IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2010.2880 unavailable Cover Vol. 7, No.2, June 2010 29 06 2010 7 2 0 0 28 12 2016 28 12 2016 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_2880.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.2010.167 Research Paper Exact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the ABS approach Exact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the ABS approach Ghanbari Reza Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran Mahdavi-Amiri Nezam Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran Yousefpour Rohollah Department of Mathematics, Mazandaran University, Babolsar, Iran 05 06 2010 7 2 1 18 05 10 2008 05 10 2009 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_167.html

We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy LR system lacks exact solutions. We show that the fuzzy LR system has an exact solution if and only if the corresponding crisp system is compatible (has a solution) and the solution of the corresponding least squares problem is equal to zero. In this case, the exact solution is determined by the solutions of the two corresponding problems. On the other hand, if the corresponding crisp system is compatible and the optimal value of the corresponding constrained least squares problem is nonzero, then we characterize approximate solutions of the fuzzy system by solution of the least squares problem. Also, we characterize solutions by defining an appropriate membership function so that an exact solution is a fuzzy LR vector having the membership function value equal to one and, when an exact solution does not exist, an approximate solution is a fuzzy LR vector with a maximal membership function value. We propose a class of algorithms based on ABS algorithm for solving the LR fuzzy systems. The proposed algorithms can also be used to solve the extended dual fuzzy linear systems. Finally, we show that, when the system has more than one solution, the proposed algorithms are flexible enough to compute special solutions of interest. Several examples are worked out to demonstrate the various possible scenarios for the solutions of fuzzy LR linear systems.

