2007
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PRICING STOCK OPTIONS USING FUZZY SETS
PRICING STOCK OPTIONS USING FUZZY SETS
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2
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.
1
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.
1
14
James J.
Buckley
James J.
Buckley
Department of Mathematics, University of Alabama at Birmingham,
Birmingham, Al 35209, USA
Department of Mathematics, University of
United States
buckley@math.uab.edu
Esfandiar
Eslami
Esfandiar
Eslami
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman and Institute for Studies in Theoretical Physics and Mathematics(IPM),
Tehran, Iran
Department of Mathematics, Shahid Bahonar
United States
eeslami@mail.uk.ac.ir
Pricing Options
Binomial methods
Fuzzy numbers
[[1] 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.##[2] J. J. Buckley and E. Eslami, Introduction to fuzzy logic sand fuzzy sets, Springer, Heidelberg,##Germany, 2002.##[3] J. J. Buckley and Y. Qu, On using cuts to evaluate fuzzy equations, Fuzzy Sets and Systems,##38(1990), 309312.##[4] J. J. Buckley, T. Feuring and E. Eslami, Applications of fuzzy sets and fuzzy logic to economics##and engineering, Springer, Heidelberg, Germany, 2002.##[5] J. C. Cox and M. Rubinstein, Options markets, PrenticeHall, Englewood Cliffs, NJ, 1985.##[6] D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications, Academic Press,##N.Y., 1980.##[7] M. Durbin, All About derivatives, McGrawHill, NY, NY, 2006.##[8] Frontline Systems (www.frontsys.com).##[9] G. J. Klir and B. Yuan, Fuzzy sets and fuzzy logic, Prentice Hall, Upper Saddle River, N.J.,##[10] S. Muzzioli and C. Torricelli, A model for pricing an option with a fuzzy payoff, Fuzzy##Economic Review, 6(2001), 4062.##[11] 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, 255264.##[12] H. T. Nguyen and E. A. Walker, A first course in fuzzy logic, Second Edition, CRC Press,##Boca Raton, FL., 2000. ##[13] 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, 467481.##[14] H. A. Taha, Operations research, Fifth Edition, Macmillan, N.Y., 1992.##[15] R. G. Tompkins, Options analysis, Revised Edition, Irwin Professional Publishing, Chicago,##USA, 1994.##[16] M. A. Wong, Trading and investing in bond options, John Wiley and Sons, NY, NY, 1991.##[17] H. C. Wu, Pricing European options based on the fuzzy pattern of blackscholes formula,##Computers and Operations Research, 31(2004),10691081.##[18] www.solver.com##]
OPTIMIZATION OF LINEAR OBJECTIVE FUNCTION SUBJECT TO FUZZY RELATION INEQUALITIES CONSTRAINTS WITH MAXAVERAGE COMPOSITION
OPTIMIZATION OF LINEAR OBJECTIVE FUNCTION SUBJECT TO FUZZY RELATION INEQUALITIES CONSTRAINTS WITH MAXAVERAGE COMPOSITION
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2
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 maxaverage 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.
1
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 maxaverage 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.
