ORIGINAL_ARTICLE
Cover vol.7, no.3
http://ijfs.usb.ac.ir/article_2878_ed328232a3eebd2751711520eb119ed6.pdf
2010-10-30T11:23:20
2018-12-16T11:23:20
0
10.22111/ijfs.2010.2878
ORIGINAL_ARTICLE
SOLVING BEST PATH PROBLEM ON MULTIMODAL TRANSPORTATION NETWORKS WITH FUZZY COSTS
Numerous algorithms have been proposed to solve the shortest-pathproblem; many of them consider a single-mode network and crispcosts. Other attempts have addressed the problem of fuzzy costs ina single-mode network, the so-called fuzzy shortest-path problem(FSPP). The main contribution of the present work is to solve theoptimum path problem in a multimodal transportation network, inwhich the costs of the arcs are fuzzy values. Metropolitantransportation systems are multimodal in that they usually containmultiple modes, such as bus, metro, and monorail. The proposedalgorithm is based on the path algebra and dioid of $k$-shortestfuzzy paths. The approach considers the number of mode changes,the correct order of the modes used, and the modeling of two-waypaths. An advantage of the method is that there is no restrictionon the number and variety of the services to be considered. Totrack the algorithm step by step, it is applied to apseudo-multimodal network.
http://ijfs.usb.ac.ir/article_184_f7dc9d13a3aa140362cfd8b83d059aef.pdf
2010-10-11T11:23:20
2018-12-16T11:23:20
1
13
10.22111/ijfs.2010.184
Transportation
Multimodal
Shortest path
Dioid
Fuzzy cost
Graph
GIS
Ali
Golnarkar
a_golnarkar@sina.kntu.ac.ir
true
1
Department of GIS Engineering,
K. N. Toosi University of Technology,
ValiAsr Street, Mirdamad cross, P.C. 19967-15433,
Tehran, Iran
Department of GIS Engineering,
K. N. Toosi University of Technology,
ValiAsr Street, Mirdamad cross, P.C. 19967-15433,
Tehran, Iran
Department of GIS Engineering,
K. N. Toosi University of Technology,
ValiAsr Street, Mirdamad cross, P.C. 19967-15433,
Tehran, Iran
LEAD_AUTHOR
Ali Asghar
Alesheikh
alesheikh@kntu.ac.ir
true
2
Department of GIS Engineering,
K. N. Toosi University of Technology,
ValiAsr Street, Mirdamad cross, P.C. 19967-15433,
Tehran, Iran
Department of GIS Engineering,
K. N. Toosi University of Technology,
ValiAsr Street, Mirdamad cross, P.C. 19967-15433,
Tehran, Iran
Department of GIS Engineering,
K. N. Toosi University of Technology,
ValiAsr Street, Mirdamad cross, P.C. 19967-15433,
Tehran, Iran
AUTHOR
Mohamad Reza
Malek
mrmalek@kntu.ac.ir
true
3
Department of GIS Engineering,
K. N. Toosi University of Technology,
ValiAsr Street, Mirdamad cross, P.C. 19967-15433,
Tehran, Iran
Department of GIS Engineering,
K. N. Toosi University of Technology,
ValiAsr Street, Mirdamad cross, P.C. 19967-15433,
Tehran, Iran
Department of GIS Engineering,
K. N. Toosi University of Technology,
ValiAsr Street, Mirdamad cross, P.C. 19967-15433,
Tehran, Iran
AUTHOR
bibitem{Abba:Alav}
1
S. Abbasbandy and M. Alavi, {it A method for solving fuzzy linear
2
systems}, Iranian Journal of Fuzzy Systems, {bf 4} (1988), 37-44.
3
bibitem{Biel:Boul:Moun}
4
M. Bielli, A. Boulmakoul and H. Mouncif, {it Object modeling and
5
path computation for multimodal travel systems}, Eur. J. Oper.
6
Res., {bf 175} (2006), 1705-1730.
7
bibitem{Boul}
8
A. Boulmakoul, {it Generalized path-finding algorithms on
9
semirings and the fuzzy shortest path problem}, Comput. Appl.
10
Math., {bf 162} (2004), 263-272.
11
bibitem{Boul:Laur:Moun:Taqa}
12
A. Boulmakoul, R. Laurini, H. Mouncif and G. Taqafi, {it
13
Path-finding operators for fuzzy multimodal spatial networks and
14
their integration in mobile-GIS}, Proceedings of the IEEE
15
International Symposium on Signal Processing and Information
16
Technology, (2002), 51-56.
17
bibitem{Buht:Mord:Rose}
18
K. R. Buhtani, J. Mordeson and A. Rosenfeld, {it On degrees of
19
end nodes and cut nodes in fuzzy graphs}, Iranian Journal of Fuzzy Systems,
20
{bf 1} (2004), 57-64.
21
bibitem{Cade:Verd}
22
K. M. Cadenas and J. L. Verdegay, {it A primer on fuzzy
23
optimization models and methods}, Iranian Journal of Fuzzy Systems, {bf
24
5} (2006), 1-22.
25
bibitem{Chua:Kung}
26
T. N. Chuang and J. Y. Kung, {it A new algorithm for the discrete
27
fuzzy shortest path problem in a network}, Appl. Math. Comput.,
28
{bf 174} (2006), 660-668.
29
bibitem{Chua:Kung2}
30
T. N. Chuang and J. Y. Kung, {it The fuzzy shortest path length and
31
the corresponding shortest path in a network}, Comput. Oper. Res.,
32
{bf 32} (2005), 1409-1428.
33
bibitem{Corm:Leis:Rive:Stei}
34
T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein, {it
35
Introduction to algorithms}, Second ed., MIT Press and
36
McGraw-Hill, (2001), 588-601.
37
bibitem{Dech:Pear}
38
R. Dechter and J. Pearl, {it Generalized best-first search
39
strategies and the optimality of $A^*$}, J. ACM, {bf 32} (1985),
40
bibitem{Dubo:Prad}
41
D. Dubois and H. Prade, {it Fuzzy sets and systems: theory and
42
applications}, Academic Press, New York, 1980.
43
bibitem{Gond:Mino}
44
M. Gondran and M. Minoux, {it Dioids and semirings: links to
45
fuzzy sets and other applications}, Fuzzy Sets and Systems, {bf
46
158} (2007), 1273-1294.
47
bibitem{Gond:Mino2}
48
M. Gondran and M. Minoux, {it Linear algebra in dioids: a survey
49
of recent results}, Ann. Discrete Math., {bf 19} (1984), 147-164.
50
bibitem{Hern:Lama:Verd:Yama}
51
F. Hernandes, M. T. Lamata, J. L. Verdegay and A. Yamakami, {it The
52
shortest path problem on networks with fuzzy parameters}, Fuzzy Sets and Systems, {bf 158} (2007), 1561-1570.
53
bibitem{Ji:Iwam:Sha}
54
X. Ji, K. Iwamura and Z. Shao, {it New models for shortest path
55
problem with fuzzy arc lengths}, Appl. Math. Modell., {bf
56
31} (2007), 259-269.
