ORIGINAL_ARTICLE
Cover Vol.4 No.2, October 2007
http://ijfs.usb.ac.ir/article_2908_ddbe99988aa5076a1f94305d5b4b0e4e.pdf
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10.22111/ijfs.2007.2908
ORIGINAL_ARTICLE
PRICING STOCK OPTIONS USING FUZZY SETS
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.
http://ijfs.usb.ac.ir/article_365_166ca7566fde953dc5de7ad3e33575c6.pdf
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14
10.22111/ijfs.2007.365
Pricing Options
Binomial methods
Fuzzy numbers
James J.
Buckley
buckley@math.uab.edu
true
1
Department of Mathematics, University of Alabama at Birmingham,
Birmingham, Al 35209, USA
Department of Mathematics, University of Alabama at Birmingham,
Birmingham, Al 35209, USA
Department of Mathematics, University of Alabama at Birmingham,
Birmingham, Al 35209, USA
AUTHOR
Esfandiar
Eslami
eeslami@mail.uk.ac.ir
true
2
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 University of Kerman,
Kerman and Institute for Studies in Theoretical Physics and Mathematics(IPM),
Tehran, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman and Institute for Studies in Theoretical Physics and Mathematics(IPM),
Tehran, Iran
AUTHOR
[1] S. S. Appadoo, R. K. Thulasiram, C. R. Bector and A. Thavaneswaran, Fuzzy algebraic
1
option pricing technique- a fundamental investigation, Proceedings ASAC Conference 2004,
2
Quebec City, Quebec.
3
[2] J. J. Buckley and E. Eslami, Introduction to fuzzy logic sand fuzzy sets, Springer, Heidelberg,
4
Germany, 2002.
5
[3] J. J. Buckley and Y. Qu, On using -cuts to evaluate fuzzy equations, Fuzzy Sets and Systems,
6
38(1990), 309-312.
7
[4] J. J. Buckley, T. Feuring and E. Eslami, Applications of fuzzy sets and fuzzy logic to economics
8
and engineering, Springer, Heidelberg, Germany, 2002.
9
[5] J. C. Cox and M. Rubinstein, Options markets, Prentice-Hall, Englewood Cliffs, NJ, 1985.
10
[6] D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications, Academic Press,
11
N.Y., 1980.
12
[7] M. Durbin, All About derivatives, McGraw-Hill, NY, NY, 2006.
13
[8] Frontline Systems (www.frontsys.com).
14
[9] G. J. Klir and B. Yuan, Fuzzy sets and fuzzy logic, Prentice Hall, Upper Saddle River, N.J.,
15
[10] S. Muzzioli and C. Torricelli, A model for pricing an option with a fuzzy payoff, Fuzzy
16
Economic Review, 6(2001), 40-62.
17
[11] S. Muzzioli and C. Torricelli, A multiperiod binomial model for pricing options in an uncertain
18
world, Proceedings Second Int. Symposium Imprecise Probabilities and Their Applications,
19
Ithaca, NY, 2001, 255-264.
20
[12] H. T. Nguyen and E. A. Walker, A first course in fuzzy logic, Second Edition, CRC Press,
21
Boca Raton, FL., 2000.
22
[13] H. Reynaerts and M. Vanmaele, A sensitivity analysis for the pricing of european call options
23
in a binary tree model, Proceedings Fourth Int. Symposium Imprecise Probabilities and Their
24
Applications, Univ. Lugano, Switzerland, 2003, 467-481.
25
[14] H. A. Taha, Operations research, Fifth Edition, Macmillan, N.Y., 1992.
26
[15] R. G. Tompkins, Options analysis, Revised Edition, Irwin Professional Publishing, Chicago,
27
USA, 1994.
28
[16] M. A. Wong, Trading and investing in bond options, John Wiley and Sons, NY, NY, 1991.
29
[17] H. -C. Wu, Pricing European options based on the fuzzy pattern of black-scholes formula,
30
Computers and Operations Research, 31(2004),1069-1081.
