IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2007.2908 unavailable Cover Vol.4 No.2, October 2007 01 10 2007 4 2 0 0 03 01 2017 03 01 2017 Copyright © 2007, University of Sistan and Baluchestan. 2007 http://ijfs.usb.ac.ir/article_2908.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.2007.365 Research Paper PRICING STOCK OPTIONS USING FUZZY SETS PRICING STOCK OPTIONS USING FUZZY SETS Buckley James J. Department of Mathematics, University of Alabama at Birmingham, Birmingham, Al 35209, USA Eslami Esfandiar Department of Mathematics, Shahid Bahonar University of Kerman, Kerman and Institute for Studies in Theoretical Physics and Mathematics(IPM), Tehran, Iran 09 10 2007 4 2 1 14 09 01 2007 09 01 2007 Copyright © 2007, University of Sistan and Baluchestan. 2007 http://ijfs.usb.ac.ir/article_365.html

We use the basic binomial option pricing method but allow someor all the parameters in the model to be uncertain and model this uncertaintyusing fuzzy numbers. We show that with the fuzzy model we can, with areasonably small number of steps, consider almost all possible future stockprices; whereas the crisp model can consider only n + 1 prices after n steps.

Pricing Options Binomial methods Fuzzy numbers
 S. S. Appadoo, R. K. Thulasiram, C. R. Bector and A. Thavaneswaran, Fuzzy algebraic option pricing technique- a fundamental investigation, Proceedings ASAC Conference 2004, Quebec City, Quebec.  J. J. Buckley and E. Eslami, Introduction to fuzzy logic sand fuzzy sets, Springer, Heidelberg, Germany, 2002.  J. J. Buckley and Y. Qu, On using -cuts to evaluate fuzzy equations, Fuzzy Sets and Systems, 38(1990), 309-312.  J. J. Buckley, T. Feuring and E. Eslami, Applications of fuzzy sets and fuzzy logic to economics and engineering, Springer, Heidelberg, Germany, 2002.  J. C. Cox and M. Rubinstein, Options markets, Prentice-Hall, Englewood Cliffs, NJ, 1985.  D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications, Academic Press, N.Y., 1980.  M. Durbin, All About derivatives, McGraw-Hill, NY, NY, 2006.  Frontline Systems (www.frontsys.com).  G. J. Klir and B. Yuan, Fuzzy sets and fuzzy logic, Prentice Hall, Upper Saddle River, N.J.,  S. Muzzioli and C. Torricelli, A model for pricing an option with a fuzzy payoff, Fuzzy Economic Review, 6(2001), 40-62.  S. Muzzioli and C. Torricelli, A multiperiod binomial model for pricing options in an uncertain world, Proceedings Second Int. Symposium Imprecise Probabilities and Their Applications, Ithaca, NY, 2001, 255-264.  H. T. Nguyen and E. A. Walker, A first course in fuzzy logic, Second Edition, CRC Press, Boca Raton, FL., 2000.  H. Reynaerts and M. Vanmaele, A sensitivity analysis for the pricing of european call options in a binary tree model, Proceedings Fourth Int. Symposium Imprecise Probabilities and Their Applications, Univ. Lugano, Switzerland, 2003, 467-481.  H. A. Taha, Operations research, Fifth Edition, Macmillan, N.Y., 1992.  R. G. Tompkins, Options analysis, Revised Edition, Irwin Professional Publishing, Chicago, USA, 1994.  M. A. Wong, Trading and investing in bond options, John Wiley and Sons, NY, NY, 1991.  H. -C. Wu, Pricing European options based on the fuzzy pattern of black-scholes formula, Computers and Operations Research, 31(2004),1069-1081.  www.solver.com
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2007.368 Research Paper OPTIMIZATION OF LINEAR OBJECTIVE FUNCTION SUBJECT TO FUZZY RELATION INEQUALITIES CONSTRAINTS WITH MAX-AVERAGE COMPOSITION OPTIMIZATION OF LINEAR OBJECTIVE FUNCTION SUBJECT TO FUZZY RELATION INEQUALITIES CONSTRAINTS WITH MAX-AVERAGE COMPOSITION SHIVANIAN ELYAS FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF TECHNOLOGY, TEHRAN 15914, IRAN KHORRAM ESMAILE FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF TECHNOLOGY, TEHRAN 15914, IRAN GHODOUSIAN AMIN FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF TECHNOLOGY, TEHRAN 15914, IRAN 09 10 2007 4 2 15 29 09 09 2006 09 04 2007 Copyright © 2007, University of Sistan and Baluchestan. 2007 http://ijfs.usb.ac.ir/article_368.html