57
bibitem{Kesh:Ales:Khei}
58
A. Keshtiarast, A. A. Alesheikh and A. Kheirbadi, {it Best route
59
finding based on cost in multimodal network with care of networks
60
constraints}, Map Asia Conference, India, {bf 66} (2006).
61
bibitem{Lin:Cher}
62
K. C. Lin and M. S. Chern, {it The fuzzy shortest path problem and
63
its most vital arcs}, Fuzzy Sets and Systems, {bf 58} (1993), 343-353.
64
bibitem{Loza:Stor}
65
A. Lozano and G. Storchi, {it Shortest viable path algorithm in
66
multimodal networks}, Transport. Res., {bf 35} (2001), 225-241.
67
bibitem{Mill:Stor:Bowe}
68
H. J. Miller, J. D. Storm and M. Bowen, {it GIS design for
69
multimodal networks analysis}, GIS/LIS 95 Annual Conference and
70
Exposition Proceedings of GIS/LIS, (1995), 750-759.
71
bibitem{Moaz}
72
S. Moazeni, {it Fuzzy shortest path problem with finite fuzzy
73
quantities}, Appl. Math. Comput., {bf 183} (2006), 160-169.
74
bibitem{Mode:Scio}
75
P. Modesti and A. Sciomachen, {it A utility measure for finding
76
multiobjective shortest paths in urban multimodal transportation
77
networks}, Eur. J. Oper. Res., {bf 111} (1998), 495-508.
78
bibitem{Naye:Pal}
79
S. Nayeem and M. Pal, {it Shortest path problem on a network
80
with imprecise edge weight}, Fuzzy Optim. Decis. Making, {bf
81
4} (2005), 293-312.
82
bibitem{Okad}
83
S. Okada, {it Fuzzy shortest path problems incorporating
84
interactivity among paths}, Fuzzy Sets and Systems, {bf 142} (2004),
85
bibitem{Okad:Sope}
86
S. Okada and T. Soper, {it A shortest path problem on a network
87
with fuzzy arc lengths}, Fuzzy Sets and Systems, {bf 109} (2000),
88
bibitem{Shie}
89
D. Shier, {it On algorithms for finding the K-shortest paths in a
90
network}, Networks, {bf 9} (1979), 195-214.
91
ORIGINAL_ARTICLE
EXTRACTION-BASED TEXT SUMMARIZATION USING FUZZY
ANALYSIS
Due to the explosive growth of the world-wide web, automatictext summarization has become an essential tool for web users. In this paperwe present a novel approach for creating text summaries. Using fuzzy logicand word-net, our model extracts the most relevant sentences from an originaldocument. The approach utilizes fuzzy measures and inference on theextracted textual information from the document to find the most significantsentences. Experimental results reveal that the proposed approach extractsthe most relevant sentences when compared to other commercially availabletext summarizers. Text pre-processing based on word-net and fuzzy analysisis the main part of our work.
http://ijfs.usb.ac.ir/article_185_f4f468a4b5cdae3e759f5223e8ee8f43.pdf
2010-10-09T11:23:20
2018-12-16T11:23:20
15
32
10.22111/ijfs.2010.185
Extraction
fuzzy logic
Text summarization
Word-net
Farshad
Kyoomarsi
true
1
Islamic Azad University of Shahrekord branch, Shahrekord,
Iran
Islamic Azad University of Shahrekord branch, Shahrekord,
Iran
Islamic Azad University of Shahrekord branch, Shahrekord,
Iran
AUTHOR
Hamid
Khosravi
true
2
Shahid Bahonar University of Kerman, International Center for
Science and High Technology and Environmental Sciences, Kerman, Iran
Shahid Bahonar University of Kerman, International Center for
Science and High Technology and Environmental Sciences, Kerman, Iran
Shahid Bahonar University of Kerman, International Center for
Science and High Technology and Environmental Sciences, Kerman, Iran
AUTHOR
Esfandiar
Eslami
esfandiar.eslami@uk.ac.ir
true
3
Shahid Bahonar University of Kerman, The centre of Excellence
for Fuzzy system and applications, Kerman, Iran
Shahid Bahonar University of Kerman, The centre of Excellence
for Fuzzy system and applications, Kerman, Iran
Shahid Bahonar University of Kerman, The centre of Excellence
for Fuzzy system and applications, Kerman, Iran
AUTHOR
Mohsen
Davoudi
true
4
Department of Energy, Electrical Engineering division, Politecnico
di Milano, Milan, Italy
Department of Energy, Electrical Engineering division, Politecnico
di Milano, Milan, Italy
Department of Energy, Electrical Engineering division, Politecnico
di Milano, Milan, Italy
LEAD_AUTHOR
[1] P. B. Baxendale, Machine made index for technical literature: an experiment, IBM Journal
1
of Research and Development, 2(4) (1958), 354-361.
2
[2] R. Brandow, K. Mitlze and L. Rau, Automatic condensation of electronic Publication by
3
sentence election, Information Processing and Management, 31(5) (1995), 675-685.
4
[3] J. J. Buckley, K. D. Reilly and L. J. Jowers, Simulating continuous fuzzy systems: I, Iranian
5
Journal of Fuzzy Systems, 2(1) (2005), 1-18.
6
[4] W. T. Chuang and J. Yang, Extracting sentences segments for text summarization: a machine
7
learning approaches, Proceedings of the 23th Annual International ACM SIGIR Conference
8
on Research and Development in Information Retrieval, Athens, Greece, (2000), 125-159.
9
[5] N. Elhadad, User-sensitive text summarization thesis summary, Thesis Summary, American
10
Association for Artificial Intelligence, USA, 2004.
11
[6] Y. Gong and X. Liu, Creating generic text summaries, IEEE, 0-7695-1263-1/01, (2001), 391-
12
[7] K. Kaikhah, Automatic text summarization with NNs, Second IEEE International Conference
13
on Intelligent Systems, June (2004), 40-44.
14
[8] A. Kiani-B, M. R. Akbarzadeh-T and M. H. Moeinzadeh, Intelligent extractive text summarization
15
using fuzzy inference systems, 1-4244-0457-6/06, IEEE, (2001), 1-4.
16
[9] J. Kupiec, J. Pederson and F. Chen, A trainable document summarizer, Proceedings of
17
the 18th Annual international ACM SIGIR Confluence on Research and Development in
18
Information Retrieval, Seattle, Washington, (1995), 68-73.
19
[10] J. Leskovec, M. Grobelnik and N. Milic-Frayling, Learning semantic graph mapping for document
20
summarization, Proceedings of ECML/PKDD-2004 Workshop on Knowledge Discovery
21
and Ontologies, KDO-2004, Pisa, Italy.
22
[11] C. Y. Lin, ROUGE: a package for automatic evaluation of summaries, Proceedings of Workshop
23
on Text Summarization Branches Out, Post-conference Workshop of ACL, Spain, 2004.