Fuzzy linear system Fuzzy LR solution ABS algorithm Least squares approximation
bibitem{ABS} J. Abaffy, C. Broyden and E. Spedicato, {it A class of direct methods for linear systems}, Numerische Mathematik, {bf45} (1984), 361-376. bibitem{ABSBOOK} J. Abaffy and E. Spedicato, {it ABS projection algorithms: mathematical techniques for linear and nonlinear equations}, Ellis Horwood, Chichester, 1989. bibitem{Abbasbandy}S. Abbasbandy and M. Alavi, {it A method for solving fuzzy linear system}, Iranian Journal of Fuzzy Systems, {bf2} (2005), 37-43. bibitem{abramovich}F. Abramovich, M. Wagenknecht and Y. I. Khurgin, {it Solution of LR-type fuzzy systems of linear algebraic equations}, Busefal, {bf35} (1988), 86-99. bibitem{Store} R. Bulrisch and J. Stoer, {it Introduction to numerical analysis (texts in applied mathematics)}, 2nd edition, Springer, 1992. bibitem{Buckley} J. J. Buckley and Y. Qu, {it Solving systems of linear fuzzy equations}, Fuzzy Sets and Systems, {bf43} (1991), 33-43. bibitem{dub}  D. Dubois and H. Prade, {it Fuzzy sets and systems theory and applications}, Academic Press, New York, 1980. bibitem{Egrvary} E. Egervary, {it On rank-diminishing operations and their applications to the solution of linear equations}, ZAMP, {bf9} (1960), 376-386. bibitem{iabs} H. Esmaeili, N. Mahdavi-Amiri and E. Spedicato, {it A class of ABS algorithms for Diophantine linear systems}, Numerische Mathematik, {bf91} (2001), 101ï؟½-115. bibitem{Frie1} M. Friedman, M. Ma and A. Kandel,  {it Fuzzy linear systems}, Fuzzy Sets and Systems, {bf96} (1998), 201-209. bibitem{Fuller}R. Fuller, {it On stability in possibilistic linear equality systems with Lipschitzian fuzzy numbers}, Fuzzy Sets and Systems, {bf34} (1990), 347ï؟½-353. bibitem{Khoram} M. Khorramizadeh and N. Mahdavi-Amiri, {it Integer extended ABS algorithms and possible control of intermediate results for linear Diophantine systems}, 4OR, {bf7(2)} (2009), 145- 167. bibitem{FrieD} M. Ma, M. Friedman and A. Kandel, {it Duality in fuzzy linear systems}, Fuzzy Sets and Systems, {bf109} (2000), 55-58. bibitem{Golab} G. H. Golub and C. F. Van Loan, {it Matrix computations}, Baltimore, MD, 3rd edition, Johns Hopkins University Press, 1996. bibitem{mah2}  N. Mahdavi-Amiri and S. H. Nasseri, {it Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables}, Fuzzy Sets and System, {bf158} (2007), 1961-1978. bibitem{mal1} H. R. Maleki, M. Tata and M. Mashinchi, {it Linear programming with fuzzy variables}, Fuzzy Sets and Systems, {bf109} (2000), bibitem{Minc} H. Minc, {it Nonnegative matrices}, Wiley, New York, 1988. bibitem{Muz1} S. Muzzioli and H. Reynaerts, {it Fuzzy linear systems of form \$A_{1}x+b_{1}=A_2x+b_2\$}, Fuzzy Sets and Systems, {bf157} ( 2006), 939-951. bibitem{fuzzy logic} H. T. Nguyen and E. A. Walker, {it A first course in fuzzy logic}, Chapman & Hall, 2000. bibitem{Nicolai}S. Nicolai and E. Spedicato, {it A bibliography of the ABS methods}, Optimization Methods and Software, {bf8} (1997), 171-183. bibitem{spidicato1} E. Spedicato, E. Bodon, A. D. Popolo and N. Mahdavi-Amiri, {it ABS methods and ABSPACK for linear systems and optimization: a review}, 4OR, {bf1} (2003), 51-66. bibitem{spedicato2} E. Spedicato, Z. Xia and L. Zhang, {it ABS algorithms for linear equations and optimization}, Journal of Computational and Applied Mathematics, {bf124} (2000), 155-170. bibitem{vorman} A. Vroman, G. Deschrijver and E. Kerre,  {it Solving systems of linear fuzzy equations by parametric  functions-an improved algorithm}, Fuzzy Sets and Systems, {bf158} (2007), 1515 ï؟½-1534. bibitem{Wang} X. Wang, Z. Zhong and M. Ha, {it Iteration algorithms for solving a system of fuzzy linear equations}, Fuzzy Sets and Systems, {bf119} (2001), 121-128. bibitem{zim2} H. J. Zimmermann, {it Fuzzy set theory and its applications}, Third ed., Kluwer Academic, Norwell, 1996.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2010.168 Research Paper Fuzzy linear regression model with crisp coefficients: A goal programming approach Fuzzy linear regression model with crisp coefficients: A goal programming approach Hassanpour H Department of Mathematics, University of Birjand, Birjand, Iran Maleki H. R Faculty of Basic Sciences, Shiraz University of Technology, Shiraz, Iran Yaghoobi M. A Department of Statistics, Shahid Bahonar University of Kerman, Kerman, Iran 05 06 2010 7 2 1 153 05 03 2013 05 03 2013 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_168.html

The fuzzy linear regression model with fuzzy input-output data andcrisp coefficients is studied in this paper. A linear programmingmodel based on goal programming is proposed to calculate theregression coefficients. In contrast with most of the previous works, theproposed model takes into account the centers of fuzzy data as animportant feature as well as their spreads in the procedure ofconstructing the regression model. Furthermore, the model can dealwith both symmetric and non-symmetric triangular fuzzy data as wellas trapezoidal fuzzy data which have rarely been considered in theprevious works. To show the efficiency of the proposed model, somenumerical examples are solved and a simulation study is performed.The computational results are compared with some earlier methods.

Fuzzy linear regression Goal programming Linear programming Fuzzy number
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2010.171 Research Paper FUZZY CONVEX SUBALGEBRAS OF COMMUTATIVE RESIDUATED LATTICES FUZZY CONVEX SUBALGEBRAS OF COMMUTATIVE RESIDUATED LATTICES Ghorbani Shokoofeh Department of Mathematics of Bam, Shahid Bahonar University of Kerman, Kerman, Iran Hasankhani Abbas Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran 06 06 2010 7 2 41 54 06 04 2008 06 07 2009 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_171.html

In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy convex subalgebras of an integral commutative residuated lattice and will prove that fuzzy filters and fuzzy convex subalgebras of an integral commutative residuated lattice coincide.