In this paper, the finitely many constraints of a fuzzy relationinequalities problem are studied and the linear objective function on the regiondefined by a fuzzy max-average operator is optimized. A new simplificationtechnique which accelerates the resolution of the problem by removing thecomponents having no effect on the solution process is given together with analgorithm and a numerical example to illustrate the steps of the problemresolution process.

Linear objective function optimization Fuzzy r e lation equations Fuzzy relation inequalities
 K. -P. Adlassnig, Fuzzy set theory in medical diagnosis, IEEE Trans. Systems Man Cybernet., 16 (1986), 260-265.  M. M. Brouke and D. G. Fisher, Solution algorithms for fuzzy relation equations with max-product composition, Fuzzy Sets and Systems, 94 (1998), 61-69.  E. Czogala and W. Pedrycz, Control problems in fuzzy systems, Fuzzy Sets and Systems, 7 (1982), 257-273.  E. Czogala and W. Predrycz, On identification in fuzzy systems and its applications in control problem, Fuzzy Sets and Systems, 6, 73-83.  E. Czogala, J. Drewniak and W. Pedrycz, Fuzzy relation equations on a finite set, Fuzzy Sets and Systems, 7 (1982), 89-101.  A. Di Nola, Relational equations in totally ordered lattices and their complete resolution, J. Math. Appl., 107 (1985), 148-155.  A. Di Nola, S. Sessa, W. Pedrycz and E. Sanchez, Fuzzy relational equations and their applications in knowledge engineering, Dordrecht: Kluwer Academic Press,1989.  S. -C. Fang and G. Li, Solving fuzzy relations equations with a linear objective function, Fuzzy Sets and Systems, 103 (1999), 107-13.  S. -C. Fang and S. Puthenpura, Linear optimization and extensions: theory and algorithm, Prentice-Hall, Englewood Cliffs, NJ, 1993.  S. Z. Guo, P. Z. Wang, A. Di Nola and S. Sessa, Further contributions to the study of finite fuzzyrelation equations, Fuzzy Sets and Systems, 26 (1988), 93-104.  F. -F. Guo and Z. -Q. Xia, An algorithm for solving optimization Problems with one linear objective function and finitely many constraints of fuzzy relation inequalities, Fuzzy Optimization and Decision Making, 5 (2006), 33-47.  M. M. Gupta and J. Qi, Design of fuzzy logic controllers based on generalized t-operators, Fuzzy Sets and Systems, 40 (1991), 473-486.  M. Guu and Y. K. Wu, Minimizing a linear objective function with fuzzy relation equation constraints, Fuzzy Optimization and Decision Making, 12 (2002), 1568-4539.  S. S. Z. Han, A. H. Song, and T. Sekiguchi, Fuzzy inequality relation system identification via sign matrix method, Proceeding of 1995 IEEE International Conference, 3 (1995), 1375-1382.  M. Higashi and G. J. Klir, Resolution of finite fuzzy relation equations, Fuzzy Sets and Systems, 13 (1984), 65-82.  