IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.2808 unavailable Cover Special Issue vol. 9, no. 5, December 2012 -- 01 12 2012 9 5 0 0 13 12 2016 13 12 2016 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_2808.html

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IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2014.85 Research Paper EXTENSION OF FUZZY CONTRACTION MAPPINGS VOSOUGHI H Department of Mathematics, Faculty of Science, Islamshahr Branch, Islamic Azad University, Islamshahr, Tehran, Iran Hosseini Ghoncheh S. J Department of mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran 20 02 2014 9 5 1 6 22 12 2013 08 12 2013 Copyright © 2014, University of Sistan and Baluchestan. 2014 http://ijfs.usb.ac.ir/article_85.html

In a fuzzy metric space (X;M; *), where * is a continuous t-norm,a locally fuzzy contraction mapping is de ned. It is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. Also, if f satis es the locally fuzzy contractivity condition then it satis es the global fuzzy contrac-tivity condition.

Fuzzy metric space Fuzzy contraction Fuzzy contractivity
 I. Altun,Some xed point theorems for single and muli valued mappingson ordered non-archimedean fuzzy metric spaces , Iranian Journal of Fuzzy Systems, 7(3)(2010), 91-96.  L. M. Blumenthal,Theory and applications of distance geometry, Oxford, Clarendon Press,1953.  Z. K. Deng,Fuzzy pseudo metric spaces, J. Math. Anal. Appl., 86(1982), 74-95.  M. A. Erceg,Metric spaces in fuzzy set theory, J. Math. Anal. Appl., 69(1979), 205-230.  A. George and P. Veeramani,On some results in fuzzy metric spaces, Fuzzy Sets and Systems,64(1994), 395-399.  M. Grabiec,Fixed point in fuzzy metric spaces, Fuzzy Sets and Systems, 27(1988), 385-389.  V. Gregori and A. Sapena,On xed-point theorems in fuzzy metric spaces , Fuzzy Sets and Systems,125 2002), 245-252.  Y. Hong, X. Fang and B. Wang,Intuitionistic fuzzy quasi-metric and pseudo-metric spaces,Iranian Journal of Fuzzy Systems,5(3)(2008), 81-88.  O. Kaleva and S. Seikkala,On fuzzy metric spaces, Fuzzy Sets and Systems, 12(1984),215-229.  F. Merghadi and A. Aliouche,A related xed point theorem in N-fuzzy metric spaces, Iranian Journal of Fuzzy Systems,7(3)(2010), 73-86.  A. Razani,A contraction theorem in fuzzy metric spaces, Fixed Point Theory Applications,3(2005), 257-265.  A. Razani,Existence of xed point for the nonexpansive mapping of intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 30(2006), 367-373.  R. Saadati, S. Sedghi and H. Zhou,A common xed point theorem for weakly commuting maps in L-uzzy metric spaces, Iranian Journal of Fuzzy Systems, 5(1)(2008), 47-53.  R. Saadati, A. R. Razani and H. Adibi,A common xed point theorem in L-fuzzy metric spaces, Chaos, Solitons and Fractals, 33(2007), 358-363.  B. Schweizer and A. Sklar,Statistical metric spaces, Paci c J. Math., 10(1960), 314-334.  S. Sedghi, K. P. R. Rao and N. Shobe,A common xed point theorem for six weakly compatible maps in M-fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 5(2)(2008), 49-62.  G. Song,Comments on: a common xed point theorem in a fuzzy metric space, Fuzzy Sets and Systems,135(2003), 409-413.  R. Vasuki,A common xed point theorem in a fuzzy metric space, Fuzzy Sets and Systems,97(1998), 395-397.  L. A. Zadeh,Fuzzy sets, Information and Control, 89(1965), 338-353.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.101 Research Paper (T,S)-BASED INTERVAL-VALUED INTUITIONISTIC FUZZY COMPOSITION MATRIX AND ITS APPLICATION FOR CLUSTERING HUANG H. L Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou 363000, China 26 12 2012 9 5 7 19 01 01 2011 25 08 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_101.html

In this paper, the notions of $(T,S)$-composition matrix and$(T,S)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(T,S)$ is a dual pair of triangular module. Theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. Furthermore, theirproperties and characterizations are presented. Then a new methodbased on $tilde{alpha}-$matrix for clustering is developed.Finally, an example is given to demonstrate our method.

Clustering Interval-valued intuitionistic fuzzy set Interval-valued intuitionistic fuzzy number Interval-valued intuitionistic fuzzy matrix Triangular dual module
 K. Atanassov,Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.  K. Atanassov,Operators over interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Sys-tems, 64 (1994), 159-174.  K. Atanassov,On intuitionistic fuzzy negations and De Morgan Laws, Proceedings of Eleventh International Conference, IPMU 2006, Paris, July 2-7, (2006), 2399-2404.  K. Atanassov and G. Gargov,Interval-valued intuitionistic fuzzy sets , Fuzzy Sets and Sys-tems,31 (1989), 343-349.  R. A. Borzooei and Y. B. Jun,Intuitionistic fuzzy hyper BCK-ideals of hyper BCK-algebras ,Iranian Journal of Fuzzy Systems,1 (2004), 65-78.  H. Bustince and P. Burillo,Correlation of interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems,74 (1995), 237-244.  Q. Chen, Z. S. Xu, S. S. Liu and X. H. Yu,A method based on interval-valued intuitionistic fuzzy entropy for multiple attribute decision making, Information: An International Interdis- ciplinary Journal,13 (2010), 67-77.  D. Coker,Fuzzy rough sets are intuitionistic L-fuzzy sets, Fuzzy Sets and Systems, 96 (1998),381-383.  G. Deschrijver,Arithmetic operators in interval-valued fuzzy set theory, Information Sciences,  177 (2007), 2906-2924.  J. Garcia and S. E. Rodabaugh, Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued intuitionistic sets, intuitionistic fuzzy sets and topologies , Fuzzy Sets and Systems, 156 (2005), 445-484.  J. Goguen,L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18(1967),145-174.   H. L. Huang and F. G. Shi,L-fuzzy numbers and their properties, Information Sciences, 178(2008), 1141-1151.  W. L. Hung and J. W. Wu,Correlation of intuitionistic fuzzy sets by centroid method ,Information Sciences,144 (2002), 219-225.  Y. Jiang, Y. Tang, J. Wang and S. Tang,Reasoning within intuitionistic fuzzy rough descrip- tion logics, Information Sciences, 189 (2009), 2362-2378.  A. Khan, Y. B. Jun and M. Shabir,Ordered semigroups characterized by their intuitionistic fuzzy BI-ideals, Iranian Journal of Fuzzy Systems, 7(2010), 55-69.  M. L. Lin and H. L. Huang,(T,S)-based intuitionistic fuzzy composite matrix and its appli-cation , International Journal of Applied Mathematics and Statistics, 23 (2011), 54-63.  T. K. Mondal and S. K. Samanta,Topology of interval-valued intuitionistic fuzzy sets, Fuzzy Sets and Systems,119 (2001), 483-494.  A. Narayanan, S. Vijayabalaji and N. Thillaigovindan,Intuitionistic fuzzy bounded linear operators, Iranian Journal of Fuzzy Systems, 4 (2007), 89-101.  D. G. Park, Y. C. Kwun, J. H. Park and et al.,Correlation coecient of interval-valued intu- itionistic fuzzy sets and its application to multiple attribute group decision making problems  ,Mathematical and Computer Modelling, 50 (2009), 1279-1293.  L. Torkzadeh, M. Abbasi and M. M. Zahedi,Some results of intuitionistic fuzzy weak dual hyper K-ideals, Iranian Journal of Fuzzy Systems, 5(2008), 65-78.  P. Z. Wang,Fuzzy set theory and its application, Shanghai Science and Technology Press, Shanghai, 1983.   Z. Wang, K. W. Li and W. Wang, An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights, Information Sciences,179  (2009), 3026-3040.  G. Wei,Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making , Applied Soft Computing, 10 (2010), 423-431.  Z. S. Xu,A method based on distance measure for interval-valued intuitionistic fuzzy group decision making, Information Sciences, 180 (2010), 181-190.  Z. S. Xu,Choquet integrals of weighted intuitionistic fuzzy information, Information Sciences,  180 (2010), 726-736.  Z. S. Xu,A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making, Group Decision and Negotiation, 19 (2010), 57-76.  Z. S. Xu,On correlation measures of intuitionistic fuzzy sets, Lecture Notes in Computer Science,  4224 (2006), 16-24.  Z. S. Xu,Intuitionistic fuzzy hierarchical clustering algorithms, Journal of Systems Engineer- ing and Electronics,20 (2009), 90-97.  Z. S. Xu and X. Cai,Incomplete interval-valued intuitionistic preference relations , Interna-tional Journal of General Systems, 38 (2009), 871-886.  Z. S. Xu and X. Q. Cai, Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information, International Journal of Intelligent Systems, 25 (2010),  489-513.  Z. S. Xu and J. Chen,Approach to group decision making based on interval-valued intuition- istic judgment matrices, Systems Engineering-Theory and Practice, 27(4) (2007), 126-133.  Z. S. Xu, J. Chen and J. Wu,Clustering algorithm for intuitionistic fuzzy sets, InformationSciences,  178 (2008), 3775-3790.  Z. S. Xu and J. J. Wu,Intuitionistic fuzzy c-means clustering algorithms, Journal of Systems Engineering and Electronics, 21 (2010), 580-590.  Z. S. Xu and R. R. Yager,Dynamic intuitionistic fuzzy multi-attribute decision making, International Journal of Approximate Reasoning,48 (2008), 246-262.  Z. S. Xu and R. R. Yager,Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group  ,Fuzzy Optimization and Decision Making,8 (2009), 123-139.  J. Ye and Multicriteria,Fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment, Expert Systems with Applications, 36(2009), 6899-6902.  J. Ye and Multicriteria,Fuzzy decision-making method using entropy weights-based correla- tion coecients of interval-valued intuitionistic fuzzy sets, Applied Mathematical Modelling,  34(2010), 3864-3870.  L. A. Zadeh,Fuzzy sets, Information Control, 8 (1965), 338-353.  H. M. Zhang, Z. S. Xu and Q. Chen,On clustering approach to intuitionistic fuzzy sets ,Control and Decision,22 (2007), 882-888.  H. Y. Zhang, W. X. Zhang and W. Z. Wu,On characterization of generalized interval- valued fuzzy rough sets on two universes of discourse, International Journal of Approximate Reasoning,51 (2009), 56-70.  L. Zhou, W. Z. Wu and W. X. Zhang,On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators, Information Sciences, 179 (2009), 883-898.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.102 Research Paper A FIXED POINT APPROACH TO THE INTUITIONISTIC FUZZY STABILITY OF QUINTIC AND SEXTIC FUNCTIONAL EQUATIONS Xu Tian Zhou School of Mathematics, Beijing Institute of Technology, Beijing 100081, People's Republic of China Rassias Matina John Department of Statistical, University College London, Science 1-19 Torrington Place, London WC1E 7HB, United Kingdom Xin Xu Wan Department of Electrical and Computer Engineering, College of En- gineering, University of Kentucky, Lexington 40506, Usa and School of Communica- tion and Information Engineering, University of Electronic Science and Technology of China 28 12 2012 9 5 21 40 27 12 2010 27 08 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_102.html