(Integral) Commutative residuated lattice Fuzzy convex subalgebra Fuzzy congruence relation Fuzzy filter
 T. S. Blyth and M. F. Janovitz,Residuation theory, Perogamon Press, 1972.  K. Blount and C. Tsinakies,The structure of residuated lattices, Internat. J. Algebra Comput., 13(4)(2003), 437-461.  P. S. Das,Fuzzy groups and level subgroups, Math. Anal. Appl., 84 (1981), 264-269.  R. P. Dilworth,Non-commutative residuated lattices, Trans. Amer. Math. Soc., (1939), 426-444.  J. Hart, L. Rafter and C. Tsinakis,The structure of commutative residuated lattices, Internat. J. Algebra Comput.,12(4) (2002), 509-524.  A. Hasankhani and A. Saadat,Some quotients on BCK-algebra generated by a fuzzy set, Iranian Journal of Fuzzy Systems,1(2) (2004), 33-43.  K. Hur, S. Y. Jang and H. W. Kang,Some intuitionistic fuzzy congruences, Iranian Journal of Fuzzy Systems,3(1) (2006), 45-57.  A. Iorgulescu,Classes of BCK algebras-part III, Preprint Series of the Institute of Mathematics of the Romanian Academy, preprint,3 (2004), 1-37.  T. Kowalski and H. Ono,Residuated lattices: an algebraic glimpse at logic without contraction, Japan Advanced Insitute of Science and Technology, 2001.  L. Lianzhen and L. Kaitai,Fuzzy filters of BL- algebras, Information Sciences, 173 (2005),141-154.  V. Murali,Fuzzy equivalence relations, Fuzzy Sets and Systems, 30 (1989), 155-163.  E. Turunen,Mathematics behind fuzzy logic, Physica-Verlag, 1999.  M. Ward,Residuated distributive lattices, Duke Math. J., (1940), 641-651.  M. Ward and R. P. Dilworth,Residuated lattices, Trans. Amer. Math. Soc., (1939), 335-354.  L. A. Zadeh,Fuzzy sets, Information and Control ,(1965), 338-353.  J. L. Zhang,Fuzzy filters of the residuated lattices, New Math. Nat. Comput., 2(1) (2006),11-28.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2010.172 Research Paper Ordered semigroups characterized by their intuitionistic fuzzy bi-ideals Ordered semigroups characterized by their intuitionistic fuzzy Khan Asghar Department of Mathematics, COMSATS Institute of IT Abbottabad, Pakistan Jun Young Bae Department of Mathematics Educations and RINS , Gyengsang National University , Chinju 660-701, Korea Shabir Muhammad Department of Mathematics Quaid-i-Azam University, Islamabad, Pakistan 06 06 2010 7 2 55 69 06 11 2008 06 07 2009 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_172.html

Fuzzy bi-ideals play an important role in the study of ordered semigroupstructures. The purpose of this paper is to initiate and study theintiuitionistic fuzzy bi-ideals in ordered semigroups and investigate thebasic theorem of intuitionistic fuzzy bi-ideals. To provide thecharacterizations of regular ordered semigroups in terms of intuitionisticfuzzy bi-ideals and to discuss the relationships of left(resp. right andcompletely regular) ordered semigroups in terms intuitionistic fuzzybi-ideals.