C. F. Hu, Generalized Variational inequalities with fuzzy relation, Journal of Computationaland Applied Mathematics, 146 (1998), 198-203.  E. Khorram and A.Ghodousian, Linear objective function optimization with fuzzy relation constraints regarding max-av composition, Applied Mathematics and Computation, 173 (2006), 827-886.  G. Li and S. -C. Fang, Resolution of finite fuzzy resolution equations, Report No. 322, North Carolina State University, Raleigh, NC, May 1996.  J. Loetamonphong and S. -C. Fang, Optimization of fuzzy relation equations with maxproduct composition, Fuzzy Sets and Systems, 118 (2001), 509-517.  J. Loetamonphong, S. -C. Fang and R.E. Young, Multi-objective optimization problems with fuzzy relation equation constraints, Fuzzy Sets and Systems, 127 (2002), 141-164.  J. Lu and S. -C. Fang, Solving nonlinear optimization problems with fuzzy relation equation constraints, Fuzzy Sets and Systems, 119 (2001), 1-20.  W. Pedrycz, On Generalized fuzzy relational equations and their applications, Journal of Mathematical Analysis and Applications, 107 (1985), 520-536.  W. Pedrycz, Proceeding in relational structures: fuzzy relational equations, Fuzzy Sets and Systems, 40 (1991), 77-106.  M. Prevot, Algorithm for the solution of fuzzy relations, Fuzzy Sets and Systems, 5 (1985), 319-322.  E. Sanchez, Resolution of composite fuzzy relation equations, Inform. Control, 30 (1976), 38-48.  W. B. Vasantha Kandasamy and F. Smarandache, Fuzzy relational maps and neutrosophic relational maps, Hexis Church Rock 2004 (chapter two).  P. Z. Wang, How many lower solutions of finite fuzzy relation equations, Fuzzy Mathematics (Chinese), 4 (1984), 67-73.  P. Z. Wang, Lattecized linear programming and fuzzy relaion inequalies, Journal of Mathematical Analysis and Applications, 159 (1991), 72-87.  W. L. Winston, Introduction to mathematical programming: application and algorithms, Duxbury Press, Belmont, CA, 1995.  L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.  H. T. Zhang, H. M. Dong and R. H. Ren, Programming problem with fuzzy relation inequality constraints, Journal of Liaoning Noramal University, 3 (2003), 231-233.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2007.369 Research Paper A NOTE ON THE ZIMMERMANN METHOD FOR SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS A NOTE ON THE ZIMMERMANN METHOD FOR SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS SAFI MOHAMMADREZA DEPARTMENT OF MATHEMATICES, UNIVERSITY OF SHAHID-BAHONAR KERMAN, KERMAN, IRAN MALEKI HAMIDREZA DEPARTMENT OF BASIC SCIENCES, SHIRAZ UNIVERSITY OF TECHNOLOGY, SHIRAZ, IRAN ZAEIMAZAD EFFAT DEPARTMENT OF MATHEMATICES, UNIVERSITY OF SHAHID-BAHONAR KERMAN, KERMAN, IRAN 09 10 2007 4 2 31 45 09 03 2006 09 01 2007 Copyright © 2007, University of Sistan and Baluchestan. 2007 http://ijfs.usb.ac.ir/article_369.html