The fixed point alternative methods are implemented to giveHyers-Ulam  stability for  the quintic functional equation $f(x+3y)- 5f(x+2y) + 10 f(x+y)- 10f(x)+ 5f(x-y) - f(x-2y) = 120f(y)$ and thesextic functional equation $f(x+3y) - 6f(x+2y) + 15 f(x+y)- 20f(x)+15f(x-y) - 6f(x-2y)+f(x-3y) = 720f(y)$   in the setting ofintuitionistic fuzzy normed spaces (IFN-spaces).  This methodintroduces a metrical context and shows that the stability isrelated to some fixed point of a suitable operator. Furthermore, theinterdisciplinary relation among the fuzzy set theory,  the theoryof intuitionistic spaces and the theory of functional equations arealso presented in the paper.

bibitem{Altun} I. Altun, {it Some fixed point theorems for single and multivalued mappings on ordered non-archimedean fuzzy metric spaces}, Iranian Journal of Fuzzy Systems, {bf 7} (2010), 91-96. bibitem{Aoki} T. Aoki, {it On the stability of the linear transformation in Banach spaces}, J. Math. Soc. Japan, {bf 2} (1950), 64-66. bibitem{Atanassov1}  K. T. Atanassov, {it Intuitionistic fuzzy sets}, Fuzzy Sets and Systems, {bf 20} (1986), 87-96. bibitem{Atanassov2}  K. T. Atanassov, {it New operations defined over the intuitionistic fuzzy sets}, Fuzzy Sets and Systems, {bf 61} (1994), bibitem{Baktash}  E. Baktash, Y. J. Cho, M. Jalili, R. Saadati and S. M. Vaezpour, {it On the stability of cubic mappings and quadratic mappings in random normed spaces}, Journal of Inequalities and Applications,  Article ID 902187, 11 pages, {bf 2008} (2008). bibitem{cadariu}  L. Cu{a}dariu and V. Radu, {it Fixed points and stability for functional equations in probabilistic metric and random normed spaces}, Fixed Point Theory and Applications, Article ID 589143, 18 pages, {bf 2009} (2009). bibitem{coker}  D. c{C}oker, {it An introduction to intuitionistic fuzzy topological spaces}, Fuzzy Sets and Systems, {bf 88} (1997), bibitem{Deschrijver}  G. Deschrijver, C. Cornelis and E. E. Kerre, {it On the representation of intuitionistic fuzzy $t$-norms and $t$-conorms}, IEEE Transaction on Fuzzy Systems, {bf 12} (2004), 45-61. bibitem{Garia} J. G. Garc'{i}a and S. E. Rodabaugh, {it Order-theoretic, topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued intuitionistic'' sets, intuitionistic'' fuzzy sets and topologies}, Fuzzy Sets and Systems, {bf 156} (2005),  445-484. bibitem{Gavruta}  P. Gu{a}vruc{t}a, {it A  generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings}, Journal of Mathematical Analysis and Applications, {bf 184} (1994), 431-436. bibitem{Hosseini} S. B. Hosseini, D. O'Regan and R. Saadati, {it Some results on intuitionistic fuzzy spaces}, Iranian Journal of Fuzzy Systems, {bf 4} (2007),  53-64. bibitem{Hyers} D. H. Hyers, {it On the stability of the linear functional equation}, Proc. Nat. Acad. Sci. USA, {bf 27} (1941), 222-224. bibitem{Isac}  G. Isac and T. M. Rassias, {it Stability of $psi$-additive mappings: applications to nonlinear analysis}, International Journal of Mathematics and Mathematical Sciences, {bf 19} (1996), bibitem{Junkim1} K. W. Jun and H. M. Kim, {it The generalized Hyers-Ulam-Rassias stability of a cubic functional equation}, Journal of Mathematical Analysis and Applications, {bf 274} (2002), bibitem{Junkimchang} K. W. Jun, H. M. Kim and I. S. Chang, {it On the Hyers-Ulam stability of an Euler-Lagrange type cubic functional equation}, Journal of Computational Analysis and Applications, {bf 7} (2005), bibitem{Merghadi} F. Merghadi and A. Aliouche, {it A related fixed point theorem in $n$ fuzzy metric spaces}, Iranian Journal of Fuzzy Systems, {bf 7} (2010), bibitem{Mihet} D. Mihec{t}, {it The fixed point method for fuzzy stability of the Jensen functional equation}, Fuzzy Sets and Systems, {bf 160} (2009), 1663-1667. bibitem{Mihetsaadati}  D. Mihec{t}, R. Saadati and S. M. Vaezpour, {it The stability of the quartic functional equation in random normed spaces}, Acta Appl.  Math., {bf 110} (2010), 797-803. bibitem{Mirmostafaee} A. K. Mirmostafaee and  M. S. Moslehian, {it Fuzzy versions of Hyers-Ulam-Rassias theorem}, Fuzzy Sets and Systems, {bf 159} (2008), 720-729. bibitem{Mohiuddine}  S. A. Mohiuddine and H. c{S}evli, {it Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space}, Journal of Computational and Applied Mathematics, {bf 235} (2011), 2137-2146. bibitem{Moslehian}  M. S. Moslehian and G. Sadeghi, {it Stability of two types of cubic functional equations in non-archimedean spaces}, Real Anal. Exchange, {bf 33} (2008), 375-383. bibitem{Moszner} Z. Moszner, {it On the stability of functional equations}, Aequationes Math., {bf 77} (2009), 33-88. bibitem{Mursaleen}  M. Mursaleen and S. A. Mohiuddine,  {it On stability of a cubic functional equation in intuitionistic fuzzy normed spaces}, Chaos, Solitons and Fractals, {bf 42} (2009), 2997-3005.  bibitem{Nozari} K. Nozari and B. Fazlpour, {it Some consequences of space-time  fuzziness}, Chaos, Solitons and Fractals, {bf 34} (2007), 224-234. bibitem{Paneah} B. Paneah, {it A new approach to the stability of linear functional operators}, Aequationes Math., {bf 78} (2009), 45-61. bibitem{Park} J. H. Park, {it  Intuitionistic fuzzy metric spaces}, Chaos, Solitons and Fractals, {bf 22} (2004), 1039-1046. bibitem{Radu} V. Radu, {it The fixed point alternative and the stability of functional equations}, Fixed Point Theory, {bf 4} (2003), bibitem{Rafi} M. Rafi and M. S. M. Noorani, {it Fixed point theorem on intuitionistic fuzzy metric spaces}, Iranian Journal of Fuzzy Systems, {bf 3} (2006), 23-29.  bibitem{JMRassias} J. M. Rassias, {it Solution of the Ulam stability problem for quartic mappings},   Glasnik Matemativ{c}ki, {bf 34} (1999), 243-252.  bibitem{ThRassias} T. M. Rassias, {it On the stability of the linear mapping in Banach spaces}, Proc. Amer. Math. Soc., {bf 72} (1978), 297-300. bibitem{Saadati} R.  Saadati, {it  A note on Some results on the IF-normed spaces''}, Chaos, Solitons and Fractals, {bf 41} (2009), 206-213. bibitem{Saadaticho} R. Saadati, Y. J. Cho and J. Vahidi, {it The stability of the quartic functional equation in various spaces}, Computers and Mathematics with Applications, {bf 60} (2010), 1994-2002.  bibitem{Saadatipark} R. Saadati and C. Park, {it Non-archimedean $mathscr{L}$-fuzzy normed spaces and stability of functional equations}, Computers and Mathematics with Applications, {bf 60} (2010), 2488-2496. bibitem{Saadatirazani} R. Saadati, A. Razani and H. Adibi, {it A common fixed point theorem in $mathscr{L}$-fuzzy metric spaces}, Chaos Solitons Fractals, {bf 33} (2007), 358-363. bibitem{Saadatisedghi} R. Saadati, S. Sedghi and N. Shobe, {it Modified intuitionistic fuzzy metric spaces and some fixed point theorems}, Chaos, Solitons and Fractals, {bf 38} (2008), 36-47. bibitem{Saadatisedghi} R. Saadati, S. Sedghi and H. Zhou, {it A common fixed point theorem for $psi$-weakly commuting maps in $mathcal {L}$-fuzzy metric spaces}, Iranian Journal of Fuzzy Systems, {bf 5} (2008), 47-53. bibitem{Saadativaezpour} R. Saadati, S. M. Vaezpour and Y. J. Cho, {it Quicksort algorithm: application of a fixed point theorem in intuitionistic fuzzy quasi-metric spaces at a domain of words},  Journal of Computational and Applied Mathematics, {bf 228} (2009), bibitem{Sedghi} S. Sedghi, K. P. R. Rao and N. Shobe, {it A common fixed point theorem for six weakly compatible mappings in $M$-fuzzy metric spaces}, Iranian Journal of Fuzzy Systems, {bf 5} (2008), 49-62. bibitem{Ulam} S. M. Ulam, {it A collection of the mathematical problems}, Interscience, New York, 1960. bibitem{xu1}  T. Z.  Xu, J. M.  Rassias, M. J. Rassias  and  W. X. Xu, {it A fixed point approach to the stability of  quintic and sextic functional equations in quasi-$beta$-normed spaces}, Journal of Inequalities and Applications, Article ID 423231, 23 pages, {bf 2010} (2010). bibitem{xu2} T. Z. Xu, J. M. Rassias and W. X. Xu, {it Intuitionistic fuzzy stability of a general mixed additive-cubic equation}, Journal of Mathematical Physics, 063519, 21 pages, {bf 51} (2010). bibitem{xu3}  T. Z. Xu, J. M. Rassias and W. X. Xu, {it Stability of a general mixed additive-cubic functional equation in non-archimedean fuzzy normed spaces}, Journal of Mathematical Physics, 093508, 19 pages, {bf 51} (2010). bibitem{xu4} T. Z. Xu, J. M. Rassias and W. X. Xu, {it On the stability of a general mixed additive-cubic functional equation in random normed spaces}, Journal of Inequalities and Applications, Article ID 328473, 16 pages, {bf 2010} (2010).  bibitem{xu5}  T. Z. Xu, J. M. Rassias and W. X. Xu, {it A fixed point approach to the stability of a general mixed AQCQ-functional equation in non-archimedean normed spaces}, Discrete Dynamics in Nature and Society, Article ID 812545,  24 pages, {bf 2010} (2010). bibitem{xu6}  T. Z.  Xu, J. M.  Rassias and W. X. Xu, {it A generalized mixed additive-cubic functional equation}, Journal of Computational Analysis and Applications, {bf 13} (2011), 1273-1282. bibitem{Zhang} S. S. Zhang, J. M. Rassias and  R. Saadati, {it  Stability of a cubic functional equation  in intuitionistic random normed spaces}, Appl. Math. Mech. -Engl. Ed., {bf 31} (2010), 21-26.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.103 Research Paper ON (L;M)-FUZZY CLOSURE SPACES ON (L;M)-FUZZY CLOSURE SPACES Aygun Halis Department of Mathematics, Kocaeli University, 41380, Kocaeli, Turkey. Cetkin Vildan Department of Mathematics, Kocaeli University, 41380, Kocaeli, Turkey. Abbas S. E. Department of Mathematics, Faculty of Science, Sohag 82524, Egypt. 28 12 2012 9 5 41 62 27 06 2010 27 08 2012 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_103.html

The aim of this paper is to introduce $(L,M)$-fuzzy closurestructure where $L$ and $M$ are strictly two-sided, commutativequantales. Firstly, we define $(L,M)$-fuzzy closure spaces and getsome relations between $(L,M)$-double fuzzy topological spaces and$(L,M)$-fuzzy closure spaces. Then, we introduce initial$(L,M)$-fuzzy closure structures and we prove that the category$(L,M)$-{bf FC} of $(L,M)$-fuzzy closure spaces and$(L,M)$-$mathcal{C}$-maps is a topological category over thecategory {bf SET}. From this fact, we define products of$(L,M)$-fuzzy closure spaces. Finally, we show that an initialstructure of $(L,M)$-double fuzzy topological spaces can be obtainedby the initial structure of $(L,M)$-fuzzy closure spaces induced bythem.