Intuitionistic fuzzy sets Intuitionistic fuzzy bi-ideals Regular Left (resp. right) regular ordered semigroups Semilattices of left and right simple ordered semigroups
bibitem{1} K. T. Atanassov, textit{Intuitionistic fuzzy sets}, Fuzzy Sets and Systems, textbf{20} (1986), 87-96. bibitem{2} K. T. Atanassov, textit{New operations defined over the intuitionistic fuzzy sets}, Fuzzy Sets and Systems, \$mathbf{61}\$ \$ (1994)\$, \$% 137 \$-\$142\$. bibitem{3} K. T. Atanassov, textit{Intuitionistic fuzzy sets, theory and applications}, Studies in Fuzziness and Soft Computing, Heidelberg, Physica-Verlag, \$mathbf{35}\$ \$ (1999)\$. bibitem{4} R. A. Borzooei and Y. B. Jun, textit{Intuitionistic fuzzy hyper BCK-ideals of hyper BCK-algebras, }Iranian Journal of Fuzzy Systems, textbf{% 1}textbf{(1)} (2006), 23-29. bibitem{5} P. Burillo and H. Bustince, textit{Vague sets are intuitionistic fuzzy sets}, Fuzzy Sets and Systems textbf{79} (1996), bibitem{6} B. Davvaz, W. A. Dudek and Y. B. Juntextit{, Intuitionistic fuzzy }\$% H_{v}\$textit{-submodules}, Information Sciences, \$mathbf{176}\$ \$(2006)\$, \$% 285 \$-\$300\$. bibitem{7} S. K. De, R. Biswas and A. R. Roy, textit{An application of intuitionistic fuzzy sets in medical diagnosis}, Fuzzy Sets and Systems, textbf{117} (2001), 209-213. bibitem{8} L. Dengfeng and C. Chunfian, textit{New similarity measures of intuitionistic fuzzy sets and applications to pattern recognitions}, Pattern Reconit. Lett., textbf{23} (2002), 221-225. bibitem{9} W. L. Gau and D. J. Buehre, textit{Vague sets}, IEEE Trans Syst Man Cybern, textbf{23} (1993), 610-614. bibitem{10} S. B. Hosseini, D. Oregan and R. Saadati, textit{Some results on intuitionistic fuzzy spaces}, Iranian Journal of Fuzzy Systems, textbf{4}textbf{(1)} (2007), 53-64. bibitem{11} K. Hur, S. Y. Jang and H. W. Kang, textit{Some intuitionistic fuzzy congruences}, Iranian Journal of Fuzzy Systems, textbf{3}textbf{(1)} (2006), bibitem{12} Y. B. Jun, textit{Intuitionistic fuzzy bi-ideals of ordered semigroups}, KYUNGPOOK Math. J., \$mathbf{45}\$ \$(2005)\$, \$527\$-\$537\$. bibitem{13} N. Kehayopulu, textit{On regular duo ordered semigroups}, Math. Japonica, \$mathbf{37}\$\$textbf{(6)}\$ \$(1990)\$, \$1051\$-\$1056\$. bibitem{14} N. Kehayopulu and M. Tsingelis, textit{Fuzzy sets in ordered groupoids}, Semigroup Forum \$mathbf{65}\$ \$(2002)\$, \$128\$-\$132\$. bibitem{15} N. Kehayopulu and M. Tsingelis, textit{Fuzzy bi-ideals in ordered semigroups}, Information Sciences, \$mathbf{171}\$ \$(2005)\$, \$13\$-\$28\$. bibitem{16} N. Kehayopulu and M. Tsingelis, textit{Regular ordered semigroups in terms of fuzzy subset}, Information Sciences, \$mathbf{176}\$ \$% (2006)\$, \$65\$-\$71\$. bibitem{17} N. Kehayopulu and M. Tsingelis, textit{Left and intra-regular ordered semigroups in terms fuzzy sets}, Quasigroups and Related Systems, textbf{14} (2006), 169-178. bibitem{18} N. Kehayopulu and M. Tsingelis, textit{Fuzzy ideals in ordered semigroups}, Quasigroups and Related Systems, textbf{15} (2007), 279-289. bibitem{19} K. H. Kim and Y. B. Jun, textit{Intuitionistic fuzzy interior ideals of semigroups,} Int. J. Math. Math. Sci., \$mathbf{{27}(5)}\$ \$ (2001)\$, \$% 261 \$-\$267.\$ bibitem{20} K. H. Kim and Y. B. Jun, textit{Intuitionistic fuzzy ideals of semigroups}, Indian J. Pure Appl. Math., \$mathbf{{33}(4)}\$ \$(2002)\$, \$443\$-\$449\$. bibitem{21} K. H. Kim, W. A. Dudek and Y. B. Jun, textit{Intuitionistic fuzzy subquasigroups of quasigroups}, Quasigroups Related Systems, textbf{7} (2000), 15-28. bibitem{22} M. Rafi and M. S. M. Noorani, textit{Fixed point theorem on intuitionistic fuzzy metric spaces}, Iranian Journal of Fuzzy Systems, textbf{{3}(1)} (2006), 23-29. bibitem{23} M. Shabir and A. Khan, textit{Characterizations of ordered semigroups by the properties of their fuzzy generalized bi-ideals}, New Math. Natural Comput., \$mathbf{{4}(2)}\$ (\$2008\$), \$237\$-\$250\$. bibitem{24} M. Shabir and A. Khan, textit{Intuitionistic fuzzy interior ideals of ordered semigroups}, to appear in J. Applied Math. and Informatics. bibitem{25} M. Shabir and A. Khan, textit{Ordered semigroups characterized by their intuitionistic fuzzy generalized bi-ideals}, to appear in Fuzzy Systems and Mathematics. bibitem{26} E. Szmidt and J. Kacprzyk, textit{Entropy for intuitionistic fuzzy sets}, Fuzzy Sets and Systems, textbf{118} (2001), 467-477. bibitem{27} L. A. Zadeh, textit{Fuzzy sets}, Information  and  Control, \$mathbf{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.2010.176 Research Paper M-FUZZIFYING DERIVED OPERATORS AND DIFFERENCE DERIVED OPERATORS M-FUZZIFYING DERIVED OPERATORS AND DIFFERENCE DERIVED OPERATORS Xin Xiu Department of Mathematics, Tianjin University of Technology, Tianjin,300384, P.R.China Shi Fu-Gui Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, P.R.China Li Sheng-Gang College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, P.R.China 06 06 2010 7 2 71 81 06 03 2013 06 03 2013 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_176.html