There are several methods for solving fuzzy linear programming (FLP)problems. When the constraints and/or the objective function are fuzzy, the methodsproposed by Zimmermann, Verdegay, Chanas and Werners are used more often thanthe others. In the Zimmerman method (ZM) the main objective function cx is addedto the constraints as a fuzzy goal and the corresponding linear programming (LP)problem with a new objective (λ ) is solved. When this new LP has alternative optimalsolutions (AOS), ZM may not always present the "best" solution. Two cases may occur:cx may have different bounded values for the AOS or be unbounded. Since all of theAOS have the same λ , they have the same values for the new LP. Therefore, unlesswe check the value of cx for all AOS, it may be that we do not present the bestsolution to the decision maker (DM); it is possible that cx is unbounded but ZMpresents a bounded solution as the optimal solution. In this note, we propose analgorithm for eliminating these difficulties.

Linear programming Fuzzy set theory Fuzzy linear programming and fuzzy efficiency
 R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Management Science, 17 (1970), 141-164.  J. M. Cadenas and J. L. Verdegay, A Primer on fuzzy optimization models and methods, Iranian Journal of Fuzzy Systems (to appear).  J. M. Cadenas and J. L. Verdegay, Using ranking functions in multi-objective fuzzy linear programming, Fuzzy sets and systems, 111 (2000), 47-53.  L. Campus and J. L. Verdegay, Linear programming problem and ranking of fuzzy numbers, Fuzzy Sets and Systems, 32 (1989), 1-11.  S. Chanas, The use of parametric programming in fuzzy linear programming, Fuzzy Sets and Systems, 11 (1983), 243-251.  M. Delgado, J. L Verdegay and M. A. Vila, A general model for fuzzy linear programming, Fuzzy Sets and Systems, 29 (1989), 21-29.  D. Dubois, H. Fargier and H. Prade, Refinements of the maximum approach to decision making in a fuzzy environment, Fuzzy Sets and Systems, 81 (1996), 103-122.  S. M. Guu and Y. K. Wu, Two phase approach for solving the fuzzy linear programming problems, Fuzzy Sets and Systems, 107 (1999), 191-195.  Y. J. Lai and C. L. Hwang, Fuzzy mathematical programming methods and applications, Springer-Verlag, Berlin, 1992.  Y. J. Lai and C. L. Hwang, Interactive fuzzy linear programming, Fuzzy Sets and Systems, 45 (1992), 169-183.  X. Li, B. Zhang and H. Li, Computing efficient solution to fuzzy multiple objective linear programming problems, Fuzzy Sets and Systems, 157 (2006), 1328-1332.  H. R. Maleki, Ranking functions and their applications to fuzzy linear programming, Far East Journal of Mathematical Sciences, 4(3) (2003), 283-301.  H. R. Maleki, M. Tata and M. Mashinchi, Linear programming with fuzzy variables, Fuzzy Set and Systems, 109 (2000), 21-33.  H. R. Maleki, M. Tata and M. Mashinchi, Fuzzy number linear programming, in: C. Lucas (Ed), Proc. Internat. Conf. on Intelligent and Cognitive System FSS ’96, sponsored by IEE ISRF, Tehran, Iran, 1996, 145-148.  WinQSB 1, Yih-Long Chang and Kiran Desai, John wiley & Sons, Inc.  J. Ramik and J. Raminak, Inequality relation between fuzzy numbers and its use in fuzzy optimization, Fuzzy Sets and Systems, 16 (1985), 123-138.  H. Tanaka, T. Okuda and K. Asai, On fuzzy mathematical programming, Journal of Cybernetics, 3(4) (1974), 37-46.  R. N. Tiwari, S. Deharmar and J. R. Rao, Fuzzy goal programming – an additive model, Fuzzy Sets and Systems, 24 (1987), 27-34.  J. L. Verdegay, Fuzzy mathematical programming, in: M. M. Gupta and E. Sanchez, Eds., Fuzzy Information and Decision Processes, North-Holland, Amsterdam, 1982, 231-  B. Werners, An interactive fuzzy programming system, Fuzzy Sets and Systems, 23 (1987),  E. Zaeimazad, Fuzzy linear programming: a geometric approach, Msc thesis, University of Shahid–Bahonar, Kerman, Iran, 2005.  H. J. Zimmermann, Description and optimization of fuzzy systems, International Journal of General Systems, 2 (1976), 209- 215.  H. J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1 (1978), 45-55.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2007.370 Research Paper LK-INTERIOR SYSTEMS AS SYSTEMS OF “ALMOST OPEN” L-SETS LK-INTERIOR SYSTEMS AS SYSTEMS OF “ALMOST OPEN” L-SETS Funiokova Tatana Department of Mathematics, Technical University of Ostrava, 17. listopadu, CZ-708 30,Ostrava , Czech Republic 09 10 2007 4 2 47 55 09 06 2005 09 11 2006 Copyright © 2007, University of Sistan and Baluchestan. 2007 http://ijfs.usb.ac.ir/article_370.html

We study interior operators and interior structures in a fuzzy setting.We investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.