Double fuzzy topological space Fuzzy closure space Initial fuzzy closure space
bibitem{Sab:Gifcs} S. E. Abbas, {it $(r,s)$-generalized intuitionistic fuzzy closed sets},  J. Egypt Math. Soc., {bf 14}textbf{(2)} (2006), 283--297. bibitem{SabHa:Ifss} S. E. Abbas and Halis Ayg"{u}n, {it Intuitionistic fuzzy semiregularization spaces}, Information Sciences, {bf 176} (2006), bibitem{Ahs:Acc} J. Adamek, H. Herrlich and G. E. Strecker, {it Abstract and concrete categories},  Wiley, New York, 1990. bibitem{Kat:Ifs} K. Atanassov, {it Intuitionistic fuzzy sets},  Fuzzy Sets and Systems, textbf{20}textbf{(1)} (1986), 87-96. bibitem{Clc:Fts}  C. L. Chang, {it Fuzzy topological spaces}, J. Math. Anal. Appl., textbf{24} (1968), 182-190. bibitem{Chs:Goft} K. C. Chattopadhyay, R. N. Hazra and S. K. Samanta, {it Gradation of openness: fuzzy topology}, Fuzzy Sets and Systems, textbf{49} (1992), 237-242. bibitem{CS:Ftfco} K. C. Chattopadhyay and S. K. Samanta, {it Fuzzy topology: fuzzy closure operator, fuzzy compactness and fuzzy connectedness}, Fuzzy Sets and Systems, {bf 54} (1993), 207-212. bibitem{Dc:Iifts} D. c{C}oker, {it An introduction to intuitionistic fuzzy topological spaces}, Fuzzy Sets and Systems, {bf 88} (1997), bibitem{DcMd:Ifts} D. c{C}oker and M. Demirci, {it An introduction to intuitionistic fuzzy topological spaces in v{S}ostak sense}, Busefal, {bf 67} (1996), 67-76. bibitem{JgSr:Ott} J. Gutierrez Garcia and S. E. Rodabaugh, {it Order-theoretic topological, categorical redundancies of interval-valued sets, grey sets, vague sets, interval-valued intuitionistic sets, intuitionistic fuzzy sets and topologies}, Fuzzy Sets and Systems, {bf 156} (2005), 445-484. bibitem{Han:Scifts} I. M. Hanafy, A. M. Abd El-Aziz and T. M. Salman, {it Semi I-compactness in intuitionistic fuzzy topological spaces}, Iranian Journal of Fuzzy Systems, textbf{3}textbf{(2)} (2006), 53-62. bibitem{Hoh:Usfs} U. H"ohle, {it Upper semicontinuous fuzzy sets and applications}, J. Math. Anall. Appl., {bf 78} (1980), 659-673. bibitem{Hoh:Mcct} U. H"ohle, {it  Monoidal closed categories, weak topoi and generalized logics}, Fuzzy Sets and Systems, {bf 42} (1991), 15-35. bibitem{Hoh:Mss} U. H"ohle, {it  M-valued sets and sheaves over integral commutative cl-monoids, in Applications of category theory of fuzzy subsets (S. Rodabaugh, E. P. Klement and U. H"ohle, eds.)}, Kluwer Academic, Dordrecht, Boston, (1992), 33-72. bibitem{Hoh:Crm} U. H"ohle, {it Commutative, residuated l-monoids}, Non-classical logics and their Applications to Fuzzy Subsets theory (Linz, 1992), Kluwer, Acad. Publ., Dordrecht, (1995), 53-106. bibitem{Hoh:Mvt} U. H"ohle, {it Many valued topology and its applications}, Kluwer Academic Publisher, Boston, 2001. bibitem{HohKl:Ncl} U. H"ohle and E. P. Klement, {it Non-classical logic and their applications to fuzzy subsets}, Kluwer Academic Publisher, Boston, 1995. bibitem{HohSos:Gtfts} U. H"ohle and A. P. v{S}ostak, {it A general theory of fuzzy topological spaces}, Fuzzy Sets and Systems, {bf 73} (1995), bibitem{HohSos:Affbft} U. H"ohle and A. P. v{S}ostak, {it Axiomatic foundations of fixed-basis fuzzy topology}, The Handbooks of Fuzzy Sets Series,  Kluwer Academic Publishers, Dordrecht (Chapter 3), {bf3} (1999). bibitem{Sj:Sgm} S. Jenei, {it Structure of Girard monoids on [0,1]}, Chapter 10, In: S. E. Rodabaugh, E. P. Klement, eds., Topological and Algebraic Structures in Fuzzy Sets, Kluwer Academic Publ., 2003. bibitem{YcKYsK:As} Y. C. Kim and Y. S. Kim, {it $(L,odot)$-approximation spaces and $(L,odot)$-fuzzy quasi-uniform spaces}, Information Sciences, {bf 179} (2009), 2028-2048. bibitem{YcKYmK:Ipf} Y. C. Kim and J. M. Ko, {it Images and preimages of L-filterbases}, Fuzzy Sets and Systems, {bf 157} (2006), 1913-1927. bibitem{Tk:Ft} T. Kubiak, {it On fuzzy topologies}, Ph. D. Thesis, A. Mickiewicz, Poznan, 1985. bibitem{TkSos:Lsft} T. Kubiak and A. P. v{S}ostak, {it Lower set-valued fuzzy topologies}, Quaestiones Math., textbf{20}textbf{(3)} (1997), bibitem{EplY:Mfts}  E. P. Lee and Y. B. Im, {it Mated fuzzy topological spaces}, J. Korea Fuzzy Logic Intell. Sys. Soc., textbf{11}textbf{(2)} (2001), 161-165. bibitem{Ym:Ft} Y. M. Liu and M. K. Luo, {it Fuzzy topology}, Scientific Publishing Co. Singapore, 1997. bibitem{Rl:Ftsfc}  R. Lowen, {it Fuzzy topological spaces and fuzzy compactness}, J. Math. Anal. Appl., textbf {56} (1976), 621-633. bibitem{Luo:Fcs} X. Luo and J. Fang, {it Fuzzifying closure systems and closure operators}, Iranian Journal of Fuzzy Systems, textbf{8}textbf{(1)} (2011), 77-94. bibitem{Mul:Q}  C. J. Mulvey, {it $&$ }, Suppl. Rend. Circ.Mat. Palermo Ser. II, textbf{12} (1986), 99-104. bibitem{SeR:Cfv} S. E. Rodabaugh, {it Categorical foundations of variable-basis topology, in U. Hohle, S. E. Rodabaugh, eds., mathematics of fuzzy sets: logic, topology and measure theory, the handbooks of fuzzy sets series}, Kluwer Academic publishers, Dordrecht, textbf{3} (1999), 273-388. bibitem{SeREpk:Tas} S. E. Rodabaugh and E. P. Klement, {it Topological and algebraic structures in fuzzy sets}, The Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trends in Logic 20, Kluwer Academic Publishers, (Boston/Dordrecht/London), 2003. bibitem{SksTkm:Igo} S. K. Samanta and T. K. Mondal, {it On intuitionistic gradation of openness}, Fuzzy Sets and Systems, textbf{131} (2002), 323-336. bibitem{FgS:Cclp} F. G. Shi, {it Countable compactness and the lindelof property of L-fuzzy sets}, Iranian Journal of Fuzzy Systems, textbf{1}textbf{(1)} (2004), 79-88. bibitem{ASos:Ofts} A. P. v{S}ostak, {it On a fuzzy topological structure}, Suppl. Rend. Circ. Matem. Palerms ser II, textbf{11} (1985), 89-103. bibitem{Asos:Dft} A. P. v{S}ostak, {it Two decades of fuzzy topology: basic ideas, notions and results}, Russian Math. Surveys, textbf{44} textbf{(6)} (1989), 125-186. bibitem{Asos:Bsft} A. P. v{S}ostak, {it Basic structures of fuzzy topology}, J. Math. Sci., textbf{78}textbf{(6)} (1996), 662-701. bibitem{Et:Mbfl} E. Turunen, {it Mathematics behind fuzzy logic}, A Springer-Verlag Co., New York, 1999. bibitem{Msy:Nafft} M. S. Ying, {it A new approach for fuzzy topology (I)}, Fuzzy Sets and Systems, textbf{39} (1991), 303-320.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.104 Research Paper A NOTE ON INTUITIONISTIC FUZZY MAPPINGS A NOTE ON INTUITIONISTIC FUZZY MAPPINGS Shen Yong-hong School of Mathematics and Statistics, Tianshui Normal Univer- sity, Tianshui 741001, People's Republic of China Wang Fa-xing Tongda College, Nanjing University of Posts and Telecommunica- tions, Nanjing, 210046, People's Republic of China Chen Wei School of Information, Capital University of Economics and Business, Beijing, 100070, People's Republic of China 28 12 2012 9 5 63 76 27 01 2011 27 09 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_104.html

In this paper, the concept of intuitionistic fuzzy mapping as a generalization of fuzzy mapping is presented, and its' relationship with intuitionistic fuzzy relations is derived. Moreover, some basicoperations of intuitionistic fuzzy mappings are defined, hence we can conclude that all of intuitionistic fuzzy mappings constitute a soft algebrawith respect to these operations. Afterwards, the Atanassov'soperator is applied to intuitionistic fuzzy mappings and thecorresponding properties are examined. Finally, the decompositionand representation theorems of intuitionistic fuzzy mappings areestablished.

