2010
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SOLVING BEST PATH PROBLEM ON MULTIMODAL TRANSPORTATION NETWORKS WITH FUZZY COSTS
SOLVING BEST PATH PROBLEM ON MULTIMODAL TRANSPORTATION NETWORKS WITH FUZZY COSTS
2
2
Numerous algorithms have been proposed to solve the shortestpathproblem; many of them consider a singlemode network and crispcosts. Other attempts have addressed the problem of fuzzy costs ina singlemode network, the socalled fuzzy shortestpath 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 twowaypaths. 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 apseudomultimodal network.
1
Numerous algorithms have been proposed to solve the shortestpathproblem; many of them consider a singlemode network and crispcosts. Other attempts have addressed the problem of fuzzy costs ina singlemode network, the socalled fuzzy shortestpath 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 twowaypaths. 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 apseudomultimodal network.
1
13
Ali
Golnarkar
Ali
Golnarkar
Department of GIS Engineering,
K. N. Toosi University of Technology,
ValiAsr Street, Mirdamad cross, P.C. 1996715433,
Tehran, Iran
Department of GIS Engineering,
K.
Iran
a_golnarkar@sina.kntu.ac.ir
Ali Asghar
Alesheikh
Ali Asghar
Alesheikh
Department of GIS Engineering,
K. N. Toosi University of Technology,
ValiAsr Street, Mirdamad cross, P.C. 1996715433,
Tehran, Iran
Department of GIS Engineering,
K.
Iran
alesheikh@kntu.ac.ir
Mohamad Reza
Malek
Mohamad Reza
Malek
Department of GIS Engineering,
K. N. Toosi University of Technology,
ValiAsr Street, Mirdamad cross, P.C. 1996715433,
Tehran, Iran
Department of GIS Engineering,
K.
Iran
mrmalek@kntu.ac.ir
Transportation
Multimodal
Shortest path
Dioid
Fuzzy cost
Graph
GIS
[bibitem{Abba:Alav}##S. Abbasbandy and M. Alavi, {it A method for solving fuzzy linear##systems}, Iranian Journal of Fuzzy Systems, {bf 4} (1988), 3744.##bibitem{Biel:Boul:Moun}##M. Bielli, A. Boulmakoul and H. Mouncif, {it Object modeling and##path computation for multimodal travel systems}, Eur. J. Oper.##Res., {bf 175} (2006), 17051730.##bibitem{Boul}##A. Boulmakoul, {it Generalized pathfinding algorithms on##semirings and the fuzzy shortest path problem}, Comput. Appl.##Math., {bf 162} (2004), 263272.##bibitem{Boul:Laur:Moun:Taqa}##A. Boulmakoul, R. Laurini, H. Mouncif and G. Taqafi, {it##Pathfinding operators for fuzzy multimodal spatial networks and##their integration in mobileGIS}, Proceedings of the IEEE##International Symposium on Signal Processing and Information##Technology, (2002), 5156.##bibitem{Buht:Mord:Rose}##K. R. Buhtani, J. Mordeson and A. Rosenfeld, {it On degrees of##end nodes and cut nodes in fuzzy graphs}, Iranian Journal of Fuzzy Systems,##{bf 1} (2004), 5764.##bibitem{Cade:Verd}##K. M. Cadenas and J. L. Verdegay, {it A primer on fuzzy##optimization models and methods}, Iranian Journal of Fuzzy Systems, {bf##5} (2006), 122.##bibitem{Chua:Kung}##T. N. Chuang and J. Y. Kung, {it A new algorithm for the discrete##fuzzy shortest path problem in a network}, Appl. Math. Comput.,##{bf 174} (2006), 660668.##bibitem{Chua:Kung2}##T. N. Chuang and J. Y. Kung, {it The fuzzy shortest path length and##the corresponding shortest path in a network}, Comput. Oper. Res.,##{bf 32} (2005), 14091428.##bibitem{Corm:Leis:Rive:Stei}##T. H. Cormen, C. E. Leiserson, R. L. Rivest and C. Stein, {it##Introduction to algorithms}, Second ed., MIT Press and##McGrawHill, (2001), 588601.##bibitem{Dech:Pear}##R. Dechter and J. Pearl, {it Generalized bestfirst search##strategies and the optimality of $A^*$}, J. ACM, {bf 32} (1985),##bibitem{Dubo:Prad}##D. Dubois and H. Prade, {it Fuzzy sets and systems: theory and##applications}, Academic Press, New York, 1980.##bibitem{Gond:Mino}##M. Gondran and M. Minoux, {it Dioids and semirings: links to##fuzzy sets and other applications}, Fuzzy Sets and Systems, {bf##158} (2007), 12731294.##bibitem{Gond:Mino2}##M. Gondran and M. Minoux, {it Linear algebra in dioids: a survey##of recent results}, Ann. Discrete Math., {bf 19} (1984), 147164.##bibitem{Hern:Lama:Verd:Yama}##F. Hernandes, M. T. Lamata, J. L. Verdegay and A. Yamakami, {it The##shortest path problem on networks with fuzzy parameters}, Fuzzy Sets and Systems, {bf 158} (2007), 15611570.