15
29
ELYAS
SHIVANIAN
ELYAS
SHIVANIAN
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF
TECHNOLOGY, TEHRAN 15914, IRAN
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE,
Iran
eshivanian@gmail.com
ESMAILE
KHORRAM
ESMAILE
KHORRAM
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF
TECHNOLOGY, TEHRAN 15914, IRAN
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE,
Iran
eskor@aut.ac.ir
AMIN
GHODOUSIAN
AMIN
GHODOUSIAN
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF
TECHNOLOGY, TEHRAN 15914, IRAN
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE,
Iran
Linear objective function optimization
Fuzzy r e lation equations
Fuzzy relation inequalities
[[1] K. P. Adlassnig, Fuzzy set theory in medical diagnosis, IEEE Trans. Systems Man##Cybernet., 16 (1986), 260265.##[2] M. M. Brouke and D. G. Fisher, Solution algorithms for fuzzy relation equations with##maxproduct composition, Fuzzy Sets and Systems, 94 (1998), 6169.##[3] E. Czogala and W. Pedrycz, Control problems in fuzzy systems, Fuzzy Sets and Systems,##7 (1982), 257273.##[4] E. Czogala and W. Predrycz, On identification in fuzzy systems and its applications in##control problem, Fuzzy Sets and Systems, 6, 7383.##[5] E. Czogala, J. Drewniak and W. Pedrycz, Fuzzy relation equations on a finite set, Fuzzy##Sets and Systems, 7 (1982), 89101.##[6] A. Di Nola, Relational equations in totally ordered lattices and their complete resolution,##J. Math. Appl., 107 (1985), 148155.##[7] A. Di Nola, S. Sessa, W. Pedrycz and E. Sanchez, Fuzzy relational equations and their##applications in knowledge engineering, Dordrecht: Kluwer Academic Press,1989.##[8] S. C. Fang and G. Li, Solving fuzzy relations equations with a linear objective function,##Fuzzy Sets and Systems, 103 (1999), 10713.##[9] S. C. Fang and S. Puthenpura, Linear optimization and extensions: theory and algorithm,##PrenticeHall, Englewood Cliffs, NJ, 1993.##[10] 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), 93104.##[11] 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), 3347.##[12] M. M. Gupta and J. Qi, Design of fuzzy logic controllers based on generalized##toperators, Fuzzy Sets and Systems, 40 (1991), 473486.##[13] M. Guu and Y. K. Wu, Minimizing a linear objective function with fuzzy relation equation##constraints, Fuzzy Optimization and Decision Making, 12 (2002), 15684539.##[14] 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), 13751382. ##[15] M. Higashi and G. J. Klir, Resolution of finite fuzzy relation equations, Fuzzy Sets and##Systems, 13 (1984), 6582.##[16] C. F. Hu, Generalized Variational inequalities with fuzzy relation, Journal of##Computationaland Applied Mathematics, 146 (1998), 198203.##[17] E. Khorram and A.Ghodousian, Linear objective function optimization with fuzzy##relation constraints regarding maxav composition, Applied Mathematics and##Computation, 173 (2006), 827886.##[18] G. Li and S. C. Fang, Resolution of finite fuzzy resolution equations, Report No. 322,##North Carolina State University, Raleigh, NC, May 1996.##[19] J. Loetamonphong and S. C. Fang, Optimization of fuzzy relation equations with maxproduct##composition, Fuzzy Sets and Systems, 118 (2001), 509517.##[20] J. Loetamonphong, S. C. Fang and R.E. Young, Multiobjective optimization problems##with fuzzy relation equation constraints, Fuzzy Sets and Systems, 127 (2002), 141164.##[21] J. Lu and S. C. Fang, Solving nonlinear optimization problems with fuzzy relation##equation constraints, Fuzzy Sets and Systems, 119 (2001), 120.##[22] W. Pedrycz, On Generalized fuzzy relational equations and their applications, Journal of##Mathematical Analysis and Applications, 107 (1985), 520536.##[23] W. Pedrycz, Proceeding in relational structures: fuzzy relational equations, Fuzzy Sets##and Systems, 40 (1991), 77106.##[24] M. Prevot, Algorithm for the solution of fuzzy relations, Fuzzy Sets and Systems,##5 (1985), 319322.##[25] E. Sanchez, Resolution of composite fuzzy relation equations, Inform. Control,##30 (1976), 3848.##[26] W. B. Vasantha Kandasamy and F. Smarandache, Fuzzy relational maps and##neutrosophic relational maps, Hexis Church Rock 2004 (chapter two).##[27] P. Z. Wang, How many lower solutions of finite fuzzy relation equations, Fuzzy##Mathematics (Chinese), 4 (1984), 6773.##[28] P. Z. Wang, Lattecized linear programming and fuzzy relaion inequalies, Journal of##Mathematical Analysis and Applications, 159 (1991), 7287.##[29] W. L. Winston, Introduction to mathematical programming: application and algorithms,##Duxbury Press, Belmont, CA, 1995.##[30] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338353.##[31] H. T. Zhang, H. M. Dong and R. H. Ren, Programming problem with fuzzy relation##inequality constraints, Journal of Liaoning Noramal University, 3 (2003), 231233.##]
A NOTE ON THE ZIMMERMANN METHOD FOR SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS
A NOTE ON THE ZIMMERMANN METHOD FOR SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS
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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.
