ORIGINAL_ARTICLE
Cover vol.7, no.3
http://ijfs.usb.ac.ir/article_2878_ed328232a3eebd2751711520eb119ed6.pdf
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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
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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
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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
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4
M. Bielli, A. Boulmakoul and H. Mouncif, {it Object modeling and
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Res., {bf 175} (2006), 1705-1730.
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A. Boulmakoul, {it Generalized path-finding algorithms on
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Math., {bf 162} (2004), 263-272.
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A. Boulmakoul, R. Laurini, H. Mouncif and G. Taqafi, {it
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Path-finding operators for fuzzy multimodal spatial networks and
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their integration in mobile-GIS}, Proceedings of the IEEE
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Technology, (2002), 51-56.
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K. R. Buhtani, J. Mordeson and A. Rosenfeld, {it On degrees of
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end nodes and cut nodes in fuzzy graphs}, Iranian Journal of Fuzzy Systems,
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{bf 1} (2004), 57-64.
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K. M. Cadenas and J. L. Verdegay, {it A primer on fuzzy
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optimization models and methods}, Iranian Journal of Fuzzy Systems, {bf
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5} (2006), 1-22.
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T. N. Chuang and J. Y. Kung, {it A new algorithm for the discrete
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fuzzy shortest path problem in a network}, Appl. Math. Comput.,
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{bf 174} (2006), 660-668.
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T. N. Chuang and J. Y. Kung, {it The fuzzy shortest path length and
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the corresponding shortest path in a network}, Comput. Oper. Res.,
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{bf 32} (2005), 1409-1428.
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bibitem{Corm:Leis:Rive:Stei}
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T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein, {it
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Introduction to algorithms}, Second ed., MIT Press and
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McGraw-Hill, (2001), 588-601.
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M. Gondran and M. Minoux, {it Dioids and semirings: links to
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fuzzy sets and other applications}, Fuzzy Sets and Systems, {bf
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158} (2007), 1273-1294.
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M. Gondran and M. Minoux, {it Linear algebra in dioids: a survey
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of recent results}, Ann. Discrete Math., {bf 19} (1984), 147-164.
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51
F. Hernandes, M. T. Lamata, J. L. Verdegay and A. Yamakami, {it The
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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
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31} (2007), 259-269.
57
bibitem{Kesh:Ales:Khei}
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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).
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K. C. Lin and M. S. Chern, {it The fuzzy shortest path problem and
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its most vital arcs}, Fuzzy Sets and Systems, {bf 58} (1993), 343-353.
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A. Lozano and G. Storchi, {it Shortest viable path algorithm in
66
multimodal networks}, Transport. Res., {bf 35} (2001), 225-241.
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bibitem{Mill:Stor:Bowe}
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H. J. Miller, J. D. Storm and M. Bowen, {it GIS design for
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multimodal networks analysis}, GIS/LIS 95 Annual Conference and
70
Exposition Proceedings of GIS/LIS, (1995), 750-759.
71
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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}
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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
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with imprecise edge weight}, Fuzzy Optim. Decis. Making, {bf
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4} (2005), 293-312.
82
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S. Okada, {it Fuzzy shortest path problems incorporating
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interactivity among paths}, Fuzzy Sets and Systems, {bf 142} (2004),
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bibitem{Okad:Sope}
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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),
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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
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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
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6
[4] W. T. Chuang and J. Yang, Extracting sentences segments for text summarization: a machine
7
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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
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[6] Y. Gong and X. Liu, Creating generic text summaries, IEEE, 0-7695-1263-1/01, (2001), 391-
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[7] K. Kaikhah, Automatic text summarization with NNs, Second IEEE International Conference
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on Intelligent Systems, June (2004), 40-44.
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[8] A. Kiani-B, M. R. Akbarzadeh-T and M. H. Moeinzadeh, Intelligent extractive text summarization
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[9] J. Kupiec, J. Pederson and F. Chen, A trainable document summarizer, Proceedings of
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22
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28
statistics, Proceedings of Language Technology Conference (HLT-NAACL 2003), Edmonton,
29
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54
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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
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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
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15
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16
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Fuzzy Sets and Systems, {bf 18} (1986), 31-43.
18
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{bf 24} (1987), 301-317.
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27
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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
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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.
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5
K. P. Adlassnig, {it Fuzzy set theory in medical diagnosis},
6
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8
A. Berrached, M. Beheshti, A. de Korvin and R. Al'{o}, {it Applying
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10
35th Hawaii International Conference on System Sciences, 2002.
11
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12
M. M. Brouke and D. G. Fisher, {it Solution algorithms for fuzzy
13
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14
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15
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17
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18
textbf{7} (1982), 89-101.
19
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21
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22
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23
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24
A. Di Nola, W. Pedrycz and S. Sessa, {it Some theoretical aspects
25
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26
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27
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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).
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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
2018-02-25T11:23:20
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
2018-02-25T11:23:20
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
2018-02-25T11:23:20
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.
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of Mathematical Analysis and Applications, 58 (1977), 135-146.
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Scandinaves, Stockholm, (1934), 45-49.
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and Applications, Hardonic Press, (1994), 199-206.
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36
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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
2018-02-25T11:23:20
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
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22
(1981), 203-215.
23
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24
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25
[15] S. Q. Li and Y. He, On semigroups whose bi-ideals are prime, Acta Mathematica Sinica, 49
26
(2006), 1189-1194.
27
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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
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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
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by Lotfi A. Zadhe, Complex Adaptive Syst. A Bradford book, MIT Press, Cambridge,
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MA, ISBN: 0-262-16171-0, xxiv (1998), 465.
35
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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.
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by computer, Fuzzy Sets and System, 5 (1981), 323-328.
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44
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45
[27] L. A. Zadeh, Fuzzy sets and systems system theory (fox J. ed.), Microwave Research Institute
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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
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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
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2
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ORIGINAL_ARTICLE
Persian-translation vol.7,no.3
http://ijfs.usb.ac.ir/article_2879_a5a23df0e4c295471d439dad9f14fd7b.pdf
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161
169
10.22111/ijfs.2010.2879