24
[12] C. Y. Lin and E. Hovy, Automatic evaluation of summaries using n-gram co-occurrence
25
statistics, Proceedings of the Human Technology conference (HLT-NAACL-2003), Canada,
26
(2003), 71-78.
27
[13] C. Y. Lin and E. H. Hovy, Automatic evaluation of summaries using n-gram co-occurrence
28
statistics, Proceedings of Language Technology Conference (HLT-NAACL 2003), Edmonton,
29
Canada, (2003), 287-292.
30
[14] I. Mani, Advances in automatic summarization, John Benjamins Publishing Company,
31
(2001), 129-165.
32
[15] E. G. Mansoori, M. J. Zolghadri and S. D. Katebi, Using distribution of data to enhance
33
performance of fuzzy classification systems, Iranian Journal of Fuzzy Systems, 4(1) (2007),
34
[16] G. A. Miller, R. Beckwith, C. Fellbaum, D. Gross, and K. Miller, Five papers on wordnet,
35
Technical Report, Princeton University, (1993), 3-12.
36
[17] T. Nomoto and Y. Matsumoto, A new approach to unsupervised text summarization, SIGIR,
37
ACM, New Orleans, Louisiana, USA, (2001), 26-34.
38
[18] P. Over and J. Yen, An introduction to duc 2003 - intrinsic evaluation of generic news
39
text summarization systems, http:// wwwnlpir.nist.gov/ projects/ duc/ pubs/ 2003slides/
40
duc2003intro.pdf, 2003.
41
[19] K. Papineni, S. Roukos, T. Ward and W. J. Zhu, BLEU: A method for automatic evaluation
42
of machine translation, IBM Research Report RC22176 (W0109-022), 2001.
43
[20] H. Saggion, D. Radev, S. Teufel and W. Lam, Meta-evaluation of summaries in a crosslingual
44
environment using content-based metrics, Proceedings of COLING, Taipei, Taiwan,
45
[21] A. K. Shaymal and M. Pal, Triangular fuzzy matrices, Iranian Journal of Fuzzy Systems,
46
4(1) (2007), 75-87.
47
[22] L. X. Wang, A cource in fuzzy system and control, Prentice Hall, Englewood Cliffs, Nj.
48
ISBN-13: 978-01354088271998.
49
[23] C. C. Yang and F. L. Wang, Fractal summarization: summarization based on fractal theory,
50
SIGIR, ACM 1-58113-646, Toronto, CA, (2003), 391-392.
51
[24] C. C. Yang and F. L. Wang, Hierarchical summarization of large documents, Journal of the
52
American Society for Information Science and Technology, 59(6) (2008), 887-902.
53
[25] L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, Elsevier,
54
Holland, (1999), 9-34.
55
ORIGINAL_ARTICLE
Numerical Methods for Fuzzy Linear Partial Differential Equations under new Definition for Derivative
In this paper difference methods to solve "fuzzy partial differential equations" (FPDE) such as fuzzy hyperbolic and fuzzy parabolic equations are considered. The existence of the solution and stability of the method are examined in detail. Finally examples are presented to show that the Hausdorff distance between the exact solution and approximate solution tends to zero.
http://ijfs.usb.ac.ir/article_187_5c3ac0b4fba64396a03b7d6e2b726a71.pdf
2010-10-09T11:23:20
2018-12-16T11:23:20
33
50
10.22111/ijfs.2010.187
Fuzzy partial differential equation
Difference
method
Tofigh
Allahviranloo
tofigh@allahviranloo.com
true
1
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
LEAD_AUTHOR
M
Afshar Kermani
mog_afshar@yahoo.com
true
2
Department of Mathematics,
Nourth Tehran Branch Islamic Azad University,
Tehran, Iran
Department of Mathematics,
Nourth Tehran Branch Islamic Azad University,
Tehran, Iran
Department of Mathematics,
Nourth Tehran Branch Islamic Azad University,
Tehran, Iran
AUTHOR
bibitem{TA} T. Allahviranloo, {it Difference methods for fuzzy partial differential equations}, Computational Methods in Appliead
1
Mathematics, {bf 2}textbf{(3)} (2002), 233-242.
2
bibitem{TAAS}T. Allahviranloo, N. Ahmadi, E. Ahmadi and K. Shamsolkotabi, {it Block jacobi two stage method for fuzzy system of
3
linear equations}, Appl. Math. and Com., {bf 175} (2006), 1217-1228.
4
bibitem{BG}B. Bede and S. Gal, {it Generalizations of the
5
differentiability of fuzzy number valued functions with
6
applications to fuzzy differential equations}, Fuzzy Sets and Systems,
7
{bf 151} (2005), 581-99.
8
bibitem{JBTHF2} J. J. Buckley and T. Feuring, {it Introduction to fuzzy
9
partial differential equations}, Fuzzy Sets and Systems, {bf 105} (1999), 241-248.
10
bibitem{BUFA} R. L. Burden and J. D. Faires, {it Numerical
11
analysis}, Brooks Cole, 2000.
12
bibitem{YH}Y. Chalco-Cano and H. Roman-Flores, {it On new solutions of
13
fuzzy differential equations}, Chaos Solutions and Fractals, {bf 38}textbf{(1)} (2008), 112-119.
14
bibitem{CHZA} S. L. Chang and L. A. Zadeh, {it On fuzzy mapping and control}, IEEE Trans Systems Man Cybernet, {bf 2} (1972), 30-34.
15
bibitem{DUPR} D. Dubois and H. Prade, {it Towards fuzzy differential calculus: Part 3}, Differentiation Fuzzy Sets and Systems, {bf 8} (1982), 225-233.
16
bibitem{GOVO} R. Goetschel and W. Voxman, {it Elementary fuzzy calculus},
17
Fuzzy Sets and Systems, {bf 18} (1986), 31-43.
18
bibitem{KA1}O. Kaleva, {it Fuzzy differential equations}, Fuzzy Sets and Systems,
19
{bf 24} (1987), 301-317.
20
bibitem{KA2}O. Kaleva, {it The cuachy problem for fuzzy differential
21
equations}, Fuzzy Sets and Systems, {bf 35} (1990), 389-396.
22
bibitem{MFAK}M. Ma, M. Friedman and A. Kandel, {it Numerical solutions
23
of fuzzy differential equatios}, Fuzzy Sets and Systems, {bf 105} (1999), 133-138.
24
bibitem{PR}M. Puri and D. Ralescu, {it Differential and fuzzy functions}, J. Math. Anal. Appl., {bf 91} (1983), 552-558.
25
bibitem{PURA} M. L. Puri and D. A. Ralescu, {it Differentials of fuzzy functions}, J. Math. Anal. Appl., {bf 91} (1983), 321-325.
26
bibitem{SE} S. Seikkala, {it On the fuzzy initial value problem}, Fuzzy Sets and Systems,
27
{bf 24} (1987), 319-330.