1
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.
31
45
MOHAMMADREZA
SAFI
MOHAMMADREZA
SAFI
DEPARTMENT OF MATHEMATICES, UNIVERSITY OF SHAHIDBAHONAR KERMAN,
KERMAN, IRAN
DEPARTMENT OF MATHEMATICES, UNIVERSITY OF
Iran
safi_mohammadreza@yahoo.com
HAMIDREZA
MALEKI
HAMIDREZA
MALEKI
DEPARTMENT OF BASIC SCIENCES, SHIRAZ UNIVERSITY OF TECHNOLOGY, SHIRAZ,
IRAN
DEPARTMENT OF BASIC SCIENCES, SHIRAZ UNIVERSITY
Iran
maleki@sutech.ac.ir
EFFAT
ZAEIMAZAD
EFFAT
ZAEIMAZAD
DEPARTMENT OF MATHEMATICES, UNIVERSITY OF SHAHIDBAHONAR KERMAN,
KERMAN, IRAN
DEPARTMENT OF MATHEMATICES, UNIVERSITY OF
Iran
effat_zaeimazad@yahoo.com
Linear programming
Fuzzy set theory
Fuzzy linear programming and fuzzy efficiency
[[1] R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Management##Science, 17 (1970), 141164.##[2] J. M. Cadenas and J. L. Verdegay, A Primer on fuzzy optimization models and methods,##Iranian Journal of Fuzzy Systems (to appear).##[3] J. M. Cadenas and J. L. Verdegay, Using ranking functions in multiobjective fuzzy linear##programming, Fuzzy sets and systems, 111 (2000), 4753.##[4] L. Campus and J. L. Verdegay, Linear programming problem and ranking of fuzzy numbers,##Fuzzy Sets and Systems, 32 (1989), 111.##[5] S. Chanas, The use of parametric programming in fuzzy linear programming, Fuzzy Sets##and Systems, 11 (1983), 243251.##[6] M. Delgado, J. L Verdegay and M. A. Vila, A general model for fuzzy linear programming,##Fuzzy Sets and Systems, 29 (1989), 2129.##[7] 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), 103122.##[8] S. M. Guu and Y. K. Wu, Two phase approach for solving the fuzzy linear programming##problems, Fuzzy Sets and Systems, 107 (1999), 191195.##[9] Y. J. Lai and C. L. Hwang, Fuzzy mathematical programming methods and applications,##SpringerVerlag, Berlin, 1992.##[10] Y. J. Lai and C. L. Hwang, Interactive fuzzy linear programming, Fuzzy Sets and Systems,##45 (1992), 169183.##[11] X. Li, B. Zhang and H. Li, Computing efficient solution to fuzzy multiple objective linear##programming problems, Fuzzy Sets and Systems, 157 (2006), 13281332. ##[12] H. R. Maleki, Ranking functions and their applications to fuzzy linear programming, Far##East Journal of Mathematical Sciences, 4(3) (2003), 283301.##[13] H. R. Maleki, M. Tata and M. Mashinchi, Linear programming with fuzzy variables, Fuzzy##Set and Systems, 109 (2000), 2133.##[14] 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, 145148.##[15] WinQSB 1, YihLong Chang and Kiran Desai, John wiley & Sons, Inc.##[16] J. Ramik and J. Raminak, Inequality relation between fuzzy numbers and its use in fuzzy##optimization, Fuzzy Sets and Systems, 16 (1985), 123138.##[17] H. Tanaka, T. Okuda and K. Asai, On fuzzy mathematical programming, Journal of##Cybernetics, 3(4) (1974), 3746.##[18] R. N. Tiwari, S. Deharmar and J. R. Rao, Fuzzy goal programming – an additive model,##Fuzzy Sets and Systems, 24 (1987), 2734.