##bibitem{Ji:Iwam:Sha}##X. Ji, K. Iwamura and Z. Shao, {it New models for shortest path##problem with fuzzy arc lengths}, Appl. Math. Modell., {bf##31} (2007), 259269.##bibitem{Kesh:Ales:Khei}##A. Keshtiarast, A. A. Alesheikh and A. Kheirbadi, {it Best route##finding based on cost in multimodal network with care of networks##constraints}, Map Asia Conference, India, {bf 66} (2006).##bibitem{Lin:Cher}##K. C. Lin and M. S. Chern, {it The fuzzy shortest path problem and##its most vital arcs}, Fuzzy Sets and Systems, {bf 58} (1993), 343353.##bibitem{Loza:Stor}##A. Lozano and G. Storchi, {it Shortest viable path algorithm in##multimodal networks}, Transport. Res., {bf 35} (2001), 225241.##bibitem{Mill:Stor:Bowe}##H. J. Miller, J. D. Storm and M. Bowen, {it GIS design for##multimodal networks analysis}, GIS/LIS 95 Annual Conference and##Exposition Proceedings of GIS/LIS, (1995), 750759.##bibitem{Moaz}##S. Moazeni, {it Fuzzy shortest path problem with finite fuzzy##quantities}, Appl. Math. Comput., {bf 183} (2006), 160169.##bibitem{Mode:Scio}##P. Modesti and A. Sciomachen, {it A utility measure for finding##multiobjective shortest paths in urban multimodal transportation##networks}, Eur. J. Oper. Res., {bf 111} (1998), 495508.##bibitem{Naye:Pal}##S. Nayeem and M. Pal, {it Shortest path problem on a network##with imprecise edge weight}, Fuzzy Optim. Decis. Making, {bf##4} (2005), 293312.##bibitem{Okad}##S. Okada, {it Fuzzy shortest path problems incorporating##interactivity among paths}, Fuzzy Sets and Systems, {bf 142} (2004),##bibitem{Okad:Sope}##S. Okada and T. Soper, {it A shortest path problem on a network##with fuzzy arc lengths}, Fuzzy Sets and Systems, {bf 109} (2000),##bibitem{Shie}##D. Shier, {it On algorithms for finding the Kshortest paths in a##network}, Networks, {bf 9} (1979), 195214.##]
EXTRACTIONBASED TEXT SUMMARIZATION USING FUZZY
ANALYSIS
EXTRACTIONBASED TEXT SUMMARIZATION USING FUZZY
ANALYSIS
2
2
Due to the explosive growth of the worldwide 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 wordnet, 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 preprocessing based on wordnet and fuzzy analysisis the main part of our work.
1
Due to the explosive growth of the worldwide 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 wordnet, 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 preprocessing based on wordnet and fuzzy analysisis the main part of our work.
15
32
Farshad
Kyoomarsi
Farshad
Kyoomarsi
Islamic Azad University of Shahrekord branch, Shahrekord,
Iran
Islamic Azad University of Shahrekord branch,
Iran
Hamid
Khosravi
Hamid
Khosravi
Shahid Bahonar University of Kerman, International Center for
Science and High Technology and Environmental Sciences, Kerman, Iran
Shahid Bahonar University of Kerman, International
Iran
Esfandiar
Eslami
Esfandiar
Eslami
Shahid Bahonar University of Kerman, The centre of Excellence
for Fuzzy system and applications, Kerman, Iran
Shahid Bahonar University of Kerman, The
Iran
esfandiar.eslami@uk.ac.ir
Mohsen
Davoudi
Mohsen
Davoudi
Department of Energy, Electrical Engineering division, Politecnico
di Milano, Milan, Italy
Department of Energy, Electrical Engineering
Iran
Extraction
Fuzzy logic
Text summarization
Wordnet
[[1] P. B. Baxendale, Machine made index for technical literature: an experiment, IBM Journal##of Research and Development, 2(4) (1958), 354361.##[2] R. Brandow, K. Mitlze and L. Rau, Automatic condensation of electronic Publication by##sentence election, Information Processing and Management, 31(5) (1995), 675685.##[3] J. J. Buckley, K. D. Reilly and L. J. Jowers, Simulating continuous fuzzy systems: I, Iranian##Journal of Fuzzy Systems, 2(1) (2005), 118.##[4] W. T. Chuang and J. Yang, Extracting sentences segments for text summarization: a machine##learning approaches, Proceedings of the 23th Annual International ACM SIGIR Conference##on Research and Development in Information Retrieval, Athens, Greece, (2000), 125159.##[5] N. Elhadad, Usersensitive text summarization thesis summary, Thesis Summary, American##Association for Artificial Intelligence, USA, 2004.##[6] Y. Gong and X. Liu, Creating generic text summaries, IEEE, 0769512631/01, (2001), 391##[7] K. Kaikhah, Automatic text summarization with NNs, Second IEEE International Conference##on Intelligent Systems, June (2004), 4044.