This paper presents characterizations of M-fuzzifying matroids bymeans of two kinds of fuzzy operators, called M-fuzzifying derived operatorsand M-fuzzifying difference derived operators.

M-fuzzifying matroid M-fuzzifying closure operator M-fuzzifying derived operator M-fuzzifying difference derived operator
 A. Borumand Saeid, Interval-valued fuzzy B-algebras, Iranian Journal of Fuzzy Systems, 3 (2006), 63-74.  P. Dwinger, Characterizations of the complete homomorphic images of a completely distributive complete lattice I, Indagationes Mathematicae (Proceedings), 85 (1982), 403-414.  R. Goetschel and W. Voxman, Fuzzy matroids, Fuzzy Sets and Systems, 27 (1988), 291-302.  R. Goetschel and W. Voxman, Bases of fuzzy matroids, Fuzzy Sets and Systems, 31 (1989),  R. Goetschel and W. Voxman, Fuzzy matroids and a greedy algorithm, Fuzzy Sets and Systems, 37 (1990), 201-214.  R. Goetschel and W. Voxman, Fuzzy rank functions, Fuzzy Sets and Systems, 42 (1991),  I. C. Hsueh, On fuzzication of matroids, Fuzzy Sets and Systems, 53 (1993), 319-327.  H. L. Huang and F. G. Shi, L-fuzzy numbers and their properties, Information Sciences, 178 (2008), 1141-1151.  S. P. Li, Z. Fang and J. Zhao, P2-connectedness in L-topological spaces, Iranian Journal of Fuzzy Systems, 2 (2005), 29-36.  L. A. Novak, A comment on ‘Bases of fuzzy matroids’, Fuzzy Sets and Systems, 87 (1997),  L. A. Novak, On fuzzy independence set systems, Fuzzy Sets and Systems, 91 (1997), 365-374.  L. A. Novak, On goetschel and voxman fuzzy matroids, Fuzzy Sets and Systems, 117 (2001),  J. G. Oxley, Matroid theory, Oxford University Press, New York, 1992.  F. G. Shi, Theory of L -nested sets and L -nested sets and its applications, Fuzzy Systems and Mathematics, in Chinese, 4 (1995), 65-72.  F. G. Shi, L-fuzzy relation and L-fuzzy subgroup, J. Fuzzy Math., 8 (2000), 491-499.  F. G. Shi, A new approach to the fuzzification of matroids, Fuzzy Sets and Systems, 160 (2009), 696-705.  F. G. Shi, (L,M)-fuzzy matroids, Fuzzy Sets and Systems, 160 (2009), 2387-2400.  G. J. Wang, Theory of topological molecular lattices, Fuzzy Sets and Systems, 47 (1992),  L. Wang and F. G. Shi, Characterization of L-fuzzifying matroids by L-fuzzifying closure operators, Iranian Journal of Fuzzy Systems, 7 (2010), 47-58.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2010.177 Research Paper LOCAL BASES WITH STRATIFIED STRUCTURE IN \$I\$-TOPOLOGICAL VECTOR SPACES LOCAL BASES WITH STRATIFIED STRUCTURE IN \$I\$-TOPOLOGICAL VECTOR SPACES Fang Jin-Xuan School of Mathematical Science, Nanjing Normal University, Nanjing, Jiangsu 210097, P. R. China 06 06 2010 7 2 83 93 06 07 2008 06 10 2009 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_177.html