Interior operator Interior system Fuzzy set Fuzzy Logic
 W. Bandler and L. Kohout, Special properties, closures and interiors of crisp and fuzzy relations, Fuzzy Sets and Systems, 26(3)(1988), 317–331.  R. Bˇelohl´avek and T. Funiokov´a, Fuzzy interior operators, Int. J. General Systems, 33(4)(2004), 315–330.  R. Bˇelohl´avek, Fuzzy closure operators, J. Math. Anal. Appl., 262(2001), 473-489.  R. Bˇelohl´avek, Fuzzy closure operators II, Soft Computing, 7(1)(2002), 53-64.  R. Bˇelohl´avek, Fuzzy relational systems: foundations and principles, Kluwer Academic/ Plenum Press, New York, 2002.  G. Gerla, Fuzzy logic. mathematical tools for approximate reasoning, Kluwer, Dordrecht,  J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl., 18(1967), 145–174.  J. A. Goguen, The logic of inexact concepts, Synthese 18(1968-9), 325–373.  S. Gottwald, A Treatise on many-valued logics, Research Studies Press, Baldock, Hertfordshire, England, 2001.  P. H´ajek, Metamathematics of fuzzy logic, Kluwer, Dordrecht, 1998.  U. H¨ohle, Commutative, residuated l-monoids., In: U, H¨ohle and E. P. Klement (Eds.), Non-classical logics and their applications to fuzzy subsets. Kluwer, Dordrecht, 1995.  U. H¨ohle, On the fundamentals of fuzzy set theory, J. Math. Anal. Appl., 201(1996), 786–826.  A. S. Mashour and M. H. Ghanim, Fuzzy closure spaces, J. Math. Anal. Appl., 106(1985), 154–170.  R. O. Rodr´ıguez, F. Esteva, P. Garcia and L. Godo, On implicative closure operators in approximate reasoning, Int. J. Approximate Reasoning, 33(2003), 159–184.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2007.375 Research Paper CHARACTERIZATION OF REGULAR \$Gamma\$−SEMIGROUPS THROUGH FUZZY IDEALS CHARACTERIZATION OF REGULAR \$Gamma\$−SEMIGROUPS THROUGH FUZZY IDEALS Dheena P. Department of Mathematics, Annamalai University, Annamalainagar- 608002, India Coumaressane S. Department of Mathematics,Annamalai University, Annamalainagar- 608002, India 09 10 2007 4 2 57 68 09 02 2006 09 12 2006 Copyright © 2007, University of Sistan and Baluchestan. 2007 http://ijfs.usb.ac.ir/article_375.html

Notions of strongly regular, regular and left(right) regular \$Gamma\$−semigroupsare introduced. Equivalent conditions are obtained through fuzzy notion for a\$Gamma\$−semigroup to be either strongly regular or regular or left regular.

\$\Gamma\$−semigroup Bi-ideal Quasi-ideal Regular Strongly regular Left(right) regular Fuzzy (left right)ideal Fuzzy quasi-ideal Fuzzy bi-ideal
 P. S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl., 84 (1981), 264-269.  Y. I. Kwon and S. K. Lee, The weakly semi-prime ideals of po−\$Gamma\$−semigroups, Kangweon- Kyungki Math. J., 5 (1997), 135-139.  Y. I. Kwon and S. K. Lee, On the left regular po−\$Gamma\$−semigroups, Kangweon-Kyungki Math. J., 6 (1998), 149-154.  W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982),  A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.  N. K. Saha, On \$Gamma\$−semigroup II, Bull. Cal. Math. Soc., 79 (1987), 331-335.  M. K. Sen, On \$Gamma\$−semigroups, Proc. of the Int. Conf. on Algebra and it’s Appl., Decker Publication, New York 301 (1981).  M. K. Sen and N. K. Saha, On \$Gamma\$−semigroup I, Bull. Cal. Math. Soc., 78 (1986), 180-186.  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.2007.378 Research Paper RESIDUAL OF IDEALS OF AN L-RING RESIDUAL OF IDEALS OF AN L-RING PRAJAPATI ANAND SWAROOP ATMA RAM SANATAN DHARMA COLLEGE, UNIVERSITY OF DELHI, DHAULA KUAN, NEW DELHI – 110021, INDIA 09 10 2007 4 2 69 82 09 09 2005 09 02 2006 Copyright © 2007, University of Sistan and Baluchestan. 2007 http://ijfs.usb.ac.ir/article_378.html

The concept of right (left) quotient (or residual) of an ideal η by anideal ν of an L-subring μ of a ring R is introduced. The right (left) quotients areshown to be ideals of μ . It is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an L-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . Most of the results pertaining to the notion of quotients(or residual) of an ideal of ordinary rings are extended to L-ideal theory ofL-subrings.