##[8] A. KianiB, M. R. AkbarzadehT and M. H. Moeinzadeh, Intelligent extractive text summarization##using fuzzy inference systems, 1424404576/06, IEEE, (2001), 14.##[9] J. Kupiec, J. Pederson and F. Chen, A trainable document summarizer, Proceedings of##the 18th Annual international ACM SIGIR Confluence on Research and Development in##Information Retrieval, Seattle, Washington, (1995), 6873.##[10] J. Leskovec, M. Grobelnik and N. MilicFrayling, Learning semantic graph mapping for document##summarization, Proceedings of ECML/PKDD2004 Workshop on Knowledge Discovery##and Ontologies, KDO2004, Pisa, Italy. ##[11] C. Y. Lin, ROUGE: a package for automatic evaluation of summaries, Proceedings of Workshop##on Text Summarization Branches Out, Postconference Workshop of ACL, Spain, 2004.##[12] C. Y. Lin and E. Hovy, Automatic evaluation of summaries using ngram cooccurrence##statistics, Proceedings of the Human Technology conference (HLTNAACL2003), Canada,##(2003), 7178.##[13] C. Y. Lin and E. H. Hovy, Automatic evaluation of summaries using ngram cooccurrence##statistics, Proceedings of Language Technology Conference (HLTNAACL 2003), Edmonton,##Canada, (2003), 287292.##[14] I. Mani, Advances in automatic summarization, John Benjamins Publishing Company,##(2001), 129165.##[15] E. G. Mansoori, M. J. Zolghadri and S. D. Katebi, Using distribution of data to enhance##performance of fuzzy classification systems, Iranian Journal of Fuzzy Systems, 4(1) (2007),##[16] G. A. Miller, R. Beckwith, C. Fellbaum, D. Gross, and K. Miller, Five papers on wordnet,##Technical Report, Princeton University, (1993), 312.##[17] T. Nomoto and Y. Matsumoto, A new approach to unsupervised text summarization, SIGIR,##ACM, New Orleans, Louisiana, USA, (2001), 2634.##[18] P. Over and J. Yen, An introduction to duc 2003  intrinsic evaluation of generic news##text summarization systems, http:// wwwnlpir.nist.gov/ projects/ duc/ pubs/ 2003slides/##duc2003intro.pdf, 2003.##[19] K. Papineni, S. Roukos, T. Ward and W. J. Zhu, BLEU: A method for automatic evaluation##of machine translation, IBM Research Report RC22176 (W0109022), 2001.##[20] H. Saggion, D. Radev, S. Teufel and W. Lam, Metaevaluation of summaries in a crosslingual##environment using contentbased metrics, Proceedings of COLING, Taipei, Taiwan,##[21] A. K. Shaymal and M. Pal, Triangular fuzzy matrices, Iranian Journal of Fuzzy Systems,##4(1) (2007), 7587.##[22] L. X. Wang, A cource in fuzzy system and control, Prentice Hall, Englewood Cliffs, Nj.##ISBN13: 97801354088271998.##[23] C. C. Yang and F. L. Wang, Fractal summarization: summarization based on fractal theory,##SIGIR, ACM 158113646, Toronto, CA, (2003), 391392.##[24] C. C. Yang and F. L. Wang, Hierarchical summarization of large documents, Journal of the##American Society for Information Science and Technology, 59(6) (2008), 887902.##[25] L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, Elsevier,##Holland, (1999), 934.##]
Numerical Methods for Fuzzy Linear Partial Differential Equations under new Definition for Derivative
Numerical Methods for Fuzzy Linear Partial Differential Equations under new Definition for Derivative
2
2
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.
1
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.
33
50
Tofigh
Allahviranloo
Tofigh
Allahviranloo
Department of Mathematics,
Science and Research Branch Islamic Azad University,
Tehran, Iran
Department of Mathematics,
Science
Iran
tofigh@allahviranloo.com
M
Afshar Kermani
M
Afshar Kermani
Department of Mathematics,
Nourth Tehran Branch Islamic Azad University,
Tehran, Iran
Department of Mathematics,
Nourth
Iran
mog_afshar@yahoo.com
Fuzzy partial differential equation
Difference method
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Optimization of linear objective function subject to
Fuzzy relation inequalities constraints with maxproduct
composition
Optimization of linear objective function subject to
Fuzzy relation inequalities constraints with maxproduct
composition
2
2
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 maxproduct 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.
1
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 maxproduct 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.