28
ORIGINAL_ARTICLE
Optimization of linear objective function subject to
Fuzzy relation inequalities constraints with max-product
composition
In this paper, we study the finitely many constraints of the fuzzyrelation inequality problem and optimize the linear objectivefunction on the region defined by the fuzzy max-product operator.Simplification operations have been given to accelerate theresolution of the problem by removing the components having noeffect on the solution process. Also, an algorithm and somenumerical and applied examples are presented to abbreviate andillustrate the steps of the problem resolution.
http://ijfs.usb.ac.ir/article_189_86cbadca8c34e4a2064af076361a2647.pdf
2010-10-09T11:23:20
2018-12-16T11:23:20
51
71
10.22111/ijfs.2010.189
Linear objective function optimization
Fuzzy relation equations
Fuzzy relation inequalities
Max-product
composition
Elyas
Shivanian
shivanian@ikiu.ac.ir
true
1
Department of Mathematics,
Faculty of Science, Imam Khomeini International University,
Qazvin 34194-288, Iran
Department of Mathematics,
Faculty of Science, Imam Khomeini International University,
Qazvin 34194-288, Iran
Department of Mathematics,
Faculty of Science, Imam Khomeini International University,
Qazvin 34194-288, Iran
AUTHOR
Esmaile
Khorram
eskhor@aut.ac.ir
true
2
Faculty of Mathematics and Computer Science,
Amirkabir University of Technology,
Tehran 15914, Iran
Faculty of Mathematics and Computer Science,
Amirkabir University of Technology,
Tehran 15914, Iran
Faculty of Mathematics and Computer Science,
Amirkabir University of Technology,
Tehran 15914, Iran
LEAD_AUTHOR
bibitem{FF1}
1
S. Abbasbandy and M. Alavi, {it A method for solving fuzzy linear
2
systems}, Iranian Journal of Fuzzy Systems, {bf
3
2}textbf{(2)} (2005), 37-43.
4
bibitem{F1}
5
K. P. Adlassnig, {it Fuzzy set theory in medical diagnosis},
6
IEEE Trans. Systems Man Cybernet, {bf 16} (1986), 260-265.
7
bibitem{F2}
8
A. Berrached, M. Beheshti, A. de Korvin and R. Al'{o}, {it Applying
9
fuzzy relation equations to threat analysis}, Proceedings of the
10
35th Hawaii International Conference on System Sciences, 2002.
11
bibitem{F3}
12
M. M. Brouke and D. G. Fisher, {it Solution algorithms for fuzzy
13
relation equations with max-product composition}, Fuzzy Sets and
14
Systems, textbf{94} (1998), 61-69.
15
bibitem{F4}
16
E. Czogala, J. Drewniak and W. Pedrycz, {it Fuzzy relation
17
equations on a finite set}, Fuzzy Sets and Systems,
18
textbf{7} (1982), 89-101.
19
bibitem{F5}
20
E. Czogala and W. Predrycz, {it On identification in fuzzy
21
systems and its applications in control problem}, Fuzzy Sets and
22
Systems, textbf{6} (1981), 73-83.
23
bibitem{F6}
24
A. Di Nola, W. Pedrycz and S. Sessa, {it Some theoretical aspects
25
of fuzzy relation equations describing fuzzy systems},
26
Information Sciences, {bf 34} (1984), 241-264.
27
bibitem{F7}
28
A. Di Nola and C. Russo, {it Lukasiewicz transform and its
29
application to compression and reconstruction of digital images},
30
Information Sciences, {bf 177} (2007), 1481-1498.
31
bibitem{F8}
32
A. Di Nola, S. Sessa, W. Pedrycz and E. Sanchez, {it Fuzzy
33
relational equations and their applications in knowledge
34
engineering}, Dordrecht: Kluwer Academic Press, 1989.
35
bibitem{F9}
36
D. Dubois and H. Prade, {it Fuzzy sets and systems: theory and
37
applications}, Academic Press, New York, 1980.
38
bibitem{F10}
39
S. C. Fang and G. Li, {it Solving fuzzy relations equations with a
40
linear objective function}, Fuzzy Sets and Systems, {bf
41
103} (1999), 107-113.
42
bibitem{F11}
43
S. C. Fang and S. Puthenpura, {it Linear optimization and
44
extensions: theory and algorithm}, Prentice-Hall, Englewood
45
Cliffs, NJ, 1993.
46
bibitem{F12}
47
M. J. Fernandez and P. Gil, {it Some specific types of fuzzy
48
relation equations}, Information Sciences, {bf 164} (2004),
49
bibitem{F13}
50
S. Z. Guo, P. Z. Wang, A. Di Nola and S. Sessa, {it Further
51
contributions to the study of finite fuzzy relation equations},
52
Fuzzy Sets and Systems, {bf 26} (1988), 93-104.
53
bibitem{F14}
54
F. F. Guo and Z. Q. Xia, {it An algorithm for solving optimization
55
problems with one linear objective function and finitely many
56
constraints of fuzzy relation inequalities}, Fuzzy Optimization
57
and Decision Making, {bf 5} (2006), 33-47.
58
bibitem{F15}
59
M. M. Gupta and J. Qi, {it Design of fuzzy logic controllers
60
based on generalized t-operators}, Fuzzy Sets and Systems, {bf
61
4} (1991), 473-486.
62
bibitem{F16}
63
S. M. Guu and Y. K. Wu, {it Minimizing a linear objective
64
function with fuzzy relation equation constraints}, Fuzzy
65
Optimization and Decision Making, {bf 12} (2002), 1568-4539.
66
bibitem{F17}
67
S. Z. Han, A. H. Song and T. Sekiguchi, {it Fuzzy inequality
68
relation system identification via sign matrix method},
69
Proceeding of IEEE International Conference 3, (1995),
70
1375-1382.
71
bibitem{F18}
72
M. Higashi and G. J. Klir, {it Resolution of finite fuzzy relation
73
equations}, Fuzzy Sets and Systems, {bf 13} (1984), 65-82.
74
bibitem{F19}
75
M. Hosseinyazdi, {it The optimization problem over a
76
distributive lattice}, Journal of Global Optimization, {bf
77
41}textbf{(2)} (2008).
78
bibitem{F20}
79
C. F. Hu, {it Generalized variational inequalities with fuzzy
80
relation}, Journal of Computational and Applied Mathematics,
81
{bf 146} (1998), 198-203.
82
bibitem{F21}
83
G. Li and S. C. Fang, {it Resolution of finite fuzzy resolution
84
equations}, North Carolina State University, Raleigh, NC, {bf
85
322} (1996).
86
bibitem{F22}
87
J. Loetamonphong and S. C. Fang, {it Optimization of fuzzy
88
relation equations with max-product composition}, Fuzzy Sets and
89
Systems, {bf 118} (2001), 509-517.
90
bibitem{F23}
91
J. Loetamonphong, S. C. Fang and R. E. Young, {it
92
Multi-objective optimization problems with fuzzy relation
93
equation constraints}, Fuzzy Sets and Systems, {bf 127} (2002),
94
bibitem{F24}
95
V. Loia and S. Sessa, {it Fuzzy relation equations for coding /
96
decoding processes of images and videos}, Information Sciences,
97
{bf 171} (2005), 145-172.