L-subring L-ideal Right quotient Left quotient
 N. Ajmal and A. S. Prajapati, Prime radical and primary decomposition of ideals in an L-subring, Communicated.  N. Ajmal and S. Kumar, Lattice of subalgebras in the category of fuzzy groups, The Journal of Fuzzy Mathematics , 10 (2) (2002), 359-369.  G. Birkhoff, Lattice theory, American Mathematical Soceity, Providence, Rhode Island  D. M. Burton, A first course in rings and ideals, Addison-Wesley, Reading, Massachusetts, 1970.  D. S. Malik and J. N. Mordeson, Fuzzy prime ideals of rings, FSS, 37 (1990), 93-98.  D. S. Malik and J. N. Mordeson, Fuzzy maximal, radical, and primary ideals of a ring, Inform. Sci., 53 (1991), 237-250.  D. S. Malik and J. N. Mordeson, Fuzzy primary representations of fuzzy ideals, Inform. Sci., 55 (1991), 151-165.  D. S. Malik and J. N. Mordeson, Radicals of fuzzy ideals, Inform. Sci., 65 (1992), 239-  D. S. Malik, J. N. Mordeson and P. S. Nair, Fuzzy normal subgroups in fuzzy subgroups, J. Korean Math. Soc., 29 (1992), 1-8.  D. S. Malik, and J. N. Mordeson, R-primary representation of L-ideals, Inform, Sci., 88 (1996), 227-246.  J. N. Mordeson, L-subspaces and L-subfield, Centre for Research in Fuzzy Mathematics and Computer Science, Creighton University, USA. 1996.  J. N. Mordeson and D. S. Malik, Fuzzy commutative algebra, World Scientific Publishing Co. USA. 1998.  A. S. Prajapati and N. Ajmal, Maximal ideals of L-subring, The Journal of Fuzzy Mathematics (preprint).  A. S. Prajapati and N. Ajmal, Maximal ideals of L-subring II, The Journal of Fuzzy Mathematics (preprint).  A. S. Prajapati and N. Ajmal, Prime ideal, Semiprime ideal and Primary ideal of an L-subring, Communicated.  G. Szasz, Introduction to lattice theory, Academic Press, New York and London, 1963.  Y. Yandong, J. N. Mordeson and S.-C. Cheng, Elements of L-algebra, Lecture notes in Fuzzy Mathematics and Computer Science 1, Center for Research in Fuzzy Mathematics and Computer Science, Creighton University, USA. 1994.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2007.379 Research Paper SOME PROPERTIES OF NEAR SR-COMPACTNESS SOME PROPERTIES OF NEAR SR-COMPACTNESS Bai Shi-Zhong Department of Mathematics, Wuyi University, Guangdong 529020, P.R.China 09 10 2007 4 2 83 87 09 06 2005 09 06 2006 Copyright © 2007, University of Sistan and Baluchestan. 2007 http://ijfs.usb.ac.ir/article_379.html

In this paper, we study some properties of the near SR-compactnessin L-topological spaces, where L is a fuzzy lattice. The near SR-compactness isa kind of compactness between Lowen’s fuzzy compactness and SR-compactness,and it preserves desirable properties of compactness in general topologicalspaces.