51
71
Elyas
Shivanian
Elyas
Shivanian
Department of Mathematics,
Faculty of Science, Imam Khomeini International University,
Qazvin 34194288, Iran
Department of Mathematics,
Faculty
Iran
shivanian@ikiu.ac.ir
Esmaile
Khorram
Esmaile
Khorram
Faculty of Mathematics and Computer Science,
Amirkabir University of Technology,
Tehran 15914, Iran
Faculty of Mathematics and Computer Science,
Iran
eskhor@aut.ac.ir
Linear objective function optimization
Fuzzy relation equations
Fuzzy relation inequalities
Maxproduct composition
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Li and S. C. Fang, {it Resolution of finite fuzzy resolution##equations}, North Carolina State University, Raleigh, NC, {bf##322} (1996). ##bibitem{F22}##J. Loetamonphong and S. C. Fang, {it Optimization of fuzzy##relation equations with maxproduct composition}, Fuzzy Sets and##Systems, {bf 118} (2001), 509517. ##bibitem{F23}##J. Loetamonphong, S. C. Fang and R. E. Young, {it##Multiobjective optimization problems with fuzzy relation##equation constraints}, Fuzzy Sets and Systems, {bf 127} (2002),##bibitem{F24}##V. Loia and S. Sessa, {it Fuzzy relation equations for coding /##decoding processes of images and videos}, Information Sciences,##{bf 171} (2005), 145172. ##bibitem{F25}##J. Lu and S. C. Fang, {it Solving nonlinear optimization##problems with fuzzy relation equation constraints}, Fuzzy Sets##and Systems, {bf 119} (2001), 120. ##bibitem{F26}##H. Nobuhara, B. Bede and K. Hirota, {it On various eigen fuzzy sets##and their application to image reconstruction}, Information##Sciences, {bf 176} (2006), 29883010. ##bibitem{F27}##W. Pedrycz, {it On generalized fuzzy relational equations and##their applications}, Journal of Mathematical Analysis and##Applications, {bf 107} (1985), 520536. ##bibitem{F28}##W. Pedrycz, {it An approach to the analysis of fuzzy systems},##Int. J. Control, {bf 34} (1981), 403421. ##bibitem{F29}##K. Peeva and Y. Kyosev, {it Fuzzy relational calculus, advances in##fuzzy systems aplications and theory}, World Scientific##Publishing Co. Pte. Ltd, Singapore, {bf 22} (2004). ##bibitem{F30}##I. Perfilieva and V. Nov'{a}k, {it System of fuzzy##relation equations as a continuous model of IFTHEN rules},##Information Sciences, {bf 177}textbf{(16)} (2007), 32183227. ##bibitem{F31}##I. Perfilieva, {it Fixed points and Solvability of systems of##fuzzy relation equations, in: O. Castillo, P. 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Ghodousian, {it Optimization of##linear objective function subject to fuzzyrelation inequalities##constraints with maxaverage composition }, Iranian Journal of##Fuzzy Systems, {bf 4}textbf{(2)} (2007), 1529. ##bibitem{F36}##B. S. Shieh, {it Solutions of fuzzy relation equations based##on continuous tnorms}, Information Sciences, {bf##177}textbf{(19)} (2007), 42084215. ##bibitem{F37}##W. B. Vasantha Kandasamy and F. Smarandache, {it Fuzzy relational##maps and neutrosophic relational maps}, Hexis Church Rock, 2004. ##bibitem{F38}##P. Z. Wang, {it How many lower solutions of finite fuzzy relation##equations}, Fuzzy Mathematics, Chinese, {bf 4} (1984), 6773. ##bibitem{F39}##P. Z. Wang, {it Lattecized linear programming and fuzzy relation##inequalities}, Journal of Mathematical Analysis and Applications,##{bf 159} (1991), 7287. ##bibitem{F40}##F. Wenstop, {it Deductive verbal models of organizations}, Int.##J. ManMachine Studies , {bf 8} (1976), 293311. ##bibitem{F41}##L. A. Zadeh, {it Fuzzy sets}, Informatio and Control, {bf 8} (1965),##bibitem{F42}##L. A. Zadeh, {it Toward a generalized theory of uncertainty##(GTU)an outline}, Information Sciences, {bf##172}textbf{(1)} (2005), 140. ##bibitem{F43}##H. T. Zhang, H. M. Dong and R. H. Ren, {it Programming problem with##fuzzy relation inequality constraints}, Journal of Liaoning##Noramal University, {bf 3} (2003), 231233.##]
A RELATED FIXED POINT THEOREM IN n FUZZY METRIC
SPACES
A RELATED FIXED POINT THEOREM IN n FUZZY METRIC
SPACES
2
2
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].
1
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].