31
[18] www.solver.com
32
ORIGINAL_ARTICLE
OPTIMIZATION OF LINEAR OBJECTIVE FUNCTION SUBJECT TO FUZZY RELATION INEQUALITIES CONSTRAINTS WITH MAX-AVERAGE COMPOSITION
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.
http://ijfs.usb.ac.ir/article_368_e3fec3b0627142fc215ec44c2ff81a1f.pdf
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29
10.22111/ijfs.2007.368
Linear objective function optimization
Fuzzy r e lation equations
Fuzzy
relation inequalities
ELYAS
SHIVANIAN
eshivanian@gmail.com
true
1
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF
TECHNOLOGY, TEHRAN 15914, IRAN
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF
TECHNOLOGY, TEHRAN 15914, IRAN
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF
TECHNOLOGY, TEHRAN 15914, IRAN
LEAD_AUTHOR
ESMAILE
KHORRAM
eskor@aut.ac.ir
true
2
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF
TECHNOLOGY, TEHRAN 15914, IRAN
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF
TECHNOLOGY, TEHRAN 15914, IRAN
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF
TECHNOLOGY, TEHRAN 15914, IRAN
AUTHOR
AMIN
GHODOUSIAN
true
3
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF
TECHNOLOGY, TEHRAN 15914, IRAN
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF
TECHNOLOGY, TEHRAN 15914, IRAN
FACULTY OF MATHEMATICS AND COMPUTER SCIENCE, AMIRKABIR UNIVERSITY OF
TECHNOLOGY, TEHRAN 15914, IRAN
AUTHOR
[1] K. -P. Adlassnig, Fuzzy set theory in medical diagnosis, IEEE Trans. Systems Man
1
Cybernet., 16 (1986), 260-265.
2
[2] M. M. Brouke and D. G. Fisher, Solution algorithms for fuzzy relation equations with
3
max-product composition, Fuzzy Sets and Systems, 94 (1998), 61-69.
4
[3] E. Czogala and W. Pedrycz, Control problems in fuzzy systems, Fuzzy Sets and Systems,
5
7 (1982), 257-273.
6
[4] E. Czogala and W. Predrycz, On identification in fuzzy systems and its applications in
7
control problem, Fuzzy Sets and Systems, 6, 73-83.
8
[5] E. Czogala, J. Drewniak and W. Pedrycz, Fuzzy relation equations on a finite set, Fuzzy
9
Sets and Systems, 7 (1982), 89-101.
10
[6] A. Di Nola, Relational equations in totally ordered lattices and their complete resolution,
11
J. Math. Appl., 107 (1985), 148-155.
12
[7] A. Di Nola, S. Sessa, W. Pedrycz and E. Sanchez, Fuzzy relational equations and their
13
applications in knowledge engineering, Dordrecht: Kluwer Academic Press,1989.
14
[8] S. -C. Fang and G. Li, Solving fuzzy relations equations with a linear objective function,
15
Fuzzy Sets and Systems, 103 (1999), 107-13.
16
[9] S. -C. Fang and S. Puthenpura, Linear optimization and extensions: theory and algorithm,
17
Prentice-Hall, Englewood Cliffs, NJ, 1993.
18
[10] S. Z. Guo, P. Z. Wang, A. Di Nola and S. Sessa, Further contributions to the study of
19
finite fuzzyrelation equations, Fuzzy Sets and Systems, 26 (1988), 93-104.
20
[11] F. -F. Guo and Z. -Q. Xia, An algorithm for solving optimization Problems with one
21
linear objective function and finitely many constraints of fuzzy relation inequalities, Fuzzy
22
Optimization and Decision Making, 5 (2006), 33-47.
23
[12] M. M. Gupta and J. Qi, Design of fuzzy logic controllers based on generalized
24
t-operators, Fuzzy Sets and Systems, 40 (1991), 473-486.
25
[13] M. Guu and Y. K. Wu, Minimizing a linear objective function with fuzzy relation equation
26
constraints, Fuzzy Optimization and Decision Making, 12 (2002), 1568-4539.
27
[14] S. S. Z. Han, A. H. Song, and T. Sekiguchi, Fuzzy inequality relation system
28
identification via sign matrix method, Proceeding of 1995 IEEE International
29
Conference, 3 (1995), 1375-1382.