98
bibitem{F25}
99
J. Lu and S. C. Fang, {it Solving nonlinear optimization
100
problems with fuzzy relation equation constraints}, Fuzzy Sets
101
and Systems, {bf 119} (2001), 1-20.
102
bibitem{F26}
103
H. Nobuhara, B. Bede and K. Hirota, {it On various eigen fuzzy sets
104
and their application to image reconstruction}, Information
105
Sciences, {bf 176} (2006), 2988-3010.
106
bibitem{F27}
107
W. Pedrycz, {it On generalized fuzzy relational equations and
108
their applications}, Journal of Mathematical Analysis and
109
Applications, {bf 107} (1985), 520-536.
110
bibitem{F28}
111
W. Pedrycz, {it An approach to the analysis of fuzzy systems},
112
Int. J. Control, {bf 34} (1981), 403-421.
113
bibitem{F29}
114
K. Peeva and Y. Kyosev, {it Fuzzy relational calculus, advances in
115
fuzzy systems aplications and theory}, World Scientific
116
Publishing Co. Pte. Ltd, Singapore, {bf 22} (2004).
117
bibitem{F30}
118
I. Perfilieva and V. Nov'{a}k, {it System of fuzzy
119
relation equations as a continuous model of IF-THEN rules},
120
Information Sciences, {bf 177}textbf{(16)} (2007), 3218-3227.
121
bibitem{F31}
122
I. Perfilieva, {it Fixed points and Solvability of systems of
123
fuzzy relation equations, in: O. Castillo, P. Melin, etal (Eds.)
124
theoretical advances and applications of fuzzy logic and soft
125
computing}, Advances in Soft Computing, {bf 42} (2007), 841-849.
126
bibitem{F32}
127
I. Perfilieva and L. Noskov'{a}, {it System of fuzzy relation
128
equations with composition in semi-linear spaces: maximal
129
solutions}, Fuzzy Sets and Systems, {bf 159} (2008), 2256-2271.
130
bibitem{F33}
131
M. Prevot, {it Algorithm for the solution of fuzzy relations},
132
Fuzzy Sets and S
133
ystems, {bf 5} (1985), 319-322.
134
bibitem{F34}
135
E. Sanchez, {it Solution in composite fuzzy relation equations:
136
application to medical diagnosis in brouwerian logic, in fuzzy
137
automata and decision processes}, North-Holland, New York,
138
(1977), 221-234.
139
bibitem{F35}
140
E. Shivanian and E. Khorram, {it Monomial geometric programming
141
with fuzzy-relation inequality constraints with max-product
142
composition}, Computer and Industrial engineering, {bf 56} (2008),
143
1386-1392.
144
bibitem{FF2}
145
E. Shivanian, E. Khorram and A. Ghodousian, {it Optimization of
146
linear objective function subject to fuzzy-relation inequalities
147
constraints with max-average composition }, Iranian Journal of
148
Fuzzy Systems, {bf 4}textbf{(2)} (2007), 15-29.
149
bibitem{F36}
150
B. S. Shieh, {it Solutions of fuzzy relation equations based
151
on continuous t-norms}, Information Sciences, {bf
152
177}textbf{(19)} (2007), 4208-4215.
153
bibitem{F37}
154
W. B. Vasantha Kandasamy and F. Smarandache, {it Fuzzy relational
155
maps and neutrosophic relational maps}, Hexis Church Rock, 2004.
156
bibitem{F38}
157
P. Z. Wang, {it How many lower solutions of finite fuzzy relation
158
equations}, Fuzzy Mathematics, Chinese, {bf 4} (1984), 67-73.
159
bibitem{F39}
160
P. Z. Wang, {it Lattecized linear programming and fuzzy relation
161
inequalities}, Journal of Mathematical Analysis and Applications,
162
{bf 159} (1991), 72-87.
163
bibitem{F40}
164
F. Wenstop, {it Deductive verbal models of organizations}, Int.
165
J. Man-Machine Studies , {bf 8} (1976), 293-311.
166
bibitem{F41}
167
L. A. Zadeh, {it Fuzzy sets}, Informatio and Control, {bf 8} (1965),
168
bibitem{F42}
169
L. A. Zadeh, {it Toward a generalized theory of uncertainty
170
(GTU)--an outline}, Information Sciences, {bf
171
172}textbf{(1)} (2005), 1-40.
172
bibitem{F43}
173
H. T. Zhang, H. M. Dong and R. H. Ren, {it Programming problem with
174
fuzzy relation inequality constraints}, Journal of Liaoning
175
Noramal University, {bf 3} (2003), 231-233.
176
ORIGINAL_ARTICLE
A RELATED FIXED POINT THEOREM IN n FUZZY METRIC
SPACES
We prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of Aliouche, et al. [2], Rao et al. [14] and [15].
http://ijfs.usb.ac.ir/article_191_dbb85a86732bdc74eac64f1c7bda6bb3.pdf
2010-10-09T11:23:20
2018-12-16T11:23:20
73
86
10.22111/ijfs.2010.191
Fuzzy metric space
Implicit relation
Sequentially compact fuzzy
metric space
Related fixed point
Faycel
Merghadi
faycel mr@yahoo.fr
true
1
Department of Mathematics, University of Tebessa, 12000, Algeria
Department of Mathematics, University of Tebessa, 12000, Algeria
Department of Mathematics, University of Tebessa, 12000, Algeria
AUTHOR
Abdelkrim
Aliouche
alioumath@yahoo.fr
true
2
Department of Mathematics, University of Larbi Ben M’Hidi,
Oum-El-Bouaghi, 04000, Algeria
Department of Mathematics, University of Larbi Ben M’Hidi,
Oum-El-Bouaghi, 04000, Algeria
Department of Mathematics, University of Larbi Ben M’Hidi,
Oum-El-Bouaghi, 04000, Algeria
LEAD_AUTHOR
[1] A. Aliouche and B. Fisher, Fixed point theorems for mappings satisfying implicit relation
1
on two complete and compact metric spaces, Applied Mathematics and Mechanics., 27(9)
2
(2006), 1217-1222.
3
[2] A. Aliouche, F. Merghadi and A. Djoudi, A related fixed point theorem in two fuzzy metric
4
spaces, J. Nonlinear Sci. Appl., 2(1) (2009), 19-24.
5
[3] Y. J. Cho, Fixed points in fuzzy metric spaces, J. Fuzzy. Math., 5(4) (1997), 949-962.
6
[4] B. Fisher, Fixed point on two metric spaces, Glasnik Mat., 16(36) (1981), 333-337.
7
[5] A. George and P. Veeramani, On some result in fuzzy metric space, Fuzzy Sets and Systems,
8
64 (1994), 395-399.
9
[6] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389.
10
[7] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica., 11
11
(1975), 326-334.
