), 73-86.
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"Al.I. Cuza" Iasi, 29 (1984), 41-48.
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St. Univ. "Al.I. Cuza" Iasi, 48 (2002), 165-200.
29
[19] A. Precupanu, A. Gavrilut and A. Croitoru, A fuzzy Gould type integral, Fuzzy Sets and
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Systems, 161 (2010), 661-680.
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[21] D. A. Ralescu and M. Sugeno, Fuzzy integral representation, Fuzzy Sets and Systems, 84
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(1996), 127-133.
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[22] H. Roman-Flores, A. Flores-Franulic and Y. Chalco-Cano, The fuzzy integral for monotone
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functions, Applied Mathematics and Computation, 185 (2007), 492-498.
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[23] C. Stamate, Vector fuzzy integral, Recent Advances in Neural Network, Fuzzy Systems and
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Evolutionary Computing, Proceeding of the 11th WSEAS International Conference on Fuzzy
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Systems (FS'10), Iasi, Romania, June 13-15, (2010), 221-224.
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[24] M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Thesis, Tokyo Institute of
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Technology, 1974.
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of Fuzzy Systems, 5(2) (2008), 93-99.
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Sets and Systems, 75 (1995), 103-109.
50
ORIGINAL_ARTICLE
ON THE FUZZY DIMENSIONS OF FUZZY VECTOR SPACES
In this paper, rstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases de ned by Shi and Huang, is equivalent to the family of its bases de ned by P. Lubczonok. Secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however, the converse is not true. Finally, fuzzy dimension of direct sum is considered, for a nite number of fuzzy vector spaces and it is proved that fuzzy dimension of their direct sum is equal to the sum of fuzzy dimensions of fuzzy vector spaces.
http://ijfs.usb.ac.ir/article_138_f039ecb754d89261c9c1e68ef58032fc.pdf
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10.22111/ijfs.2012.138
Fuzzy vector space
Fuzzy basis
Fuzzy dimension
Direct sum
Chun-E
Huang
hce 137@163.com, hchune@yahoo.com
true
1
Biochemical engineering college, Beijing Union University, Beijing
100023, P. R. China
Biochemical engineering college, Beijing Union University, Beijing
100023, P. R. China
Biochemical engineering college, Beijing Union University, Beijing
100023, P. R. China
LEAD_AUTHOR
Fu-Gui
Shi
fuguishi@bit.edu.cn, f.g.shi@263.net
true
2
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing 100081, P. R. China
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing 100081, P. R. China
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing 100081, P. R. China
AUTHOR
[1] K. S. Abdulkhalikov, The dual of a fuzzy subspace, Fuzzy Sets and Systems, 82 (1996),
1
[2] A. K. Katsaras and D. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, J.
2
Math. Anal. Appl., 58 (1977), 135-146.
3
[3] R. Kumar, On the dimension of a fuzzy subspace, Fuzzy Sets and Systems, 54 (1993), 229-
4
[4] R. Lowen, Convex fuzzy sets, Fuzzy Sets and Systems, 3 (1980), 291-310.
5
[5] G. Lubczonok and V. Murali, On
6
ags and fuzzy subspaces of vector spaces, Fuzzy Sets and
7
Systems, 125 (2002), 201-207.
8
[6] P. Lubczonok, Fuzzy vector spaces, Fuzzy Sets and Systems, 38 (1990), 329-343.
9
[7] F. G. Shi, A new approach to the fuzzication of matroids, Fuzzy Sets and Systems, 160
10
(2009), 696-705.
11
[8] F. G. Shi and C. E. Huang, Fuzzy bases and the fuzzy dimension of fuzzy vector spaces,
12
Mathematical Communications, 15(2) (2010), 303-310.
13
[9] L. Wang and F. G. Shi, Characterization of L-fuzzifying matroids by L-fuzzifying closure
14
operators, Iranian Journal of Fuzzy Systems, 7(1) (2010), 47-58.
15
[10] L. A. Zadeh, A computational approach to fuzzy quantiers in natural languages, Comput.
16
Math. Appl., 9 (1983), 149-184.
17
ORIGINAL_ARTICLE
ON COMPACTNESS AND G-COMPLETENESS IN FUZZY
METRIC SPACES
In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case, for which we present an example of a compact fuzzy metric space that is not complete in Grabiecs sense. On the other hand, Grabiec used a notion of compactness to obtain a fuzzy version of Edelstein s contraction principle. We present here a generalized version of Grabiecs version of the Edelstein xed point theorem and dierent interesting facts on the topology of fuzzy metric spaces.
http://ijfs.usb.ac.ir/article_139_bcc0473d0d21e8f848502062a387e278.pdf
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10.22111/ijfs.2012.139
Fuzzy metric space
Cauchy sequence
G-completeness
Compactness
Fixed point theorem
Pedro
Tirado
pedtipe@mat.upv.es
true
1
Instituto Universitario de Matematica Pura y Aplicada, Universidad
Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
Instituto Universitario de Matematica Pura y Aplicada, Universidad
Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
Instituto Universitario de Matematica Pura y Aplicada, Universidad
Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
LEAD_AUTHOR
[1] I. Altun, Some xed point theorems for single and multi valued mappings on ordered non-
1
archimedean fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 7(1) (2010), 91-96.
2
[2] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,
3
64 (1994), 395-399.
4
[3] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389.
5
[4] V. Gregori and S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Sys-
6
tems, 115 (2000), 485-489.
7
[5] I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11
8
(1975), 336-344.
9
[6] D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems,
10
144 (2004), 431-439.
11
[7] D. Mihet, Fuzzy quasi-metric versions of a theorem of Gregori and Sapena, Iranian Journal
12
of Fuzzy Systems, 7(1) (2010), 59-64.
13
[8] S. Romaguera, A. Sapena and P. Tirado, The Banach xed point theorem in fuzzy quasi-
14
metric spaces with application to the domain of words, Topology Appl., 154 (2007), 2196-
15
[9] R. Saadati, S. Sedghi and H. Zhou, A common xed point theorem for -weakly commuting
16
maps in L-fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 5(1) (2008), 47-54.
17
[10] A. Sapena, A contribution to the study of fuzzy metric spaces, Appl. Gen. Topology, 2 (2001),
18
[11] B. Schweizer and A. Sklar, Statistical metric spaces, Pacic J. Math., 10 (1960), 314-334.
19
[12] R. Vasuki and P. Veeramani, Fixed point theorems and Cauchy sequences in fuzzy metric
20
spaces, Fuzzy Sets and Systems, 135 (2003), 415-417.
21
ORIGINAL_ARTICLE
Persian-translation vol. 9, no. 4, October 2012
http://ijfs.usb.ac.ir/article_2811_1713f6a89b3a4f736a6bda87ff922381.pdf
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