##[19] J. L. Verdegay, Fuzzy mathematical programming, in: M. M. Gupta and E. Sanchez, Eds.,##Fuzzy Information and Decision Processes, NorthHolland, Amsterdam, 1982, 231##[20] B. Werners, An interactive fuzzy programming system, Fuzzy Sets and Systems, 23 (1987),##[21] E. Zaeimazad, Fuzzy linear programming: a geometric approach, Msc thesis, University of##Shahid–Bahonar, Kerman, Iran, 2005.##[22] H. J. Zimmermann, Description and optimization of fuzzy systems, International Journal of##General Systems, 2 (1976), 209 215.##[23] H. J. Zimmermann, Fuzzy programming and linear programming with several objective##functions, Fuzzy Sets and Systems, 1 (1978), 4555.##]
LKINTERIOR SYSTEMS AS SYSTEMS OF “ALMOST OPEN” LSETS
LKINTERIOR SYSTEMS AS SYSTEMS OF “ALMOST OPEN” LSETS
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2
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.
1
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.
47
55
Tatana
Funiokova
Tatana
Funiokova
Department of Mathematics, Technical University of Ostrava,
17. listopadu, CZ708 30,Ostrava , Czech Republic
Department of Mathematics, Technical University
Czech Republic
tatana.funiokova@vsb.cz
Interior operator
Interior system
Fuzzy set
Fuzzy logic
[[1] W. Bandler and L. Kohout, Special properties, closures and interiors of crisp and fuzzy##relations, Fuzzy Sets and Systems, 26(3)(1988), 317–331.##[2] R. Bˇelohl´avek and T. Funiokov´a, Fuzzy interior operators, Int. J. General Systems,##33(4)(2004), 315–330.##[3] R. Bˇelohl´avek, Fuzzy closure operators, J. Math. Anal. Appl., 262(2001), 473489.##[4] R. Bˇelohl´avek, Fuzzy closure operators II, Soft Computing, 7(1)(2002), 5364.##[5] R. Bˇelohl´avek, Fuzzy relational systems: foundations and principles, Kluwer Academic/##Plenum Press, New York, 2002.##[6] G. Gerla, Fuzzy logic. mathematical tools for approximate reasoning, Kluwer, Dordrecht,##[7] J. A. Goguen, Lfuzzy sets, J. Math. Anal. Appl., 18(1967), 145–174.##[8] J. A. Goguen, The logic of inexact concepts, Synthese 18(19689), 325–373.##[9] S. Gottwald, A Treatise on manyvalued logics, Research Studies Press, Baldock, Hertfordshire,##England, 2001.##[10] P. H´ajek, Metamathematics of fuzzy logic, Kluwer, Dordrecht, 1998.##[11] U. H¨ohle, Commutative, residuated lmonoids., In: U, H¨ohle and E. P. Klement (Eds.),##Nonclassical logics and their applications to fuzzy subsets. Kluwer, Dordrecht, 1995.##[12] U. H¨ohle, On the fundamentals of fuzzy set theory, J. Math. Anal. Appl., 201(1996), 786–826.##[13] A. S. Mashour and M. H. Ghanim, Fuzzy closure spaces, J. Math. Anal. Appl., 106(1985),##154–170. ##[14] 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.##]
CHARACTERIZATION OF REGULAR $Gamma$−SEMIGROUPS THROUGH FUZZY IDEALS
CHARACTERIZATION OF REGULAR $Gamma$−SEMIGROUPS THROUGH FUZZY IDEALS
2
2
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.
1
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.
57
68
P.
Dheena
P.
Dheena
Department of Mathematics, Annamalai University, Annamalainagar
608002, India
Department of Mathematics, Annamalai University,
India
dheenap@yahoo.com
S.