73
86
Faycel
Merghadi
Faycel
Merghadi
Department of Mathematics, University of Tebessa, 12000, Algeria
Department of Mathematics, University of
Algeria
faycel mr@yahoo.fr
Abdelkrim
Aliouche
Abdelkrim
Aliouche
Department of Mathematics, University of Larbi Ben M’Hidi,
OumElBouaghi, 04000, Algeria
Department of Mathematics, University of
Algeria
alioumath@yahoo.fr
Fuzzy metric space
Implicit relation
Sequentially compact fuzzy metric space
Related fixed point
[[1] A. Aliouche and B. Fisher, Fixed point theorems for mappings satisfying implicit relation##on two complete and compact metric spaces, Applied Mathematics and Mechanics., 27(9)##(2006), 12171222.##[2] A. Aliouche, F. Merghadi and A. Djoudi, A related fixed point theorem in two fuzzy metric##spaces, J. Nonlinear Sci. Appl., 2(1) (2009), 1924.##[3] Y. J. Cho, Fixed points in fuzzy metric spaces, J. Fuzzy. Math., 5(4) (1997), 949962.##[4] B. Fisher, Fixed point on two metric spaces, Glasnik Mat., 16(36) (1981), 333337.##[5] A. George and P. Veeramani, On some result in fuzzy metric space, Fuzzy Sets and Systems,##64 (1994), 395399.##[6] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385389.##[7] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica., 11##(1975), 326334.##[8] M. S. El Naschie, On the uncertainty of Cantorian geometry and twoslit experiment, Chaos,##Solitons and Fractals., 9 (1998), 51729.##[9] M. S. El Naschie, A review of Einfinity theory and the mass spectrum of high energy particle##physics, Chaos, Solitons and Fractals., 19 (2004), 20936.##[10] M. S. El Naschie, On a fuzzy Kahlerlike manifold which is consistent with twoslit experiment,##Int. J. of Nonlinear Science and Numerical Simulation., 6 (2005), 9598.##[11] M. S. El Naschie, The idealized quantum twoslit gedanken experiment revisited criticism and##reinterpretation, Chaos, Solitons and Fractals., 27 (2006), 913.##[12] M. S. El Naschie On two new fuzzy Kahler manifols, Klein modular space and ’t Hooft##holographic principles, Chaos, Solitons & Fractals., 29 (2006), 876881. ##[13] V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation,##Demonstratio Math., 32 (1999), 157163.##[14] K. P. R. Rao, N. Srinivasa Rao, T. Ranga Rao and J. Rajendra Prasad, Fixed and related fixed##point theorems in sequentially compact fuzzy metric spaces, Int. Journal of Math. Analysis,##2(28) (2008), 13531359##[15] K. P. R. Rao, A. Aliouche and G. Ravi Babu, Related fixed point theorems in fuzzy metric##spaces, J. Nonlinear Sci. Appl., 1(3) (2008), 194202##[16] J. Rodr´ıguez L´opez and S. Ramaguera, The hausdorff fuzzy metric on compact sets, Fuzzy##Sets and Systems, 147 (2004), 273283.##[17] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 313334.##[18] Y. Tanaka, Y. Mizno, T. Kado, Chaotic dynamics in friedmann equation, Chaos, Solitons##and Fractals., 24 (2005), 407422.##[19] M. Telci, Fixed points on two complete and compact metric spaces, Applied Mathematics##and Mechanics, 22(5) (2001), 564568.##[20] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##]
BEST SIMULTANEOUS APPROXIMATION IN FUZZY NORMED
SPACES
BEST SIMULTANEOUS APPROXIMATION IN FUZZY NORMED
SPACES
2
2
The main purpose of this paper is to consider the tbest simultaneousapproximation in fuzzy normed spaces. We develop the theory of tbestsimultaneous approximation in quotient spaces. Then, we discuss the relationshipin tproximinality and tChebyshevity of a given space and its quotientspace.
1
The main purpose of this paper is to consider the tbest simultaneousapproximation in fuzzy normed spaces. We develop the theory of tbestsimultaneous approximation in quotient spaces. Then, we discuss the relationshipin tproximinality and tChebyshevity of a given space and its quotientspace.