Truncation projection Intuitionistic fuzzy mapping Truncation map- ping Decomposition theorem Representation theorem
 K. Atanassov,Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 26 (1986), 87-96.  K. Atanassov,More on intuitionistic fuzzy sets, Fuzzy Sets and Systems, 33 (1989), 37-45.  K. Atanassov,Intuitionistic fuzzy relations, First Scienti c Session of the Mathematical Foun-dation Arti cial Intelligence, So a IM-MFAIS, (1989), 1-3.  A. Azam and I. Beg,Common xed points of fuzzy mappings, Mathematical and Computer Modelling,49 (2009), 1331-1336.  Y. E. Bao and C. X. Wu,Convexity and semicontinuity of fuzzy mappings, Computers &Mathematics with Applications,51 (2006), 1809-1816.  P. Burillo and H. Bustince,Intuitionistic fuzzy relations (Part I), Mathware Soft Computing,2(1995), 5-38.  P. Burillo and H. Bustince,Intuitionistic fuzzy relations (Part II), Mathware Soft Computing,2(1995), 117-148.  H. Bustince and P. Burillo,Structures on intuitionistic fuzzy relations, Fuzzy Sets and Sys-tems,78 (1996), 293-303.  H. Bustince,Construction of intuitionistic fuzzy relations with predetermined properties,Fuzzy Sets and Systems,109 (2000), 379-403.  S. Heilpern,Fuzzy mappings and xed point theorem, Journal of Mathematical Analysis andApplications,83 (1981), 566-569.  S. B. Hosseini, D. O'regan and R. Saadati, Some results on intuitionistic fuzzy spaces, Iranian Journal of Fuzzy Systems,4(1) (2007), 53-64.  K. Hur, S. Y. Jand and H. W. Kang,Some intuitionistic fuzzy congruences, Iranian Journal of Fuzzy Systems,3(1) (2006), 45-57.  B. S. Lee and S. J. Cho,A xed point theorem for contractive type fuzzy mappings, Fuzzy Sets and Systems,61(1994), 309-312.  B. S. Lee, G. M. Lee, S. J. Cho, etc,A common xed point theorem for a pair of fuzzy mappings, Fuzzy Sets and Systems, 98 (1998), 133-136.  H. W. Liu,Basic theorems of the Intuitionistic fuzzy sets, Journal of Mathematics for Tech-nology, (in chinese),16 (2000), 55-60.  C. Z. Luo,Fuzzy set theory, Beijing Normal University Press, Beijing, (in chinese), 2005.  S. Nanda and K. Kar,Convex fuzzy mappings, Fuzzy Sets and Systems, 48 (1992), 129-132.  J. Y. Park and J. U. Jeong,Fixed point theorems for fuzzy mappings, Fuzzy Sets and Systems,87(1997), 111-116.  M. Ra and and M. S. M. Noorani,Fixed point theorem on intuitionistic fuzzy metris spaces,Iranian Journal of Fuzzy Systems,3(1) (2006), 23-29.  Y. R. Syau,On convex and concave fuzzy mappings, Fuzzy Sets and Systems, 103 (1999),163-168.  Y. R. Syau,Closed and convex fuzzy sets, Fuzzy Sets and Systems, 110 (2000), 287-291.  Y. R. Syau,Some properties of weakly convex fuzzy mappings, Fuzzy Sets and Systems, 123(2001), 203-207.  Y. R. Syau and E. S. Lee, note on convexity and semicontinuity of fuzzy mappings, Applied Mathematics Letters,21 (2008), 814-819.  Y. R. Syau, L. F. Sugianto and E. S. Lee,A class of semicontinuous fuzzy mappings, Applied Mathematics Letters,21 (2008), 824-827.  L. Zhou, W. Z. Wu and W. X. Zhang,On properties of the cut sets of intuitionistic fuzzy relations, Fuzzy Systems and Mathematics, (in chinese), 23 (2009), 110-115.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.105 Research Paper COMMON FIXED POINT THEOREMS IN MODIFIED INTUITIONISTIC FUZZY METRIC SPACES COMMON FIXED POINT THEOREMS IN MODIFIED Imdad M. Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India Ali Javid Departament de Matematica Aplicada III (MA3), Universitat Politecnica de Catalunya, Colom 1, 08222 Terrassa (Barcelona), Spain Hasan M. Department of Applied Mathematics, Aligarh Muslim University, Aligarh 202002, India 28 12 2012 9 5 77 92 27 01 2011 27 10 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_105.html

In this paper, we introduce a new class of implicit functions and also common property (E.A) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. We are not aware of any paper dealing with such implicit functions in modified intuitionistic fuzzy metric spaces.

Fuzzy metric space Modi ed intuitionistic fuzzy metric space Prop- erty (E.A) Common property (E.A)
bibitem {Aamri} M. Aamri and D. El Moutawakil, {em Some new common fixed point theorems under strict contractive conditions}, J. Math. Anal. Appl., {bf 270} (2002), 181-188. bibitem {Abbas} M. Abbas, M. Imdad and D. Gopal, {em $psi-$weak contractions in fuzzy metric spaces}, Iranian Journal of Fuzzy Systems, {bf 8(5)} (2011), 141-148. bibitem {Alaca} C. Alaca, D. Turkoglu and C. Yildiz, {em Fixed point in intuitionistic fuzzy metric spaces}, Chaos Solitons Fractals, {bf 29} (2006), 1073-1078. bibitem {Ali} J. Ali and  M. Imdad, {em An implicit function implies several contraction conditions}, Sarajevo J. Math., {bf 17(4)} (2008), 269-285. bibitem {Altun} I. Altun, {em Some fixed point theorems for single and multivalued mappings on ordered non-Archimedean fuzzy metric spaces}, Iranian Journal of Fuzzy Systems, {bf 7(1)} (2010), 91-96. bibitem {Atanassov86} K. T. Atanassov, {em Intuitionistic fuzzy sets}, Fuzzy Sets and Systems, {bf 20} (1986), 87-96. bibitem {Deschrijver} G. Deschrijver and E. E. Kerre, {em On the relationship between some extensions of fuzzy set theory}, Fuzzy Sets and Systems, {bf 133} (2003), 227-235. bibitem {Naschie06} M. S. El Naschie, {em On the verification of heterotic strings theory and $epsilon^{infty}$ theory}, Chaos Solitons Fractals, {bf 11} (2000), 2397-2408. bibitem {Naschie2006} M. S. El Naschie, {em The two-slit experiment as the foundation of E-infinity of high energy physics}, Chaos Solitons Fractals, {bf 25} (2005), 509-514. bibitem {Fang} J. X. Fang, {em On fixed point theorems in fuzzy metric spaces}, Fuzzy Sets and Systems, {bf 46} (1992), 107-113. bibitem {Veeramani94} A. George and P. Veeramani, {em On some results in fuzzy metric spaces}, Fuzzy Sets and Systems, {bf 64} (1994), 395-399. bibitem {Grabiec} M. Grabiec, {em Fixed points in fuzzy metric spaces}, Fuzzy Sets and Systems, {bf 27} (1988), 385-389. bibitem {Gregori} V. Gregori, S. Romaguera and P. Veeramani, {em A note on intuitionistic fuzzy metric spaces}, Chaos Solitons Fractals, {bf 28} (2006), 902-905. bibitem {Huang} X. Huang, C. Zhu and X. Wen, {em Common fixed point theorems for families of compatible mappings in intuitionistic fuzzy metric spaces}, Ann. Univ. Ferrara, {bf 56} (2010), 305-326. bibitem{Imdad06} M. Imdad and J. Ali, {em Some common fixed point theorems in fuzzy metric spaces}, Math. Commun., {bf 11} (2006), 153-163. bibitem{Imdad08} M. Imdad and J. Ali, {em A general fixed point theorem in fuzzy metric spaces via an implicit function}, J. Appl. Math. Informatics, {bf 26} (2008), 591-603. bibitem {Imdad09} M. Imdad, J. Ali and M. Tanveer, {em Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces}, Chaos Solitons Fractals, {bf 42} (2009), 3121-3129. bibitem {Jungck} G. Jungck, {em Common fixed points for noncontinuous nonself maps on nonmetric spaces}, Far East J. Math. Sci., {bf 4(2)} (1996), 199-215. bibitem {Klement84} E. P. Klement, {em Operations on fuzzy sets- an axiomatic approach}, Information Sciences, {bf 27} (1982), 221-232. bibitem {Kramosil75} O. Kramosil and J. Michalek, {em Fuzzy metric and statistical metric spaces}, Kybernetica, {bf 11} (1975), 326-334. bibitem {Liu} Y. Liu, Jun Wu and Z. Li, {em Common fixed points of single-valued and multi-valued maps}, Internat. J. Math. Math. Sci., {bf 19} (2005), 3045-3055. bibitem {PantV} V. Pant, {em Some fixed point theorems in fuzzy metric space}, Tamkang J. Math., {bf 40(1)} (2009), 59-66. bibitem {Park} J. H. Park, {em Intuitionistic fuzzy metric spaces}, Chaos Solitons Fractals, {bf 22} (2004), 1039-1046. bibitem {Rodriguez} L.J. Rodriguez and S. Ramaguera, {em The Hausdorff fuzzy metric on compact sets}, Fuzzy Sets Syst., {bf 147} (2004), 273–283. bibitem {Romaguera} S. Romaguera and P. Tirado, {em On fixed point theorems in intuitionistic fuzzy metric spaces}, Internat. J. Nonlinear Sci. Numer. Siml., {bf 8} (2007), 233-238. bibitem {Saadati} R. Saadati and J. H. Park, {em On the intuitionistic topological spaces}, Chaos Solitons Fractals, {bf 27} (2006), 331-344. bibitem {Saadati08} R. Saadati, S. Sedghi and N. Shobe, {em Modified intuitionistic fuzzy metric spaces and some fixed point theorems}, Chaos Solitons Fractals, {bf 38} (2008), 36–47. bibitem {Schweizer} B. Schweizer and A. Sklar, {em Statistical metric spaces}, Pacific J. Math., {bf 10} (1960), 313-334. bibitem {Sedghi} S. Sedghi, K. P. R. Rao and N. Shobe, {em A common fixed point theorem for six weakly compatible mappings in $M-$ fuzzy metric spaces}, Iranian Journal of Fuzzy Systems, {bf 5(2)} (2008), 49-62. bibitem {Turkoglu06} D. Turkoglu, C. Alaca, Y. J. Cho and C. Yildiz, {em Common fixed point theorems in intuitionistic fuzzy metric spaces}, J. Appl. Math. Computing, {bf 22} (2006), 411-424. bibitem {Vijayaraju} P. Vijayaraju and Z. M. I. Sajath, {em Some common fixed point theorems in fuzzy metric spaces}, Int. J. Math. Anal., {bf 15(3)} (2009), 701-710. bibitem {Zadeh} L. A. Zadeh, {em Fuzzy sets}, Information and Control, {bf 8} (1965), 338-353.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.106 Research Paper ON LOCAL BOUNDEDNESS OF I-TOPOLOGICAL VECTOR SPACES ON LOCAL BOUNDEDNESS OF I-TOPOLOGICAL Fang Jin-Xuan School of Mathematical Science, Nanjing Normal University, Nan- jing, Jiangsu 210023, P. R. China Zhang Hui Department of Mathematics, Anhui NormalUniversity, Wuhu, Anhui 241000, P. R. China 28 12 2012 9 5 93 104 27 01 2011 27 10 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_106.html