In this paper, the concept of {sl local base with  stratifiedstructure} in \$I\$-topological vector spaces is introduced. Weprove that every \$I\$-topological vector space has a balanced localbase with stratified structure. Furthermore, a newcharacterization of \$I\$-topological vector spaces by means of thelocal base with stratified structure is given.

\$I\$-topological vector spaces \$Q\$-neighborhood base \$W\$-neighborhood base Local base with stratified structure
bibitem{Chang} C. L. Chang, {it Fuzzy topological spaces}, J. Math. Anal. Appl., {bf 24} (1968), 182-190. bibitem{Fang1} J. X. Fang, {it On local bases of fuzzy topological vector spaces}, Fuzzy Sets and Systems, {bf 87} (1997), 341-347. bibitem{Fang2} J. X. Fang, {it Fuzzy linear order-homomorphism and its structures}, J. Fuzzy Math., {bf 4}textbf{(1)} (1996), 93-102. bibitem{Fe} C. Felbin, {it Finite dimensional fuzzy normed linear space}, Fuzzy Sets and Systems, {bf 48} (1992), 239-248. bibitem{HR} U. H"{o}hle and S. E. Rodabaugh (Eds.), {it Mathematics of fuzzy sets: logic, topology and measure theory}, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, {bf 3} (1999). bibitem{JY} S. Q. Jing and C. H. Yan, {it Fuzzy bounded sets and totally fuzzy bounded sets in \$I\$-topological vector spaces}, Iranian Journal of Fuzzy Systems, {bf 4}textbf{(1)} (2009). bibitem{KL} A. K. Katsaras and D. B. Liu, {it Fuzzy vector spaces and fuzzy topological vector spaces}, J. Math. Anal. Appl., {bf 58} (1997), 135-146. bibitem{Ka} A. K. Katsaras, {it Fuzzy topological vector spaces I}, Fuzzy Sets and Systems, {bf 6} (1981), 85-95. bibitem{PL} P. M. Pu and Y. M. Liu, {it Fuzzy topology I, neighborhood structures of a fuzzy points and Moore-Smith convergence}, J. Math. Anal. Appl., {bf 76} (1980), 571-599. bibitem{Wan} G. J. Wang, {it Order-homomorphism of fuzzes}, Fuzzy Sets and Systems, {bf 12} (1982), 281-288. bibitem{War} R. H. Warren, {it Neighborhoods bases and continuity in fuzzy topological spaces}, Rocky Mountain J. Math., {bf 8} (1978), bibitem{WF} C. X. Wu and J. X. Fang, {it Redefine of fuzzy topological vector space}, Since Exploration, in Chinese, {bf 2}textbf{(4)} (1982), bibitem{XF} G. H. Xu and J. X. Fang, {it A new \$I\$-vector topology generated by a fuzzy norm}, Fuzzy Sets and Systems, {bf 158} (2007), 2375-2385. bibitem{YF} C. H. Yan and J. X. Fang, {it \$L\$-fuzzy bilinear operator and its continuity}, Iranian Journal of Fuzzy Systems, {bf 4}textbf{(1)} (2007), 65-73.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2010.178 Research Paper About the fuzzy grade of the direct product of two hypergroupoids About the fuzzy grade of the direct product of two hypergroupoids Cristea Irina DIEA, University of Udine, Via delle Scienze 2008, 33100 Udine, Italy 06 06 2010 7 2 95 108 06 07 2008 06 10 2009 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_178.html