87
96
Mozafar
Goudarzi
Mozafar
Goudarzi
Department of Mathematics and Computer Sciences, Amirkabir
University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran
Department of Mathematics and Computer Sciences,
Iran
goudarzi@mail.yu.ac.ir
S. Mansour
Vaezpour
S. Mansour
Vaezpour
Department of Mathematics and Computer Sciences, Amirkabir
University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran
Department of Mathematics and Computer Sciences,
Iran
vaez@aut.ac.ir
tbest simultaneous approximation
tproximinality
tChebyshevity
Quotient spaces
[[1] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math.,##11(3) (2003), 678705.##[2] S. C. Cheng and J. N. Morsden, Fuzzy linear operator and fuzzy normed linear spaces, Bull.##Calculatta Math. Soc., 86 (1994), 429436. ##[3] M. S. El Naschie, On the uncertainty of cantorian geometry and twoslit experiment, Chaos,##Solitons and Fractals, 9 (1998), 517529.##[4] M. S. El Naschie, On a fuzzy Kahlerlike manifold which is consistent with twoslit experiment,##Int. Journal of Nonlinear Science and Numerical Simulation, 6 (2005), 9598.##[5] M. S. El Naschie, A review of Einfinity theory and the mass spectrum of high energy particle##physics, Chaos, Solitons and Fractals, 19 (2004), 209236.##[6] A. George and P. V. Veermani, On some results in fuzzy metric spaces, Fuzzy Sets and##Systems, 64 (1994), 395399.##[7] S. B. Hosseini, D. O,regan and R. Saadati, Some results on intuitionistic fuzzy spaces, Iranian##Journal of Fuzzy Systems, 1 (2007), 5364.##[8] I. Kramosil and J. Mischalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11##(1975), 326334.##[9] J. RodriguezLopez and S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy##Sets and Systems, 147 (2004), 273283.##[10] M. Rafi, M. Salmi and M. Noorani, Fixed point theorem on intuitionistic fuzzy metric spaces,##Iranian Journal of Fuzzy Systems, 3 (2008), 2330.##[11] R. Saadati, S. Sedghi and H. Zhou, A common fixed point theorem for weakly commuting##maps in Lfuzzy metric spaces, Iranian Journal of Fuzzy Systems, 5 (2008), 4754.##[12] R. Saadati and S. M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math and##Computing., 17(12) (2005), 475484.##[13] Y. Tanaka, Y. Minzno and T. Kado, Chaotic dynamics in friedman equation, Chaos, Solitons##and Fractals, 24 (2005), 407422.##[14] S. M. Vaezpour and F. Karimi, Tbest approximation in fuzzy normed spaces, Iranian Journal##of Fuzzy Systems, 2 (2008), 9399.##[15] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##]
FUZZY BASIS OF FUZZY HYPERVECTOR SPACES
FUZZY BASIS OF FUZZY HYPERVECTOR SPACES
2
2
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.
1
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.
97
113
Reza
Ameri
Reza
Ameri
School of Mathematics, Statistics and Computer Science, College of
Sciences, University of Tehran, Tehran, Iran
School of Mathematics, Statistics and Computer
Iran
rameri@ut.ac.ir
omid reza
dehghan
omid reza
dehghan
Department of Mathematics, Faculty of Basic Sciences, University
of Mazandaran, Babolsar, Iran
Department of Mathematics, Faculty of Basic
Iran
dehghan@umz.ac.ir
Fuzzy hypervector space
Fuzzy linear independence
Fuzzy basis
Dimension
[[1] R. Ameri, Fuzzy hypervector spaces over valued fields, Iranian Journal of Fuzzy Systems, 2##(2005), 3747.##[2] R. Ameri, H. Hedayati and A. Molaee, On fuzzy hyperideals of hyperrings, Iranian Journal##of Fuzzy Systems, to appear.##[3] R. Ameri, Fuzzy (co)norm hypervector spaces, Proceeding of the 8th International Congress##in Algebraic Hyperstructures and Applications, Samotraki, Greece, September 19 (2002),##[4] R. Ameri and O. R. Dehghan, On dimension of hypervector spaces, European Journal of##Pure and Applied Mathematics, 1(2) (2008), 3250.##[5] R. Ameri and O. R. Dehghan, Fuzzy hypervector spaces, Advances in Fuzzy Systems, Article##ID 295649, 2008.##[6] R. Ameri and M. M. Zahedi, Hypergroup and join spaces induced by a fuzzy subset, PU.M.A##8 (1997), 155168.##[7] R. Ameri and M. M. Zahedi, Fuzzy subhypermodules over fuzzy hyperrings, 6th International##Congress in Algebraic Hyperstructures and Applications, Democritus University, (1996), 114.##[8] P. Corsini, Prolegomena of hypergroup theory, Second edition, Aviani editor, (1993). ##[9] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publications,##[10] P. Corsini and V. Leoreanu, Fuzzy sets and join spaces associated with rough sets, Rend.##Circ. Mat., Palermo, 51 (2002), 527536.##[11] P. Corsini and I. Tofan, On fuzzy hypergroups, PU. M. A, 8 (1997), 2937.##[12] B. Davvaz, Fuzzy HV submodules, Fuzzy Sets and Systems, 117 (2001), 477484.##[13] B. Davvaz, Fuzzy HV groups, Fuzzy Sets and Systems, 101 (1999), 191195.##[14] A. De Luca and S. Termini, A definition of nonprobabilistic entropy in the setting of fuzzy##sets theory, Information and control, 20 (1970), 301312.##[15] A. K. Katsaras and D. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, Journal##of Mathematical Analysis and Applications, 58 (1977), 135146.##[16] P. Lubczonok, Fuzzy vector spaces, Fuzzy Sets and Systems, 38 (1990) 329343.##[17] F. Marty, Sur une generalization de la notion de groupe, 8th Congress Des Mathematiciens##Scandinaves, Stockholm, (1934), 4549.##[18] J. N. Mordeson and D. S. Malik, Fuzzy commutative algebra, World Scientific Pub. Co. Inc.,##[19] S. Nanda, Fuzzy linear spaces over valued fields, Fuzzy Sets and Systems, 42 (1991), 351354.##[20] S. Nanda, Fuzzy fields and fuzzy linear spaces, Fuzzy Sets and Systems, 19 (1986), 8994.##[21] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512517.##[22] M. S. Tallini, Hypervector spaces, Fourth Int. Congress on AHA, (1990), 167174.##[23] M. S. Tallini, Weak hypervector spaces and norms in such spaces, Algebraic Hyperstructures##and Applications, Hardonic Press, (1994), 199206.##[24] T. Vougiouklis, Hyperstructures and their representations, Hardonic, Press, Inc., 1994.##[25] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##]
ON PRIME FUZZY BIIDEALS OF SEMIGROUPS
ON PRIME FUZZY BIIDEALS OF SEMIGROUPS
2
2
In this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy biideals of a semigroup. We characterize thosesemigroups for which each fuzzy biideal is semiprime. We also characterizethose semigroups for which each fuzzy biideal is strongly prime.