Coumaressane
S.
Coumaressane
Department of Mathematics,Annamalai University, Annamalainagar
608002, India
Department of Mathematics,Annamalai University,
India
coumaressane_s@yahoo.com
$Gamma$−semigroup
Biideal
Quasiideal
Regular
Strongly regular
Left(right) regular
Fuzzy (left
right)ideal
Fuzzy quasiideal
Fuzzy biideal
[[1] P. S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl., 84 (1981), 264269.##[2] Y. I. Kwon and S. K. Lee, The weakly semiprime ideals of po−$Gamma$−semigroups, Kangweon##Kyungki Math. J., 5 (1997), 135139.##[3] Y. I. Kwon and S. K. Lee, On the left regular po−$Gamma$−semigroups, KangweonKyungki Math.##J., 6 (1998), 149154.##[4] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982),##[5] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512517.##[6] N. K. Saha, On $Gamma$−semigroup II, Bull. Cal. Math. Soc., 79 (1987), 331335.##[7] M. K. Sen, On $Gamma$−semigroups, Proc. of the Int. Conf. on Algebra and it’s Appl., Decker##Publication, New York 301 (1981).##[8] M. K. Sen and N. K. Saha, On $Gamma$−semigroup I, Bull. Cal. Math. Soc., 78 (1986), 180186.##[9] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338353.##]
RESIDUAL OF IDEALS OF AN LRING
RESIDUAL OF IDEALS OF AN LRING
2
2
The concept of right (left) quotient (or residual) of an ideal η by anideal ν of an Lsubring 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 Lsubring 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 Lideal theory ofLsubrings.
1

69
82
ANAND SWAROOP
PRAJAPATI
ANAND SWAROOP
PRAJAPATI
ATMA RAM SANATAN DHARMA COLLEGE, UNIVERSITY OF DELHI,
DHAULA KUAN, NEW DELHI – 110021, INDIA
ATMA RAM SANATAN DHARMA COLLEGE, UNIVERSITY
India
prajapati_anand@yahoo.co.in
Lsubring
Lideal
Right quotient
Left quotient
[[1] N. Ajmal and A. S. Prajapati, Prime radical and primary decomposition of ideals in an##Lsubring, Communicated.##[2] N. Ajmal and S. Kumar, Lattice of subalgebras in the category of fuzzy groups, The##Journal of Fuzzy Mathematics , 10 (2) (2002), 359369.##[3] G. Birkhoff, Lattice theory, American Mathematical Soceity, Providence, Rhode Island##[4] D. M. Burton, A first course in rings and ideals, AddisonWesley, Reading,##Massachusetts, 1970.##[5] D. S. Malik and J. N. Mordeson, Fuzzy prime ideals of rings, FSS, 37 (1990), 9398.##[6] D. S. Malik and J. N. Mordeson, Fuzzy maximal, radical, and primary ideals of a ring,##Inform. Sci., 53 (1991), 237250.##[7] D. S. Malik and J. N. Mordeson, Fuzzy primary representations of fuzzy ideals, Inform.##Sci., 55 (1991), 151165.##[8] D. S. Malik and J. N. Mordeson, Radicals of fuzzy ideals, Inform. Sci., 65 (1992), 239##[9] D. S. Malik, J. N. Mordeson and P. S. Nair, Fuzzy normal subgroups in fuzzy subgroups,##J. Korean Math. Soc., 29 (1992), 18.##[10] D. S. Malik, and J. N. Mordeson, Rprimary representation of Lideals, Inform, Sci., 88##(1996), 227246.##[11] J. N. Mordeson, Lsubspaces and Lsubfield, Centre for Research in Fuzzy Mathematics##and Computer Science, Creighton University, USA. 1996.##[12] J. N. Mordeson and D. S. Malik, Fuzzy commutative algebra, World Scientific Publishing##Co. USA. 1998.##[13] A. S. Prajapati and N. Ajmal, Maximal ideals of Lsubring, The Journal of Fuzzy##Mathematics (preprint).##[14] A. S. Prajapati and N. Ajmal, Maximal ideals of Lsubring II, The Journal of Fuzzy##Mathematics (preprint).##[15] A. S. Prajapati and N. Ajmal, Prime ideal, Semiprime ideal and Primary ideal of an##Lsubring, Communicated.##[16] G. Szasz, Introduction to lattice theory, Academic Press, New York and London, 1963.##[17] Y. Yandong, J. N. Mordeson and S.C. Cheng, Elements of Lalgebra, Lecture notes in##Fuzzy Mathematics and Computer Science 1, Center for Research in Fuzzy Mathematics##and Computer Science, Creighton University, USA. 1994.##]
SOME PROPERTIES OF NEAR SRCOMPACTNESS
SOME PROPERTIES OF NEAR SRCOMPACTNESS
2
2
In this paper, we study some properties of the near SRcompactnessin Ltopological spaces, where L is a fuzzy lattice. The near SRcompactness isa kind of compactness between Lowen’s fuzzy compactness and SRcompactness,and it preserves desirable properties of compactness in general topologicalspaces.