L-topology SS-remote neighborhood family -net Compactness Near SR-compact L-subset
 S. Z. Bai, Fuzzy strongly semiopen sets and fuzzy strong semicontinuity, Fuzzy Sets and Systems, 52 (1992), 345-351.  S. Z. Bai, The SR-compactness in L-fuzzy topological spaces, Fuzzy Sets and Systems, 87 (1997), 219-225.  C. L. Chang, Fuzzy topological spaces, J.Math.Anal.Appl., 24 (1968), 182-190.  S. G. Li, S. Z. Bai and N. Liu, The near SR-compactness axiom in L-topological spaces, Fuzzy Sets and Systems, 174 (2004), 307-316.  Y. M. Liu and M. K. Luo, Fuzzy topology, World Scientific Publishing, Singapore, 1998.  R. Lowen, A comparison of different compactness notions in fuzzy topological spaces, J. Math. Anal. Appl., 64 (1978), 446-454.  G. J. Wang, A new fuzzy compactness defined by fuzzy nets, J. Math. Anal. Appl., 94 (1983),  G. J. Wang, Theory of L-fuzzy topological spaces, Shaanxi Normal University, Xian, 1988.  D. S. Zhao, The N-compactness in L-fuzzy topological spaces, J. Math. Anal. Appl., 128 (1987), 64-79.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2007.381 Research Paper COUNTABLY NEAR PS-COMPACTNESS IN L-TOPOLOGICAL SPACES COUNTABLY NEAR PS-COMPACTNESS IN L-TOPOLOGICAL SPACES Bai Shi-Zhong Department of Mathematics, Wuyi University, Guangdong 529020, P.R.China 09 10 2007 4 2 89 94 09 12 2005 09 09 2006 Copyright © 2007, University of Sistan and Baluchestan. 2007 http://ijfs.usb.ac.ir/article_381.html

In this paper, the concept of countably near PS-compactness inL-topological spaces is introduced, where L is a completely distributive latticewith an order-reversing involution. Countably near PS-compactness is definedfor arbitrary L-subsets and some of its fundamental properties are studied.

L-topology Pre-semiclosed set Remote-neighborhood Countably near PS-compact set
 S. Z. Bai, The SR-compactness in L-fuzzy topological spaces, Fuzzy Sets and Systems, 87 (1997), 219-225.  S. Z. Bai, L-fuzzy PS-compactness, IJUFKS, 10 (2002), 201-209.  S. Z. Bai, Near PS-compact L-subsets, Information Sciences, 115 (2003), 111-118.  S. Z. Bai, Pre-semiclosed sets and PS-convergence in L-fuzzy topological spaces, J. Fuzzy Math. 9 (2001), 497-509.  C. L. Chang, Fuzzy topological spaces, J.Math.Anal.Appl. 24 (1968), 182-190.  B. Hutton, Products of fuzzy topological spaces, Topology Appl. 11 (1980), 59-67.  Y. M. Liu and M. K. Luo, Induced spaces and fuzzy Stone-Cech compactifications, Scientia Sinica (A), 30 (1987), 1034-1044.  Y. M. Liu and M. K. Luo, Fuzzy topology, World Scientific Publishing, Singapore, 1998.  R. Lowen, Fuzzy topological spaces and fuzzy compactness, J.Math.Anal.Appl. 56 (1976),  F. G. Shi, Countable compactness and Lindeloff property of L-fuzzy sets, Iranian journal of fuzzy systems, 1 (2004), 79-88.  B. M. Pu and Y. M. Liu, Fuzzy topological,I.Neighborhood structure of a fuzzy point and Moore-Smith convergence0, J. Math. Anal. Appl. 76 (1980), 571-599.  G. J. Wang, A new fuzzy compactness defined by fuzzy nets, J.Math.Anal.Appl. 94 (1983),  G. J. Wang, Theory of L-fuzzy topological spaces, Shaanxi Normal University, Xian, 1988.  D. S. Zhao, The N-compactness in L-fuzzy topological spaces, J. Math. Anal. Appl. 128 (1987), 64-79.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2007.2909 unavailable Persian-translation Vol.4 No.2, October 2007 30 10 2007 4 2 97 104 03 01 2017 03 01 2017 Copyright © 2007, University of Sistan and Baluchestan. 2007 http://ijfs.usb.ac.ir/article_2909.html

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