30
[15] M. Higashi and G. J. Klir, Resolution of finite fuzzy relation equations, Fuzzy Sets and
31
Systems, 13 (1984), 65-82.
32
[16] C. F. Hu, Generalized Variational inequalities with fuzzy relation, Journal of
33
Computationaland Applied Mathematics, 146 (1998), 198-203.
34
[17] E. Khorram and A.Ghodousian, Linear objective function optimization with fuzzy
35
relation constraints regarding max-av composition, Applied Mathematics and
36
Computation, 173 (2006), 827-886.
37
[18] G. Li and S. -C. Fang, Resolution of finite fuzzy resolution equations, Report No. 322,
38
North Carolina State University, Raleigh, NC, May 1996.
39
[19] J. Loetamonphong and S. -C. Fang, Optimization of fuzzy relation equations with maxproduct
40
composition, Fuzzy Sets and Systems, 118 (2001), 509-517.
41
[20] J. Loetamonphong, S. -C. Fang and R.E. Young, Multi-objective optimization problems
42
with fuzzy relation equation constraints, Fuzzy Sets and Systems, 127 (2002), 141-164.
43
[21] J. Lu and S. -C. Fang, Solving nonlinear optimization problems with fuzzy relation
44
equation constraints, Fuzzy Sets and Systems, 119 (2001), 1-20.
45
[22] W. Pedrycz, On Generalized fuzzy relational equations and their applications, Journal of
46
Mathematical Analysis and Applications, 107 (1985), 520-536.
47
[23] W. Pedrycz, Proceeding in relational structures: fuzzy relational equations, Fuzzy Sets
48
and Systems, 40 (1991), 77-106.
49
[24] M. Prevot, Algorithm for the solution of fuzzy relations, Fuzzy Sets and Systems,
50
5 (1985), 319-322.
51
[25] E. Sanchez, Resolution of composite fuzzy relation equations, Inform. Control,
52
30 (1976), 38-48.
53
[26] W. B. Vasantha Kandasamy and F. Smarandache, Fuzzy relational maps and
54
neutrosophic relational maps, Hexis Church Rock 2004 (chapter two).
55
[27] P. Z. Wang, How many lower solutions of finite fuzzy relation equations, Fuzzy
56
Mathematics (Chinese), 4 (1984), 67-73.
57
[28] P. Z. Wang, Lattecized linear programming and fuzzy relaion inequalies, Journal of
58
Mathematical Analysis and Applications, 159 (1991), 72-87.
59
[29] W. L. Winston, Introduction to mathematical programming: application and algorithms,
60
Duxbury Press, Belmont, CA, 1995.
61
[30] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.
62
[31] H. T. Zhang, H. M. Dong and R. H. Ren, Programming problem with fuzzy relation
63
inequality constraints, Journal of Liaoning Noramal University, 3 (2003), 231-233.
64
ORIGINAL_ARTICLE
A NOTE ON THE ZIMMERMANN METHOD FOR SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS
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.
http://ijfs.usb.ac.ir/article_369_c50bd5faf59078df22d9c02d540aade9.pdf
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10.22111/ijfs.2007.369
Linear programming
Fuzzy set theory
Fuzzy linear programming and fuzzy
efficiency
MOHAMMADREZA
SAFI
safi_mohammadreza@yahoo.com
true
1
DEPARTMENT OF MATHEMATICES, UNIVERSITY OF SHAHID-BAHONAR KERMAN,
KERMAN, IRAN
DEPARTMENT OF MATHEMATICES, UNIVERSITY OF SHAHID-BAHONAR KERMAN,
KERMAN, IRAN
DEPARTMENT OF MATHEMATICES, UNIVERSITY OF SHAHID-BAHONAR KERMAN,
KERMAN, IRAN
LEAD_AUTHOR
HAMIDREZA
MALEKI
maleki@sutech.ac.ir
true
2
DEPARTMENT OF BASIC SCIENCES, SHIRAZ UNIVERSITY OF TECHNOLOGY, SHIRAZ,
IRAN
DEPARTMENT OF BASIC SCIENCES, SHIRAZ UNIVERSITY OF TECHNOLOGY, SHIRAZ,
IRAN
DEPARTMENT OF BASIC SCIENCES, SHIRAZ UNIVERSITY OF TECHNOLOGY, SHIRAZ,
IRAN
AUTHOR
EFFAT
ZAEIMAZAD
effat_zaeimazad@yahoo.com
true
3
DEPARTMENT OF MATHEMATICES, UNIVERSITY OF SHAHID-BAHONAR KERMAN,
KERMAN, IRAN
DEPARTMENT OF MATHEMATICES, UNIVERSITY OF SHAHID-BAHONAR KERMAN,
KERMAN, IRAN
DEPARTMENT OF MATHEMATICES, UNIVERSITY OF SHAHID-BAHONAR KERMAN,
KERMAN, IRAN
AUTHOR
[1] R. E. Bellman and L. A. Zadeh, Decision making in a fuzzy environment, Management
1
Science, 17 (1970), 141-164.