12
[8] M. S. El Naschie, On the uncertainty of Cantorian geometry and two-slit experiment, Chaos,
13
Solitons and Fractals., 9 (1998), 517-29.
14
[9] M. S. El Naschie, A review of E-infinity theory and the mass spectrum of high energy particle
15
physics, Chaos, Solitons and Fractals., 19 (2004), 209-36.
16
[10] M. S. El Naschie, On a fuzzy Kahler-like manifold which is consistent with two-slit experiment,
17
Int. J. of Nonlinear Science and Numerical Simulation., 6 (2005), 95-98.
18
[11] M. S. El Naschie, The idealized quantum two-slit gedanken experiment revisited criticism and
19
reinterpretation, Chaos, Solitons and Fractals., 27 (2006), 9-13.
20
[12] M. S. El Naschie On two new fuzzy Kahler manifols, Klein modular space and ’t Hooft
21
holographic principles, Chaos, Solitons & Fractals., 29 (2006), 876-881.
22
[13] V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation,
23
Demonstratio Math., 32 (1999), 157-163.
24
[14] K. P. R. Rao, N. Srinivasa Rao, T. Ranga Rao and J. Rajendra Prasad, Fixed and related fixed
25
point theorems in sequentially compact fuzzy metric spaces, Int. Journal of Math. Analysis,
26
2(28) (2008), 1353-1359
27
[15] K. P. R. Rao, A. Aliouche and G. Ravi Babu, Related fixed point theorems in fuzzy metric
28
spaces, J. Nonlinear Sci. Appl., 1(3) (2008), 194-202
29
[16] J. Rodr´ıguez L´opez and S. Ramaguera, The hausdorff fuzzy metric on compact sets, Fuzzy
30
Sets and Systems, 147 (2004), 273-283.
31
[17] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334.
32
[18] Y. Tanaka, Y. Mizno, T. Kado, Chaotic dynamics in friedmann equation, Chaos, Solitons
33
and Fractals., 24 (2005), 407-422.
34
[19] M. Telci, Fixed points on two complete and compact metric spaces, Applied Mathematics
35
and Mechanics, 22(5) (2001), 564-568.
36
[20] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
37
ORIGINAL_ARTICLE
BEST SIMULTANEOUS APPROXIMATION IN FUZZY NORMED
SPACES
The main purpose of this paper is to consider the t-best simultaneousapproximation in fuzzy normed spaces. We develop the theory of t-bestsimultaneous approximation in quotient spaces. Then, we discuss the relationshipin t-proximinality and t-Chebyshevity of a given space and its quotientspace.
http://ijfs.usb.ac.ir/article_192_36f51554bb9dcefe1c3bb01a0018eb3a.pdf
2010-10-09T11:23:20
2018-12-16T11:23:20
87
96
10.22111/ijfs.2010.192
t-best simultaneous approximation
t-proximinality
t-Chebyshevity
Quotient spaces
Mozafar
Goudarzi
goudarzi@mail.yu.ac.ir
true
1
Department of Mathematics and Computer Sciences, Amirkabir
University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran
Department of Mathematics and Computer Sciences, Amirkabir
University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran
Department of Mathematics and Computer Sciences, Amirkabir
University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran
AUTHOR
S. Mansour
Vaezpour
vaez@aut.ac.ir
true
2
Department of Mathematics and Computer Sciences, Amirkabir
University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran
Department of Mathematics and Computer Sciences, Amirkabir
University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran
Department of Mathematics and Computer Sciences, Amirkabir
University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran
LEAD_AUTHOR
[1] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math.,
1
11(3) (2003), 678-705.
2
[2] S. C. Cheng and J. N. Morsden, Fuzzy linear operator and fuzzy normed linear spaces, Bull.
3
Calculatta Math. Soc., 86 (1994), 429-436.
4
[3] M. S. El Naschie, On the uncertainty of cantorian geometry and two-slit experiment, Chaos,
5
Solitons and Fractals, 9 (1998), 517-529.
6
[4] M. S. El Naschie, On a fuzzy Kahler-like manifold which is consistent with two-slit experiment,
7
Int. Journal of Nonlinear Science and Numerical Simulation, 6 (2005), 95-98.
8
[5] M. S. El Naschie, A review of E-infinity theory and the mass spectrum of high energy particle
9
physics, Chaos, Solitons and Fractals, 19 (2004), 209-236.
10
[6] A. George and P. V. Veermani, On some results in fuzzy metric spaces, Fuzzy Sets and
11
Systems, 64 (1994), 395-399.
12
[7] S. B. Hosseini, D. O,regan and R. Saadati, Some results on intuitionistic fuzzy spaces, Iranian
13
Journal of Fuzzy Systems, 1 (2007), 53-64.
14
[8] I. Kramosil and J. Mischalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11
15
(1975), 326-334.
16
[9] J. Rodriguez-Lopez and S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy
17
Sets and Systems, 147 (2004), 273-283.
18
[10] M. Rafi, M. Salmi and M. Noorani, Fixed point theorem on intuitionistic fuzzy metric spaces,
19
Iranian Journal of Fuzzy Systems, 3 (2008), 23-30.
20
[11] R. Saadati, S. Sedghi and H. Zhou, A common fixed point theorem for -weakly commuting
21
maps in L-fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 5 (2008), 47-54.
22
[12] R. Saadati and S. M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math and
23
Computing., 17(1-2) (2005), 475-484.
24
[13] Y. Tanaka, Y. Minzno and T. Kado, Chaotic dynamics in friedman equation, Chaos, Solitons
25
and Fractals, 24 (2005), 407-422.
26
[14] S. M. Vaezpour and F. Karimi, T-best approximation in fuzzy normed spaces, Iranian Journal
27
of Fuzzy Systems, 2 (2008), 93-99.
28
[15] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
29
ORIGINAL_ARTICLE
FUZZY BASIS OF FUZZY HYPERVECTOR SPACES
The aim of this paper is the study of fuzzy basis and dimensionof fuzzy hypervector spaces. In this regard, first the notions of fuzzy linearindependence and fuzzy basis are introduced and then some related results areobtained. In particular, it is shown that for a large class of fuzzy hypervectorspace the fuzzy basis exist. Finally, dimension of a fuzzy hypervector space isdefined and the basic properties of that are investigated.
http://ijfs.usb.ac.ir/article_193_79de888ed0a4241f5c2fdeddeda24391.pdf
2010-10-09T11:23:20
2018-12-16T11:23:20
97
113
10.22111/ijfs.2010.193
Fuzzy hypervector space
Fuzzy linear independence
Fuzzy basis
Dimension
Reza
Ameri
rameri@ut.ac.ir
true
1
School of Mathematics, Statistics and Computer Science, College of
Sciences, University of Tehran, Tehran, Iran
School of Mathematics, Statistics and Computer Science, College of
Sciences, University of Tehran, Tehran, Iran
School of Mathematics, Statistics and Computer Science, College of
Sciences, University of Tehran, Tehran, Iran
LEAD_AUTHOR
omid reza
dehghan
dehghan@umz.ac.ir
true
2
Department of Mathematics, Faculty of Basic Sciences, University
of Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Basic Sciences, University
of Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Basic Sciences, University
of Mazandaran, Babolsar, Iran
AUTHOR
[1] R. Ameri, Fuzzy hypervector spaces over valued fields, Iranian Journal of Fuzzy Systems, 2
1
(2005), 37-47.