1
In this paper, we introduce and study the prime, strongly prime,semiprime and irreducible fuzzy biideals of a semigroup. We characterize thosesemigroups for which each fuzzy biideal is semiprime. We also characterizethose semigroups for which each fuzzy biideal is strongly prime.
115
128
Muhammad
Shabir
Muhammad
Shabir
Department of Mathematics, QuaidiAzam University, Islamabad,
Pakistan
Department of Mathematics, QuaidiAzam University
Pakistan
mshabirbhatti@yahoo.co.uk
Young Bae
Jun
Young Bae
Jun
Department of Mathematics Education and RINS, Gyeongsang National
University, Chinju 660701, Korea
Department of Mathematics Education and RINS,
Korea
ybjun@nongae.gsnu.ac.kr
Mahwish
Bano
Mahwish
Bano
Department of Mathematics, Air University E9, PAF Complex, Islamabad,
Pakistan
Department of Mathematics, Air University
Pakistan
sandiha pinky2005@yahoo.com
Prime fuzzy biideals
Semiprime fuzzy biideals
Strongly prime fuzzy biideals
Irreducible fuzzy biideals
Strongly irreducible fuzzy biideals
[[1] J. Ahsan, R. M. Latif and M. Shabir, Fuzzy quasiideals in Semigroups, Journal of Fuzzy##Mathematics, 9 (2001), 259270.##[2] J. Ahsan, K. Y. Li and M. Shabir, Semigroups characterized by their fuzzy biideals, Journal##of Fuzzy Mathematics, 10 (2002), 441449.##[3] J. Ahsan, K. Saifullah and M. F. Khan, Semigroups characterized by their fuzzy ideals, Fuzzy##Systems and Mathematics, 9 (1995), 2932.##[4] J. Ahsan, K. Saifullah and M. Shabir, Fuzzy prime and semiprime Ssubacts over monoids,##New Mathematics and Natural Computation, 3 (2007), 4156.##[5] A. Bargiela and W. Pedrycz, Granular computing: an introduction, The Kluwer Inter. Series##in Engginearing and Computer Science, Kluwe Academic Publishers, Boston MA., ISBN##1402072732, 717(xx) (2003), 452. ##[6] G. Birkhoff, Lattice theory, Amer. Math. Soc., Coll. Publ., Providence, Rhode Island, 1967.##[7] N. Kehayopulu and M. Tsingelis, The embeding of an ordered groupoid into a poegroupoid##in terms of fuzzy sets, Information Sciences, 152 (2003), 231236.##[8] N. Kehayopulu and M. Tsingelis, Fuzzy biideals in ordered semigroups, Information Sciences,##171 (2004), 1328.##[9] N. Kehayopulu and M. Tsingelis, Regular ordered semigroups in terms of fuzzy subsets, Information##Sciences, 176 (2006), 36753693.##[10] G. J. Klir and B. Yuan, Fuzzy sets and fuzzy logic theory and applications, Prentice Hall Inc,##New Jersey, 1995.##[11] N. Kuroki, Fuzzy biideals in semigroups, Comment. Math. Univ. St. Paul, 28 (1979), 1721.##[12] N. Kuroki, On fuzzy ideals and fuzzy biideals in semigroups, Fuzzy Sets and Systems, 5##(1981), 203215.##[13] N. Kuroki, Fuzzy semiprime ideals in semigroups, Fuzzy Sets and Systems, 8 (1982), 7179.##[14] N. Kuroki, On fuzzy semigroups, Information Sciences, 53 (1991), 203236.##[15] S. Q. Li and Y. He, On semigroups whose biideals are prime, Acta Mathematica Sinica, 49##(2006), 11891194.##[16] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982),##[17] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages, Theory and Applications,##Computational Mathematics Series, Chapman and Hall/CRC, Boca Raton, 2002.##[18] J. N. Mordeson, D. S. Malik and N. Kuroki, Fuzzy semigroups, Studies in Fuzziness and Soft##Computing, SpringerVerlag, Berlin, 131 (2003).##[19] W. Pedrycz and F. Gomide, An introduction to fuzzy sets: analysis and design, With a Foreword##by Lotfi A. Zadhe, Complex Adaptive Syst. A Bradford book, MIT Press, Cambridge,##MA, ISBN: 0262161710, xxiv (1998), 465.##[20] A. Rosenfeld, Fuzzy groups, Journal of Mathematical Analysis and Applications, 35 (1971),##[21] M. Shabir, Fully fuzzy prime semigroups, International Journal of Mathematics and Mathematical##Sciences, 1 (2005), 163168.##[22] M. Shabir and Naila Kanwal, Prime biideals in semigroups, Southeast Asian Bulletin of##Mathematics, 31 (2007), 757764.##[23] E. Trillas, On the use of words and fuzzy sets, Information Sciences, 176 (2006), 14631487.