The notion of generalized locally bounded $I$-topological vectorspaces is introduced. Some of their important properties arestudied. The relationship between this kind of spaces and thelocally bounded $I$-topological vector spaces introduced by Wu andFang [Boundedness and locally bounded fuzzy topological vectorspaces, Fuzzy Math. 5 (4) (1985) 87$-$94] is discussed. Moreover, wealso use the family of generalized fuzzy quasi-norms to characterizethe generalized locally bounded $I$-topological vector spaces, andgive some applications of this characterization.

I-topological vector spaces Generalized locally bounded I-topological vector spaces Family of generalized fuzzy quasi-norms
 J. X. Fang,Local bases with strati ed structure in I-topological vector spaces , Iranian Journal of Fuzzy Systems,7(2) (2010), 83-93.  U. Hohle and S. E. Rodabaugh, eds.Mathematics of fuzzy sets: logic, topology and measure theor, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, 3(1999).  A. K. Katsaras,Fuzzy topological vector spaces I, Fuzzy Sets and Systems, 6 (1981), 85-95.  P. M. Pu and Y. M. Liu,Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571-599.  S. E. Rodabaugh,Point-set lattice-theoretic topology, Fuzzy Sets and Systems, 40(1991),291-347.  C. X. Wu and J. X. Fang,Rede ne of fuzzy topological vector spaces, Science Exploration,(in Chinese),2(4) (1982), 113-116.  C. X. Wu and J. X. Fang,(QL)-type fuzzy topological vector spaces, Chinese Ann. Math.,(in Chinese),6A(3) (1985), 355􀀀364 or (English summary) 6B(3) (1985), 376.  C. X. Wu and J. X. Fang,Boundedness and locally bounded fuzzy topological vector spaces,Fuzzy Math., (in Chinese),5(4) (1985), 87-94.  C. H. Yan and J. X. Fang,Locally bounded L-topological vector spaces, Information Sciences,159 (2004), 273-281.  H. Zhang and J. X. Fang,On locally convex I-topological vector spaces, Fuzzy Sets and Systems,157 (2006), 1995-2002.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.107 Research Paper NEW TYPES OF FUZZY n-ARY SUBHYPERGROUPS OF AN n-ARY HYPERGROUP NEW TYPES OF FUZZY n-ARY SUBHYPERGROUPS OF AN Yin Yunqiang College of Mathematics and Information Sciences, East China Insti- tute of Technology, Fuzhou, Jiangxi 344000, China Zhan Jianming Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province 445000, China Davvaz Bijan Department of Mathematics, Yazd University, Yazd, Iran 28 12 2012 9 5 105 124 27 05 2010 27 10 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_107.html

In this paper, the new notions of belongingness ($in_{gamma}$)"and quasi-coincidence ($q_delta$)"  of a fuzzy point with a fuzzyset are  introduced. By means of this new idea, the  concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$,  andit is shown that, in 16 kinds of $(alpha,beta)$-fuzzy $n$-arysubhypergroups, the significant ones are the$(in_{gamma},in_{gamma})$-fuzzy $n$-ary subhypergroups,$(in_{gamma},ivq)$-fuzzy $n$-ary subhypergroups and the$(in_{gamma}wedge q_{delta},in_{gamma})$-fuzzy $n$-arysubhypergroups.