1
In this paper, we study some properties of the near SRcompactnessin Ltopological spaces, where L is a fuzzy lattice. The near SRcompactness isa kind of compactness between Lowen’s fuzzy compactness and SRcompactness,and it preserves desirable properties of compactness in general topologicalspaces.
83
87
ShiZhong
Bai
ShiZhong
Bai
Department of Mathematics, Wuyi University, Guangdong 529020,
P.R.China
Department of Mathematics, Wuyi University,
China
shizhongbai@yahoo.com
Ltopology
SSremote neighborhood family
net
Compactness
Near SRcompact Lsubset
[[1] S. Z. Bai, Fuzzy strongly semiopen sets and fuzzy strong semicontinuity, Fuzzy Sets and##Systems, 52 (1992), 345351.##[2] S. Z. Bai, The SRcompactness in Lfuzzy topological spaces, Fuzzy Sets and Systems, 87##(1997), 219225.##[3] C. L. Chang, Fuzzy topological spaces, J.Math.Anal.Appl., 24 (1968), 182190.##[4] S. G. Li, S. Z. Bai and N. Liu, The near SRcompactness axiom in Ltopological spaces, Fuzzy##Sets and Systems, 174 (2004), 307316.##[5] Y. M. Liu and M. K. Luo, Fuzzy topology, World Scientific Publishing, Singapore, 1998.##[6] R. Lowen, A comparison of different compactness notions in fuzzy topological spaces, J. Math.##Anal. Appl., 64 (1978), 446454.##[7] G. J. Wang, A new fuzzy compactness defined by fuzzy nets, J. Math. Anal. Appl., 94 (1983),##[8] G. J. Wang, Theory of Lfuzzy topological spaces, Shaanxi Normal University, Xian, 1988.##[9] D. S. Zhao, The Ncompactness in Lfuzzy topological spaces, J. Math. Anal. Appl., 128##(1987), 6479.##]
COUNTABLY NEAR PSCOMPACTNESS IN LTOPOLOGICAL SPACES
COUNTABLY NEAR PSCOMPACTNESS IN LTOPOLOGICAL SPACES
2
2
In this paper, the concept of countably near PScompactness inLtopological spaces is introduced, where L is a completely distributive latticewith an orderreversing involution. Countably near PScompactness is definedfor arbitrary Lsubsets and some of its fundamental properties are studied.
1
In this paper, the concept of countably near PScompactness inLtopological spaces is introduced, where L is a completely distributive latticewith an orderreversing involution. Countably near PScompactness is definedfor arbitrary Lsubsets and some of its fundamental properties are studied.
89
94
ShiZhong
Bai
ShiZhong
Bai
Department of Mathematics, Wuyi University, Guangdong 529020,
P.R.China
Department of Mathematics, Wuyi University,
China
shizhongbai@yahoo.com
Ltopology
Presemiclosed set
Remoteneighborhood
Countably near PScompact set
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