2
[2] J. M. Cadenas and J. L. Verdegay, A Primer on fuzzy optimization models and methods,
3
Iranian Journal of Fuzzy Systems (to appear).
4
[3] J. M. Cadenas and J. L. Verdegay, Using ranking functions in multi-objective fuzzy linear
5
programming, Fuzzy sets and systems, 111 (2000), 47-53.
6
[4] L. Campus and J. L. Verdegay, Linear programming problem and ranking of fuzzy numbers,
7
Fuzzy Sets and Systems, 32 (1989), 1-11.
8
[5] S. Chanas, The use of parametric programming in fuzzy linear programming, Fuzzy Sets
9
and Systems, 11 (1983), 243-251.
10
[6] M. Delgado, J. L Verdegay and M. A. Vila, A general model for fuzzy linear programming,
11
Fuzzy Sets and Systems, 29 (1989), 21-29.
12
[7] D. Dubois, H. Fargier and H. Prade, Refinements of the maximum approach to decision
13
making in a fuzzy environment, Fuzzy Sets and Systems, 81 (1996), 103-122.
14
[8] S. M. Guu and Y. K. Wu, Two phase approach for solving the fuzzy linear programming
15
problems, Fuzzy Sets and Systems, 107 (1999), 191-195.
16
[9] Y. J. Lai and C. L. Hwang, Fuzzy mathematical programming methods and applications,
17
Springer-Verlag, Berlin, 1992.
18
[10] Y. J. Lai and C. L. Hwang, Interactive fuzzy linear programming, Fuzzy Sets and Systems,
19
45 (1992), 169-183.
20
[11] X. Li, B. Zhang and H. Li, Computing efficient solution to fuzzy multiple objective linear
21
programming problems, Fuzzy Sets and Systems, 157 (2006), 1328-1332.
22
[12] H. R. Maleki, Ranking functions and their applications to fuzzy linear programming, Far
23
East Journal of Mathematical Sciences, 4(3) (2003), 283-301.
24
[13] H. R. Maleki, M. Tata and M. Mashinchi, Linear programming with fuzzy variables, Fuzzy
25
Set and Systems, 109 (2000), 21-33.
26
[14] H. R. Maleki, M. Tata and M. Mashinchi, Fuzzy number linear programming, in: C. Lucas
27
(Ed), Proc. Internat. Conf. on Intelligent and Cognitive System FSS ’96, sponsored by
28
IEE ISRF, Tehran, Iran, 1996, 145-148.
29
[15] WinQSB 1, Yih-Long Chang and Kiran Desai, John wiley & Sons, Inc.
30
[16] J. Ramik and J. Raminak, Inequality relation between fuzzy numbers and its use in fuzzy
31
optimization, Fuzzy Sets and Systems, 16 (1985), 123-138.
32
[17] H. Tanaka, T. Okuda and K. Asai, On fuzzy mathematical programming, Journal of
33
Cybernetics, 3(4) (1974), 37-46.
34
[18] R. N. Tiwari, S. Deharmar and J. R. Rao, Fuzzy goal programming – an additive model,
35
Fuzzy Sets and Systems, 24 (1987), 27-34.