n-ary subhypergroup $(\in_{\gamma} in_{gamma})$-fuzzy $n$-ary subhypergroups ivq)$-fuzzy$n$-ary subhypergroups and the$(in_{gamma}wedge q_{delta} in_{gamma})$-fuzzy$n$-ary subhypergroups bibitem{Bhakat1992} S. K. Bhakat and P. Das, {it On the definition of a fuzzy subgroup}, Fuzzy Sets and Systems, {bf 51} (1992), 235-241. bibitem{Bhakat1996} S. K. Bhakat and P. Das, {it$(in,invee q)$-fuzzy subgroups}, Fuzzy Sets and Systems, {bf80} (1996), 359-368. bibitem{Corsini1993} P. Corsini, {it Prolegomena of hypergroup theory}, Aviani editore, Italy, 1993. bibitem{Corsini2003} P. Corsini and V. Leoreanu, {it Applications of hyperstructure theory}, Advances in Mathematics (Dordrecht), Kluwer Academic Publishers, Dordrecht, 2003. bibitem{500} I. Cristea, {it About the fuzzy grade of the direct product of two hypergroupoids}, Iranian Journal of Fuzzy Systems, {bf7(2)} (2010), 95-108. bibitem{300} B. Davvaz, {it Fuzzy hyperideals in ternary semihyperrings}, Iranian Journal of Fuzzy Systems, {bf 6}textbf{(4)} (2009), 21-36. bibitem{10} B. Davvaz, {it Fuzzy$H_v$-groups}, Fuzzy Sets and Systems, {bf 101} (1999), 191-195. bibitem{cem} B. Davvaz, A. Dehghan Nezad and A. Benvidi, {it Chain reactions as experimental examples of ternary algebraic hyperstructures}, MATCH Communications in Mathematical and in Computer Chemistry, {bf 65}textbf{(2)} (2011), 491-499. bibitem{143} B. Davvaz and V. Leoreanu-Fotea, {it Intuitionistic fuzzy$n$-ary hypergroups}, Journal of Multiple-Valued Logic and Soft Computing, {bf 16}textbf{(1-2)} (2010), 87-104. bibitem{600} B. Davvaz and P. Corsini, {it On$(alpha,beta)$-fuzzy$Hsb v$-ideals of$Hsb v$-rings}, Iranian Journal of Fuzzy Systems, {bf 5}textbf{(2)} (2008), 35-47. bibitem{123} B. Davvaz, P. Corsini and V. Leoreanu-Fotea, {it Atanassov's intuitionistic$(S,T)$-fuzzy$n$-ary subhypergroups and their properties}, Information Sciences, {bf 179} (2009), 654-666. bibitem{136} B. Davvaz, O. Kazanc{i} and S. Yamak, {it Interval-valued fuzzy$n$-ary subhypergroups of$n$-ary hypergroups}, Neural Comput. & Applic., {bf18} (2009), 903-911. bibitem{140} B. Davvaz and W. A. Dudek, {it Fuzzy$n$-ary groups as a generalization of Rosenfeld's fuzzy groups}, Journal of Multiple-Valued Logic and Soft Computing, {bf 15}textbf{(5-6)} (2009), 451-469. bibitem{DP} B. Davvaz and P. Corsini, {it Fuzzy$n$-ary hypergroups}, J. Intell. Fuzzy. Syst., {bf 18}textbf{(4)} (2007), 377-382. bibitem{DP1} B. Davvaz and P. Corsini, {it Generalized fuzzy sub-hyperquasigroups of hyperquasigroups}, Soft Computing, {bf10}textbf{(11)} (2006), 1109-1114. bibitem{DP2} B. Davvaz and P. Corsini, {it Generalized fuzzy hyperideals of hypernear-rings and many valued implications}, J. Intell. Fuzzy Syst., {bf 17}textbf{(3)} (2006), 241-251. bibitem{book} B. Davvaz and V. Leoreanu-Fotea, {it Hyperring theory and applications}, International Academic Press, USA, 2007. bibitem{DV} B. Davvaz and T. Vougiouklis, {it$n$-ary hypergroups}, Iran. J. Sci. Technol. Trans. A Sci., {bf 30} (2006), 165-174. bibitem{D} W. D{"o}rnte, {it Untersuchungen Auber einen verallgemeinerten Gruppenbegri}, Math. Z., {bf 2} (1928), 1-9. bibitem{DSI} W. A. Dudek, M. Shabir and M. Irfan Ali, {it$(alpha,beta)$-fuzzy ideals of hemirings}, Comput. Math. Appl., {bf 58} (2009), 310-321. bibitem{J} Y. J. Jun, {it Generalizations of$(in,invee q)$-fuzzy subalgebras in BCK/BCI-algebras}, Comput. Math. Appl., {bf 58} (2009), 1383-1390. bibitem{100} O. Kazanc{i}, S. Yamak and B. Davvaz, {it On$n$-ary hypergroups and fuzzy$n$-ary homomorphism}, Iranian Journal of Fuzzy Systems, {bf8}textbf{(1)} (2011), 65-76. bibitem{OBS} O. Kazanc{i}, B. Davvaz and S. Yamak, {it Fuzzy$n$-ary polygroups related to fuzzy points}, Comput. Math. Appl., {bf 58} (2009), 1466-1474. bibitem{OBS1} O. Kazanc{i}, B. Davvaz and S. Yamak, {it Fuzzy$n$-ary hypergroups related to fuzzy points}, Neural Comput. Applic., {bf 19} (2010), 649-655. bibitem{400} V. Leoreanu Fotea, {it Fuzzy rough$n$-ary subhypergroups}, Iranian Journal of Fuzzy Systems, {bf 5}textbf{(3)} (2008), 45-56. bibitem{LD} V. Leoreanu-Fotea and B. Davvaz, {it$n$-hypergroups and binary relations}, European J. Combin., {bf 29}textbf{(5)} (2008), 1207-1218. bibitem{LD1} V. Leoreanu-Fotea and B. Davvaz, {it Join$n$-spaces and lattices}, J. Mult.-Valued Logic Soft Comput., {bf 15} (2009), 421-432. bibitem{Marty1934} F. Marty, {it Sur une generalization de la notion de groupe}, In: 8th Congress Math. Scandianaves, Stockholm, (1934), 45-49. bibitem{V} V. Murali, {it Fuzzy points of equivalent fuzzy subsets}, Information Sciences, {bf 158} (2004), 277-288. bibitem{PM} P. M. Pu and Y. M. Liu, {it Fuzzy topology I: neighbourhood structure of a fuzzy point and Moore-Smith convergence}, J. Math. Anal. Appl., {bf76} (1980), 571-599. bibitem{Rosenfeld} A. Rosenfeld, {it Fuzzy groups}, J. Math. Anal. Appl., {bf 35} (1971), bibitem{Vougiouklis1994} T. Vougiouklis, {it Hyperstructures and their representations}, Hadronic Press Inc., Palm Harbor, USA, bibitem{Yin} Y. Yin and H. Li, {it Note on Generalized fuzzy interior ideals in semigroups"}, Information Sciences, {bf 177} (2007), 5798-5800. bibitem{Yin1} Y. Yin, X. Huang, D. Xu and F. Li, {it The characterization of$h$-semisimple hemirings}, Int. J. Fuzzy Syst., {bf 11} (2009), 116-122. bibitem{Yuan} X. Yuan, H. Li and E. S. Lee, {it On the definition of the intuitionistic fuzzy subgroups}, Comput. Math. Appl., {bf 59} (2010), 3117-3129. bibitem{Zadeh1965} L. A. Zadeh, {it Fuzzy sets}, Information Sciences, {bf 8} (1965), bibitem{Zhan} J. Zhan, B. Davvaz and K. P. Shum, {it A new view of fuzzy hypernear- rings}, Information Sciences, {bf 178} (2008), 425-438. bibitem{Zhan1} J. Zhan, B. Davvaz and K. P. Shum, {it Generalized fuzzy hyperideals of hyperrings}, Comput. Math. Appl., {bf 56} (2008), 1732-1740. bibitem{Zhan2}J. Zhan, B. Davvaz and K. P. Shum, {it A new view of fuzzy hyperquasigroups}, J. Intell. Fuzzy Syst., {bf 20} (2009), 147-157. bibitem{Zhan3} J. Zhan, B. Davvaz and K. P. Shum, {it On probabilitic$n$-ary hypergroups}, Information Sciences, {bf 180} (2010), 1159-1166. bibitem{200} J. Zhan, Y. B. Jun and B. Davvaz, {it On$(in,invee q)$-fuzzy ideals of BCI-algebras}, Iranian Journal of Fuzzy Systems, {bf 6}textbf{(1)} (2009), 81-94. IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.108 Research Paper MIXED VARIATIONAL INCLUSIONS INVOLVING INFINITE FAMILY OF FUZZY MAPPINGS MIXED VARIATIONAL INCLUSIONS INVOLVING INFINITE Ahmad R. Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India Dilshad M. Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India YAO J. C. Center for General Education, Kaohsiung Medical University, Kaohsiung 807, Taiwan 28 12 2012 9 5 125 135 27 10 2010 27 12 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_108.html In this paper, we introduce and study a mixed variational inclusion problem involving infinite family of fuzzy mappings. An iterative algorithm is constructed for solving a mixed variational inclusion problem involving infinite family of fuzzy mappings and the convergence of iterative sequences generated by the proposed algorithm is proved. Some illustrative examples are also given. Mixed variational inclusions In nite family Fuzzy mappings Algo- rithm bibitem {Aubin}J. P. Aubin, {em Optima and equilibria}, Second ed., Springer, Berlin, 1998. bibitem {Chang1}S. S. Chang and N. J. Huang, {em Generalized complementarity problem for fuzzy mappings}, Fuzzy Sets and Systems, {bf 55} (1993), 227-234. bibitem {Chang2} S. S. Chang and Y. Zhu, {em On variational inequalities for fuzzy mappings}, Fuzzy Sets and Systems, {bf 32} (1989), 359-367. bibitem {Ding2} X. P. Ding, {em Algorithm of solutions for mixed implicit quasi-variational inequalities with fuzzy mappings}, Comput. Math. Appl., {bf 38(5-6)} (1999), 231-249. bibitem {Ding1} X. P. Ding and J. Y. Park, {em A new class of generalized nonlinear implicit quasi variational inclusions with fuzzy mapping}, J. Comput. Appl. Math., {bf 138} (2002), 243-257. bibitem {Heilpern} S. Heilpern, {em Fuzzy mappings and fixed point theorems}, J. Math. Anal. Appl., {bf 83} (1981), 566-569. bibitem {Heng} W. Y. Heng, {em Infinite family of generalized set-valued quasi-variational inclusions in Banach spaces}, Acta. Anal. Functionalis Applicata, {bf 10} (2008), 1009-1327. bibitem {Huang1} N. J. Huang, {em A new class of generalized set-valued implicit variational inclusions in Banach spaces with an application}, Comput. Math. Appl., {bf 41(718)} (2001), 937-943. bibitem {Huang2} N. J. Huang, {em A new method for a class of nonlinear variational inequalities with fuzzy mappings}, Appl. Math. Lett., {bf 10(6)} (1997), 129-133. bibitem {Janfada} M. Janfada, H. Baghani and O. Baghani, {em On Felbinos-type fuzzy normed linear spaces and fuzzy bounded operators}, Iranian Journal of Fuzzy Systems, {bf8(5)} (2011), 117-130. bibitem {Kumam} P. Kumam and N. Petrol, {em Mixed variational-like inequality for fuzzy mappings in reflexive Banach spaces}, J. Inequal. Appl., {bf2009} (2009), 1-15. bibitem {Lan1} H. Y. Lan, {em An approach for solving fuzzy implicit variational inequalities with linear membership functions}, Comput. Math. Appl., {bf 55(3)} (2008), 563-572. bibitem {Lan2} H. Y. Lan, Y. J. Cho and R. U. Verma, {em On nonlinear relaxed cocoercive variational inclusions involving$(A,eta)\$-accretive mappings in Banach spaces}, Comput. Math. Appl., {bf 51} (2006), 1529-1538. bibitem {Lassonde} M. Lassonde, {em On the use of KKM multi function in fixed point theory and related topics}, J. Math. Anal. Appl., {bf 97} (1983), 151-201. bibitem {Lee} B. S. Lee, M. F. Khan and Salahuddin, {em Fuzzy nonlinear set-valued variational inclusions}, Comput. Math. Appl., {bf 60(6)} (2010), 1768-1775. bibitem  {Nadler} J. S. B. Nadler, {em Multivalued contraction mappings}, Pacific. J. math., {bf 30} (1969), 475-488. bibitem {Noor} M. A. Noor, {em Variational inequalities with fuzzy mappings (I)}, Fuzzy Sets and Systems, {bf 55} (1989), 309-314. bibitem {Perk1} J. Y. Park and J. U. Jeong, {em Iterative algorithm for finding approximate solutions to completely generalized strongly quasi-variational inequalities for fuzzy mappings}, Fuzzy Sets and Systems, {bf 115} (2000), 413-418. bibitem {Perk2} J. Y. Park and J. U. Jeong, {em A perturbed algorithm of variational inclusions for fuzzy mappings}, Fuzzy Sets and Systems, {bf 115} (2000), 419-424. bibitem {Petryshyn} W. V. Petryshyn, {em A characterization of strictly convexity of Banach spaces and other uses of duality mappings}, J. Funct. Anal., {bf 6} (1997), 282-291. bibitem {Shih} M. H. Shih and K. K. Tan, {em Generalized quasi-variational inequalities in locally convex spaces}, J. Math. Anal. Appl., {bf 108} (1985), 333-343. bibitem {Shivanan} E. Shivanan and E. Khorram, {em  Optimization of linear objective function subject to fuzzy relation inequalities constraints with max-product compozition}, Iranian Journal of Fuzzy Systems, {bf 7(5)} (2010), 51-71. bibitem {Siddiqi} A. H. Siddiqi, R. Ahmad and S. S Irfan, {em Set- valued variational inclusions with fuzzy mappings in Banach spaces}, J. Concrete. Applicable. Math., {bf 4} (2006), 171-181. bibitem  {Takahashi} W. Takahashi, {em Nonlinear variational inequalities and fixed point theorems}, J. Math. Soc. Japan, {bf 28} (1976), 168-181. bibitem {Wu} Z. Wu and J. Xu, {em Generalized convex fuzzy mappings and fuzzy variational-like inequalities}, Fuzzy Sets and Systems, {bf 160(11)} (2009), 1590-1619. bibitem  {Yen} C. L. Yen, {em A minimax inequality and its application to variational inequalities}, Pacific J. Math., {bf 97} (1981), 142-150. bibitem {Zadeh} L. A. Zadeh, {em Fuzzy sets}, Information and Control, {bf 8} (1965), 338-353. bibitem {Zimmermann} H. J. Zimmermann, {em Fuzzy set theory and its applications}, Kluwer Academic Publishers, Dordrecht, 1988.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.109 Research Paper SOME RESULTS ON t-BEST APPROXIMATION IN FUZZY n-NORMED SPACES SOME RESULTS ON t-BEST APPROXIMATION IN FUZZY Gumus Serkan Turkish Military Academy, Cankaya, 06580, Ankara, Turkey Efe Hakan Department of Mathematics, Faculty of Science and Arts, Gazi University, Teknikokullar, 06500 Ankara, Turkey Yildiz ﻿Cemil Department of Mathematics, Faculty of Science and Arts, Gazi University, Teknikokullar, 06500 Ankara, Turkey 28 12 2012 9 5 137 146 27 03 2011 27 12 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_109.html