##[24] D. Willaeys and N. Malvache, The use of fuzzy sets for the treatment of fuzzy information##by computer, Fuzzy Sets and System, 5 (1981), 323328.##[25] X. Y. Xie, On prime fuzzy ideals of a semigroup, Journal of Fuzzy Mathematics, 8 (2000),##[26] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##[27] L. A. Zadeh, Fuzzy sets and systems system theory (fox J. ed.), Microwave Research Institute##symposia series xv, Polytechnic Press Brook lyn, NY, (1965b), 2937. Reprinted in Int. J. of##General Systems, 17 (1990), 129138.##[28] L. A. Zadeh, Fuzzy sets and applications selected papers, Edited and with a Preface by R.##R. Yager, R. M. Tong, S. Ovchinnikov and H. T. Nguyen, A WileyInterscience Publication,##John Wiley and Sons Inc., New York, 1987.##[29] L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1##(1987), 328.##[30] L. A. Zadeh, Fuzzy Sets, Fuzzy Logic and Fuzzy Systems Selected Papers by Lotfi A. Zadeh,##Edited and with a preface by George J. Klir and Bo Yuan, Advances in Fuzzy Systems##Applications and Theory, World Scientific Publishing Co., 6 (1996).##[31] L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)an outline, Information##Sciences, 172 (2005), 140.##[32] H. J. Zimmermann, Fuzzy set theory and its applications, With a Foreword by L. A. Zadeh,##International Series in Management Science/Operation Research, KluwerNijhoff Publishing,##Boston, 1985. ##[33] H. J. Zimmermann, Fuzzy set theory and its applications, With a Foreword by L. A. Zadeh,##fourth edition, Kluwer Academic Publishers, Boston, 2001.##]
SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM
OF OPERATORS
SOME PROPERTIES OF FUZZY HILBERT SPACES AND NORM
OF OPERATORS
2
2
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 CauchySchwarz 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.
1
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 CauchySchwarz 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.
129
157
Abbas
Hasankhani,
Abbas
Hasankhani
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar
Iran
abhasan@ mail.uk.ac.ir
Akbar
Nazari
Akbar
Nazari
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar
Iran
nazari@ mail.uk.ac.ir
Morteza
Saheli
Morteza
Saheli
Department of Mathematics, ValieAsr University of Rafsanjan,
Rafsanjan, Iran
Department of Mathematics, ValieAsr University
Iran
Fuzzy norm
Fuzzy inner product
Fuzzy normed linear space
Fuzzy boundedness
Strong continuity
[[1] T. Bag and S. K. Samanta, Fuzzy bounded linear operators in Felbin’s type fuzzy normed##linear spaces, Fuzzy Sets and Systems, 159 (2008), 685707.##[2] T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151##(2005), 513547.##[3] C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48 (1992),##[4] C. Felbin, The completion of a fuzzy normed linear space, Mathematical Analysis and Applications,##174 (1993), 428440.##[5] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),##[6] E. Kreyszig, Introductory functional analysis with applications, John Wiley and Sons, New##York, 1978.##[7] A. Narayanan, S. Vijayabalaji and N. Thillaigovindan, Intuitionistic fuzzy bounded linear##operators, Iranian Journal of Fuzzy Systems, 4(1) (2007), 89101.##[8] M. Rafi and M. S. M. Noorani, Fixed point theorem on intuitionistic fuzzy metric spaces,##Iranian Journal of Fuzzy Systems, 3(1) (2006), 2329.##[9] R. Saadati, S. Sedghi and H. Zhou, A common fixed point theorem for weakly commuting##maps in Lfuzzy metric spaces, Iranian Journal of Fuzzy Systems, 5(1) (2008), 4753.##[10] J. Xiao and X. Zhu, Fuzzy normed space of operators and its completeness, Fuzzy Sets and##Systems, 133 (2003), 389399.##[11] J. Xiao and X. Zhu, On linearly topological structure and property of fuzzy normed linear##space, Fuzzy Sets and Systems, 125 (2002), 153161.##]
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