36
[19] J. L. Verdegay, Fuzzy mathematical programming, in: M. M. Gupta and E. Sanchez, Eds.,
37
Fuzzy Information and Decision Processes, North-Holland, Amsterdam, 1982, 231-
38
[20] B. Werners, An interactive fuzzy programming system, Fuzzy Sets and Systems, 23 (1987),
39
[21] E. Zaeimazad, Fuzzy linear programming: a geometric approach, Msc thesis, University of
40
Shahid–Bahonar, Kerman, Iran, 2005.
41
[22] H. J. Zimmermann, Description and optimization of fuzzy systems, International Journal of
42
General Systems, 2 (1976), 209- 215.
43
[23] H. J. Zimmermann, Fuzzy programming and linear programming with several objective
44
functions, Fuzzy Sets and Systems, 1 (1978), 45-55.
45
ORIGINAL_ARTICLE
LK-INTERIOR SYSTEMS AS SYSTEMS OF “ALMOST OPEN” L-SETS
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.
http://ijfs.usb.ac.ir/article_370_d6c63315b1797d8518b3230c75dedb5e.pdf
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10.22111/ijfs.2007.370
Interior operator
Interior system
Fuzzy set
Fuzzy logic
Tatana
Funiokova
tatana.funiokova@vsb.cz
true
1
Department of Mathematics, Technical University of Ostrava,
17. listopadu, CZ-708 30,Ostrava , Czech Republic
Department of Mathematics, Technical University of Ostrava,
17. listopadu, CZ-708 30,Ostrava , Czech Republic
Department of Mathematics, Technical University of Ostrava,
17. listopadu, CZ-708 30,Ostrava , Czech Republic
AUTHOR
[1] W. Bandler and L. Kohout, Special properties, closures and interiors of crisp and fuzzy
1
relations, Fuzzy Sets and Systems, 26(3)(1988), 317–331.
2
[2] R. Bˇelohl´avek and T. Funiokov´a, Fuzzy interior operators, Int. J. General Systems,
3
33(4)(2004), 315–330.
4
[3] R. Bˇelohl´avek, Fuzzy closure operators, J. Math. Anal. Appl., 262(2001), 473-489.
5
[4] R. Bˇelohl´avek, Fuzzy closure operators II, Soft Computing, 7(1)(2002), 53-64.
6
[5] R. Bˇelohl´avek, Fuzzy relational systems: foundations and principles, Kluwer Academic/
7
Plenum Press, New York, 2002.
8
[6] G. Gerla, Fuzzy logic. mathematical tools for approximate reasoning, Kluwer, Dordrecht,
9
[7] J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl., 18(1967), 145–174.
10
[8] J. A. Goguen, The logic of inexact concepts, Synthese 18(1968-9), 325–373.
11
[9] S. Gottwald, A Treatise on many-valued logics, Research Studies Press, Baldock, Hertfordshire,
12
England, 2001.
13
[10] P. H´ajek, Metamathematics of fuzzy logic, Kluwer, Dordrecht, 1998.
14
[11] U. H¨ohle, Commutative, residuated l-monoids., In: U, H¨ohle and E. P. Klement (Eds.),
15
Non-classical logics and their applications to fuzzy subsets. Kluwer, Dordrecht, 1995.
16
[12] U. H¨ohle, On the fundamentals of fuzzy set theory, J. Math. Anal. Appl., 201(1996), 786–826.
17
[13] A. S. Mashour and M. H. Ghanim, Fuzzy closure spaces, J. Math. Anal. Appl., 106(1985),
18
154–170.
19
[14] R. O. Rodr´ıguez, F. Esteva, P. Garcia and L. Godo, On implicative closure operators in
20
approximate reasoning, Int. J. Approximate Reasoning, 33(2003), 159–184.
21
ORIGINAL_ARTICLE
CHARACTERIZATION OF REGULAR $\Gamma$−SEMIGROUPS THROUGH FUZZY IDEALS
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.
http://ijfs.usb.ac.ir/article_375_dbea687f85b19c156e13c580580b59e3.pdf
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68
10.22111/ijfs.2007.375
$Gamma$−semigroup
Bi-ideal
Quasi-ideal
Regular
Strongly regular
Left(right) regular
Fuzzy (left
right)ideal
Fuzzy quasi-ideal
Fuzzy bi-ideal
P.