The aim of this paper is to give the set of all t -best approximations on fuzzy n-normed spaces and prove some theorems in the sense of Vaezpour and Karimi .

n-normed spaces Fuzzy n-norms Best approximation. 2000 Mathematics Subject Classi cation. 46A30 46A70 54A40
 C. Alaca, A new perspective to the Mazur-Ulam problem in 2-fuzzy 2-normed linear spaces, Iranian Journal of Fuzzy Systems, 7(2) (2010), 109-119.  T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math., 11(3) (2003), 687-705.  T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151 (2005), 513-547.  H. Efe and C. Yildiz, Some results in fuzzy compact linear operators, Journal of Computational Analysis Applications, 12(1-B) (2010), 251-262.  S. Gahler, Lineare 2-normierte Raume, Math. Nachr., 28 (1964), 1-43.  S. Gahler, Untersuchungen uber verallgemeinerte m-metrische Raume, I, Math. Nachr., 40 (1969), 165-189.  M. Goudarzi and S. M. Vaezpour, Best simultaneous approximaton in fuzzy normed spaces, Iranian Journal of Fuzzy Systems, 7(3) (2010), 87-96.  H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27(10) (2001),  N. Huang and H. Lan, A couple of nonlilear equaions with fuzzy mappings in fuzzy normed spaces, Fuzzy Sets and Systems, 152 (2005), 209-222.  S. S. Kim and Y. J. Cho, Strict convexity in linear n-normed spaces, Demonstratio Math., 29(4) (1996), 739-744.  R. Malceski, Strong n-convex n-normed spaces, Mat. Bilten, 21(47) (1997), 81-102.  A. Misiak, n-inner product spaces, Math. Nachr., 140 (1989), 299-319.  A. Narayanan and S. Vijayabalaji, Fuzzy n-normed linear space, Int. J. Math. Math. Sci., 24 (2005), 3963-3977.  I. Singer, Best approximation in normed linear spaces by elements of linear subspaces, Springer-Verlag, 1970.  S. M. Vaezpour and F. Karimi, t-Best approximation in fuzzy normed spaces, Iranian Journal of Fuzzy Systems, 5(2) (2008), 93-99.  S. Vijayabalaji and N. Thillaigovindan, Complete fuzzy n-normed linear space, Journal of Fundamental Sci., 3(1) (2007), 119-126.  S. Vijayabalaji and N. Thillaigovindan, Best approximation sets in n-normed space corresponding to intuitionistic fuzzy n-normed linear space, Iranian Journal of Fuzzy Systems, 5(3) (2008), 57-69.  H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27(10) (2001),  N. Huang and H. Lan, A couple of nonlilear equaions with fuzzy mappings in fuzzy normed spaces, Fuzzy Sets and Systems, 152 (2005), 209-222.  S. S. Kim and Y. J. Cho, Strict convexity in linear n-normed spaces, Demonstratio Math., 29(4) (1996), 739-744.  R. Malceski, Strong n-convex n-normed spaces, Mat. Bilten, 21(47) (1997), 81-102.  A. Misiak, n-inner product spaces, Math. Nachr., 140 (1989), 299-319.  A. Narayanan and S. Vijayabalaji, Fuzzy n-normed linear space, Int. J. Math. Math. Sci., 24 (2005), 3963-3977.  I. Singer, Best approximation in normed linear spaces by elements of linear subspaces, Springer-Verlag, 1970.  S. M. Vaezpour and F. Karimi, t-Best approximation in fuzzy normed spaces, Iranian Journal of Fuzzy Systems, 5(2) (2008), 93-99.  S. Vijayabalaji and N. Thillaigovindan, Complete fuzzy n-normed linear space, Journal of Fundamental Sci., 3(1) (2007), 119-126.  S. Vijayabalaji and N. Thillaigovindan, Best approximation sets in n-normed space corresponding to intuitionistic fuzzy n-normed linear space, Iranian Journal of Fuzzy Systems, 5(3) (2008), 57-69.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.2809 unavailable Persian-translation vol. 9, no. 5, December 2012 01 12 2012 9 5 149 158 13 12 2016 13 12 2016 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_2809.html

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