The aim of this paper is the study of the sequence of join spacesand fuzzy subsets associated with a hypergroupoid. In thispaper we give some properties of the membership function\$widetildemu_{otimes}\$ corresponding to the direct pro-duct oftwo hypergroupoids and we determine the fuzzy grade of thehypergroupoid \$langle Htimes H, otimesrangle\$ in a particularcase.

Fuzzy set Hypergroup Join space Fuzzy grade. } newlineindent{footnotesize This work was partially supported by the Grant no.88/2008 of the Romanian Academy
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2010.179 Research Paper A new perspective to the Mazur-Ulam problem in \$2\$-fuzzy \$2\$-normed linear spaces A new perspective to the Mazur-Ulam problem in \$2\$-fuzzy \$2\$-normed linear spaces Alaca Cihangir Department of Mathematics, Faculty of Science and Arts, Sinop University, 57000 Sinop, Turkey 06 06 2010 7 2 109 119 06 06 2009 06 10 2009 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_179.html

In this paper, we introduce the concepts of \$2\$-isometry, collinearity, \$2\$%-Lipschitz mapping in \$2\$-fuzzy \$2\$-normed linear spaces. Also, we give anew generalization of the Mazur-Ulam theorem when \$X\$ is a \$2\$-fuzzy \$2\$%-normed linear space or \$Im (X)\$ is a fuzzy \$2\$-normed linear space, thatis, the Mazur-Ulam theorem holds, when the \$2\$-isometry mapped to a \$2\$%-fuzzy \$2\$-normed linear space is affine.

\$alpha \$-\$2\$-Norm \$2\$-Fuzzy \$2\$-Normed linear spaces \$2\$-Isometry \$2\$-Lipschitz mapping
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2010.180 Research Paper Regular ordered semigroups and intra-regular ordered semigroups in terms of fuzzy subsets Regular ordered semigroups and intra-regular ordered semigroups in terms of fuzzy subsets Xie Xiang-Yun Department of Mathematics and Physics, Wuyi University , Jiangmen, Guangdong, 529020, P.R.China Tang Jian Jian Tang\\ School of Mathematics and Computational Science, Fuyang Normal College, Fuyang, Anhui, 236041, P.R.China 06 06 2010 7 2 121 140 06 12 2007 06 11 2009 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_180.html

Let \$S\$ be an ordered semigroup. A fuzzy subset of \$S\$ is anarbitrary mapping   from \$S\$ into \$[0,1]\$, where \$[0,1]\$ is theusual interval of real numbers. In this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup \$S\$ is introduced.Regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.Finally, two main theorems which characterize  regular orderedsemigroups and intra-regular ordered semigroups in terms of fuzzyleft ideals, fuzzy right ideals, fuzzy bi-ideals or fuzzyquasi-ideals are given. The paper shows that one can pass fromresults in terms of fuzzy subsets in semigroups to orderedsemigroups. The corresponding results of unordered semigroups arealso obtained.