2
[2] R. Ameri, H. Hedayati and A. Molaee, On fuzzy hyperideals of -hyperrings, Iranian Journal
3
of Fuzzy Systems, to appear.
4
[3] R. Ameri, Fuzzy (co-)norm hypervector spaces, Proceeding of the 8th International Congress
5
in Algebraic Hyperstructures and Applications, Samotraki, Greece, September 1-9 (2002),
6
[4] R. Ameri and O. R. Dehghan, On dimension of hypervector spaces, European Journal of
7
Pure and Applied Mathematics, 1(2) (2008), 32-50.
8
[5] R. Ameri and O. R. Dehghan, Fuzzy hypervector spaces, Advances in Fuzzy Systems, Article
9
ID 295649, 2008.
10
[6] R. Ameri and M. M. Zahedi, Hypergroup and join spaces induced by a fuzzy subset, PU.M.A
11
8 (1997), 155-168.
12
[7] R. Ameri and M. M. Zahedi, Fuzzy subhypermodules over fuzzy hyperrings, 6th International
13
Congress in Algebraic Hyperstructures and Applications, Democritus University, (1996), 1-14.
14
[8] P. Corsini, Prolegomena of hypergroup theory, Second edition, Aviani editor, (1993).
15
[9] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publications,
16
[10] P. Corsini and V. Leoreanu, Fuzzy sets and join spaces associated with rough sets, Rend.
17
Circ. Mat., Palermo, 51 (2002), 527-536.
18
[11] P. Corsini and I. Tofan, On fuzzy hypergroups, PU. M. A, 8 (1997), 29-37.
19
[12] B. Davvaz, Fuzzy HV -submodules, Fuzzy Sets and Systems, 117 (2001), 477-484.
20
[13] B. Davvaz, Fuzzy HV -groups, Fuzzy Sets and Systems, 101 (1999), 191-195.
21
[14] A. De Luca and S. Termini, A definition of non-probabilistic entropy in the setting of fuzzy
22
sets theory, Information and control, 20 (1970), 301-312.
23
[15] A. K. Katsaras and D. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, Journal
24
of Mathematical Analysis and Applications, 58 (1977), 135-146.
25
[16] P. Lubczonok, Fuzzy vector spaces, Fuzzy Sets and Systems, 38 (1990) 329-343.
26
[17] F. Marty, Sur une generalization de la notion de groupe, 8th Congress Des Mathematiciens
27
Scandinaves, Stockholm, (1934), 45-49.
28
[18] J. N. Mordeson and D. S. Malik, Fuzzy commutative algebra, World Scientific Pub. Co. Inc.,
29
[19] S. Nanda, Fuzzy linear spaces over valued fields, Fuzzy Sets and Systems, 42 (1991), 351-354.
30
[20] S. Nanda, Fuzzy fields and fuzzy linear spaces, Fuzzy Sets and Systems, 19 (1986), 8994.
31
[21] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
32
[22] M. S. Tallini, Hypervector spaces, Fourth Int. Congress on AHA, (1990), 167-174.
33
[23] M. S. Tallini, Weak hypervector spaces and norms in such spaces, Algebraic Hyperstructures
34
and Applications, Hardonic Press, (1994), 199-206.
35
[24] T. Vougiouklis, Hyperstructures and their representations, Hardonic, Press, Inc., 1994.
36
[25] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
37
ORIGINAL_ARTICLE
ON PRIME FUZZY BI-IDEALS OF SEMIGROUPS
In this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy bi-ideals of a semigroup. We characterize thosesemigroups for which each fuzzy bi-ideal is semiprime. We also characterizethose semigroups for which each fuzzy bi-ideal is strongly prime.
http://ijfs.usb.ac.ir/article_194_99c31c34b2db27922370768b4f44c69c.pdf
2010-10-09T11:23:20
2018-12-16T11:23:20
115
128
10.22111/ijfs.2010.194
Prime fuzzy bi-ideals
Semiprime fuzzy bi-ideals
Strongly prime fuzzy
bi-ideals
Irreducible fuzzy bi-ideals
Strongly irreducible fuzzy bi-ideals
Muhammad
Shabir
mshabirbhatti@yahoo.co.uk
true
1
Department of Mathematics, Quaid-i-Azam University, Islamabad,
Pakistan
Department of Mathematics, Quaid-i-Azam University, Islamabad,
Pakistan
Department of Mathematics, Quaid-i-Azam University, Islamabad,
Pakistan
LEAD_AUTHOR
Young Bae
Jun
ybjun@nongae.gsnu.ac.kr
true
2
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
Mahwish
Bano
sandiha pinky2005@yahoo.com
true
3
Department of Mathematics, Air University E-9, PAF Complex, Islamabad,
Pakistan
Department of Mathematics, Air University E-9, PAF Complex, Islamabad,
Pakistan
Department of Mathematics, Air University E-9, PAF Complex, Islamabad,
Pakistan
AUTHOR
[1] J. Ahsan, R. M. Latif and M. Shabir, Fuzzy quasi-ideals in Semigroups, Journal of Fuzzy
1
Mathematics, 9 (2001), 259-270.
2
[2] J. Ahsan, K. Y. Li and M. Shabir, Semigroups characterized by their fuzzy bi-ideals, Journal
3
of Fuzzy Mathematics, 10 (2002), 441-449.
4
[3] J. Ahsan, K. Saifullah and M. F. Khan, Semigroups characterized by their fuzzy ideals, Fuzzy
5
Systems and Mathematics, 9 (1995), 29-32.
6
[4] J. Ahsan, K. Saifullah and M. Shabir, Fuzzy prime and semiprime S-subacts over monoids,
7
New Mathematics and Natural Computation, 3 (2007), 41-56.
8
[5] A. Bargiela and W. Pedrycz, Granular computing: an introduction, The Kluwer Inter. Series
9
in Engginearing and Computer Science, Kluwe Academic Publishers, Boston MA., ISBN
10
1-4020-7273-2, 717(xx) (2003), 452.
11
[6] G. Birkhoff, Lattice theory, Amer. Math. Soc., Coll. Publ., Providence, Rhode Island, 1967.
12
[7] N. Kehayopulu and M. Tsingelis, The embeding of an ordered groupoid into a poe-groupoid
13
in terms of fuzzy sets, Information Sciences, 152 (2003), 231-236.
14
[8] N. Kehayopulu and M. Tsingelis, Fuzzy bi-ideals in ordered semigroups, Information Sciences,
15
171 (2004), 13-28.
16
[9] N. Kehayopulu and M. Tsingelis, Regular ordered semigroups in terms of fuzzy subsets, Information
17
Sciences, 176 (2006), 3675-3693.
18
[10] G. J. Klir and B. Yuan, Fuzzy sets and fuzzy logic theory and applications, Prentice Hall Inc,
19
New Jersey, 1995.
20
[11] N. Kuroki, Fuzzy bi-ideals in semigroups, Comment. Math. Univ. St. Paul, 28 (1979), 17-21.
21
[12] N. Kuroki, On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems, 5
22
(1981), 203-215.
23
[13] N. Kuroki, Fuzzy semiprime ideals in semigroups, Fuzzy Sets and Systems, 8 (1982), 71-79.
24
[14] N. Kuroki, On fuzzy semigroups, Information Sciences, 53 (1991), 203-236.
25
[15] S. Q. Li and Y. He, On semigroups whose bi-ideals are prime, Acta Mathematica Sinica, 49
26
(2006), 1189-1194.
27
[16] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982),
28
[17] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages, Theory and Applications,
29
Computational Mathematics Series, Chapman and Hall/CRC, Boca Raton, 2002.
30
[18] J. N. Mordeson, D. S. Malik and N. Kuroki, Fuzzy semigroups, Studies in Fuzziness and Soft
31
Computing, Springer-Verlag, Berlin, 131 (2003).
32
[19] W. Pedrycz and F. Gomide, An introduction to fuzzy sets: analysis and design, With a Foreword
33
by Lotfi A. Zadhe, Complex Adaptive Syst. A Bradford book, MIT Press, Cambridge,
34
MA, ISBN: 0-262-16171-0, xxiv (1998), 465.
35
[20] A. Rosenfeld, Fuzzy groups, Journal of Mathematical Analysis and Applications, 35 (1971),
36
[21] M. Shabir, Fully fuzzy prime semigroups, International Journal of Mathematics and Mathematical
37
Sciences, 1 (2005), 163-168.
38
[22] M. Shabir and Naila Kanwal, Prime bi-ideals in semigroups, Southeast Asian Bulletin of
39
Mathematics, 31 (2007), 757-764.
40
[23] E. Trillas, On the use of words and fuzzy sets, Information Sciences, 176 (2006), 1463-1487.
41
[24] D. Willaeys and N. Malvache, The use of fuzzy sets for the treatment of fuzzy information
42
by computer, Fuzzy Sets and System, 5 (1981), 323-328.
43
[25] X. Y. Xie, On prime fuzzy ideals of a semigroup, Journal of Fuzzy Mathematics, 8 (2000),
44
[26] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
45
[27] L. A. Zadeh, Fuzzy sets and systems system theory (fox J. ed.), Microwave Research Institute
46
symposia series xv, Polytechnic Press Brook lyn, NY, (1965b), 29-37. Reprinted in Int. J. of
47
General Systems, 17 (1990), 129-138.
48
[28] L. A. Zadeh, Fuzzy sets and applications selected papers, Edited and with a Preface by R.
49
R. Yager, R. M. Tong, S. Ovchinnikov and H. T. Nguyen, A Wiley-Interscience Publication,
50
John Wiley and Sons Inc., New York, 1987.
51
[29] L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1
52
(1987), 3-28.
53
[30] L. A. Zadeh, Fuzzy Sets, Fuzzy Logic and Fuzzy Systems Selected Papers by Lotfi A. Zadeh,
54
Edited and with a preface by George J. Klir and Bo Yuan, Advances in Fuzzy Systems-
55
Applications and Theory, World Scientific Publishing Co., 6 (1996).
56
[31] L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outline, Information
57
Sciences, 172 (2005), 1-40.
58
[32] H. J. Zimmermann, Fuzzy set theory and its applications, With a Foreword by L. A. Zadeh,
59
International Series in Management Science/Operation Research, Kluwer-Nijhoff Publishing,
60
Boston, 1985.
61
[33] H. J. Zimmermann, Fuzzy set theory and its applications, With a Foreword by L. A. Zadeh,
62
fourth edition, Kluwer Academic Publishers, Boston, 2001.
63
ORIGINAL_ARTICLE
SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM
OF OPERATORS
In the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. In particular, it isshown that the Cauchy-Schwarz inequality holds. Moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy Hilbert space has a complementary subspace.Finally, the notions of fuzzy boundedness and operator norm are introducedand the relationship between continuity and boundedness are investigated. Itis shown also that the space of all fuzzy bounded operators is complete.
http://ijfs.usb.ac.ir/article_196_0e9bc69f70cca84530a0ad485e65cabb.pdf
2010-10-09T11:23:20
2018-12-16T11:23:20
129
157
10.22111/ijfs.2010.196
Fuzzy norm
Fuzzy inner product
Fuzzy normed linear space
Fuzzy
boundedness
Strong continuity
Abbas
Hasankhani
abhasan@ mail.uk.ac.ir
true
1
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
AUTHOR
Akbar
Nazari
nazari@ mail.uk.ac.ir
true
2
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
AUTHOR
Morteza
Saheli
true
3
Department of Mathematics, Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran
Department of Mathematics, Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran
Department of Mathematics, Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran
LEAD_AUTHOR
[1] T. Bag and S. K. Samanta, Fuzzy bounded linear operators in Felbin’s type fuzzy normed
1
linear spaces, Fuzzy Sets and Systems, 159 (2008), 685-707.
2
[2] T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151
3
(2005), 513-547.
4
[3] C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48 (1992),
5
[4] C. Felbin, The completion of a fuzzy normed linear space, Mathematical Analysis and Applications,
6
174 (1993), 428-440.
7
[5] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),
8
[6] E. Kreyszig, Introductory functional analysis with applications, John Wiley and Sons, New
9
York, 1978.
10
[7] A. Narayanan, S. Vijayabalaji and N. Thillaigovindan, Intuitionistic fuzzy bounded linear
11
operators, Iranian Journal of Fuzzy Systems, 4(1) (2007), 89-101.
12
[8] M. Rafi and M. S. M. Noorani, Fixed point theorem on intuitionistic fuzzy metric spaces,
13
Iranian Journal of Fuzzy Systems, 3(1) (2006), 23-29.
14
[9] R. Saadati, S. Sedghi and H. Zhou, A common fixed point theorem for -weakly commuting
15
maps in L-fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 5(1) (2008), 47-53.
16
[10] J. Xiao and X. Zhu, Fuzzy normed space of operators and its completeness, Fuzzy Sets and
17
Systems, 133 (2003), 389-399.
18
[11] J. Xiao and X. Zhu, On linearly topological structure and property of fuzzy normed linear
19
space, Fuzzy Sets and Systems, 125 (2002), 153-161.
20
ORIGINAL_ARTICLE
Persian-translation vol.7,no.3
http://ijfs.usb.ac.ir/article_2879_a5a23df0e4c295471d439dad9f14fd7b.pdf
2010-10-30T11:23:20
2018-12-16T11:23:20
161
169
10.22111/ijfs.2010.2879