Ordered semigroup Regular ordered semigroup Intra-regular ordered semigroup Fuzzy left (right) ideal Fuzzy (generalized) bi-ideal Fuzzy quasi-ideal
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2010.182 Research Paper Actions, Norms, Subactions and Kernels of (Fuzzy) Norms Actions, Norms, Subactions and Kernels of (Fuzzy) Norms Han Jeong Soon Department of Applied Mathematics, Hanyang University , Ahnsan, 426-791, Korea Kim Hee Sik Department of Mathematics, Hanyang University , Seoul, 133-791, Korea Neggers J Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U. S. A 06 06 2010 7 2 141 147 06 09 2008 06 09 2009 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_182.html

In this paper, we introduce the notion of an action \$Y_X\$as a generalization of the notion of a module,and the notion of a norm \$vt: Y_Xto F\$, where \$F\$ is a field and \$vartriangle(xy)vartriangle(y') =\$ \$ vartriangle(y)vartriangle(xy')\$ as well as the notion of fuzzy norm, where \$vt: Y_Xto [0, 1]subseteq {bf R}\$, with \$bf R\$  the set of all real numbers. A great many standard mappings on algebraic systems can be modeled on norms as shown in the examples and it is seen that \$mathrm{Ker}vt ={y|vt(y)=0}\$ has many useful properties. Some are explored, especially in the discussion of fuzzy norms as they relate to the complements of subactions \$N_X\$ of \$Y_X\$.

(Fuzzy) norm (Sub) action Kernel
bibitem{BS}     T. Bag and S. K. Samata, textit{A comparative study of fuzzy norms on a linear space}, Fuzzy Sets and Systems textbf{159} (2008), 670-684. bibitem{K} A. K. Katsaras, textit{Fuzzy topological vector space} II, Fuzzy Sets and Systems textbf{12} (1984), 143-154. bibitem{O} O. T. O'meara, textrm{Introduction to quadratic forms}, Springer-Verlag, Berlin, 1963. bibitem{RS} J. R. Raftery and T. Sturm, textit{On completions of pseudo-normed \$BCK\$-algebras and pseudo-metric universal algebras}, Math. Japonica textbf{33} (1988), 919-929. bibitem{ZS} O. Zariski and P. Samuel, textrm{Commutative algebra}, D. Van Nostrand, Toronto, textbf{I, II} (1958).
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2010.183 Research Paper Fuzzy Subgroups of Rank Two Abelian p-Group Fuzzy Subgroups of Rank Two Abelian p-Group Ngcibi S Department of Mathematics (P\&A), University of Fort Hare, Alice, 5700, South Africa Murali V Department of Mathematics (P\&A), Rhodes University, Grahamstown, 6140, South Africa Makamba B. B B. B. Makamba, Department of Mathematics (P\&A), University of Fort Hare, Alice, 5700, South Africa 06 06 2010 7 2 149 153 06 04 2008 06 08 2009 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_183.html

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the subgroups of maximal chains in a special way which enables us to count the number of fuzzy subgroups.

Equivalence Fuzzy subgroup p-groups Keychain
bibitem{mur:01} V.Murali, and B.B.Makamba, On an Equivalence of Fuzzy Subgroups I , Fuzzy Sets and Systems, 123 (2001) 163-168. bibitem{mur:03} V.Murali and B.B. Makamba, On an Equivalence of Fuzzy Subgroups II, Fuzzy sets and Systems, 136 (2003), 93-104. bibitem{mur:04} V.Murali and B.B. Makamba, Counting the number of fuzzy subgroups of an abelian group of order \$p^n q^m\$, Fuzzy sets and Systems, 144 (2004), 459-470. bibitem{ros:71} A.Rosenfeld, Fuzzy Groups, J. Math. Anal. Appl., 35 (1971) 512-517. bibitem{zad:65} L.A.Zadeh, Fuzzy sets, Inform. and control, 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.2010.2881 unavailable Persian-translation Vol. 7, No.2, June 2010 30 06 2010 7 2 157 167 28 12 2016 28 12 2016 Copyright © 2010, University of Sistan and Baluchestan. 2010 http://ijfs.usb.ac.ir/article_2881.html

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