Dheena
dheenap@yahoo.com
true
1
Department of Mathematics, Annamalai University, Annamalainagar-
608002, India
Department of Mathematics, Annamalai University, Annamalainagar-
608002, India
Department of Mathematics, Annamalai University, Annamalainagar-
608002, India
AUTHOR
S.
Coumaressane
coumaressane_s@yahoo.com
true
2
Department of Mathematics,Annamalai University, Annamalainagar-
608002, India
Department of Mathematics,Annamalai University, Annamalainagar-
608002, India
Department of Mathematics,Annamalai University, Annamalainagar-
608002, India
LEAD_AUTHOR
[1] P. S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl., 84 (1981), 264-269.
1
[2] Y. I. Kwon and S. K. Lee, The weakly semi-prime ideals of po−$Gamma$−semigroups, Kangweon-
2
Kyungki Math. J., 5 (1997), 135-139.
3
[3] Y. I. Kwon and S. K. Lee, On the left regular po−$Gamma$−semigroups, Kangweon-Kyungki Math.
4
J., 6 (1998), 149-154.
5
[4] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982),
6
[5] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
7
[6] N. K. Saha, On $Gamma$−semigroup II, Bull. Cal. Math. Soc., 79 (1987), 331-335.
8
[7] M. K. Sen, On $Gamma$−semigroups, Proc. of the Int. Conf. on Algebra and it’s Appl., Decker
9
Publication, New York 301 (1981).
10
[8] M. K. Sen and N. K. Saha, On $Gamma$−semigroup I, Bull. Cal. Math. Soc., 78 (1986), 180-186.
11
[9] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338-353.
12
ORIGINAL_ARTICLE
RESIDUAL OF IDEALS OF AN L-RING
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.
http://ijfs.usb.ac.ir/article_378_18e934871298c269162e4614b21f86e1.pdf
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82
10.22111/ijfs.2007.378
L-subring
L-ideal
Right quotient
Left quotient
ANAND SWAROOP
PRAJAPATI
prajapati_anand@yahoo.co.in
true
1
ATMA RAM SANATAN DHARMA COLLEGE, UNIVERSITY OF DELHI,
DHAULA KUAN, NEW DELHI – 110021, INDIA
ATMA RAM SANATAN DHARMA COLLEGE, UNIVERSITY OF DELHI,
DHAULA KUAN, NEW DELHI – 110021, INDIA
ATMA RAM SANATAN DHARMA COLLEGE, UNIVERSITY OF DELHI,
DHAULA KUAN, NEW DELHI – 110021, INDIA
AUTHOR
[1] N. Ajmal and A. S. Prajapati, Prime radical and primary decomposition of ideals in an
1
L-subring, Communicated.
2
[2] N. Ajmal and S. Kumar, Lattice of subalgebras in the category of fuzzy groups, The
3
Journal of Fuzzy Mathematics , 10 (2) (2002), 359-369.
4
[3] G. Birkhoff, Lattice theory, American Mathematical Soceity, Providence, Rhode Island
5
[4] D. M. Burton, A first course in rings and ideals, Addison-Wesley, Reading,
6
Massachusetts, 1970.
7
[5] D. S. Malik and J. N. Mordeson, Fuzzy prime ideals of rings, FSS, 37 (1990), 93-98.
8
[6] D. S. Malik and J. N. Mordeson, Fuzzy maximal, radical, and primary ideals of a ring,
9
Inform. Sci., 53 (1991), 237-250.
10
[7] D. S. Malik and J. N. Mordeson, Fuzzy primary representations of fuzzy ideals, Inform.
11
Sci., 55 (1991), 151-165.
12
[8] D. S. Malik and J. N. Mordeson, Radicals of fuzzy ideals, Inform. Sci., 65 (1992), 239-
13
[9] D. S. Malik, J. N. Mordeson and P. S. Nair, Fuzzy normal subgroups in fuzzy subgroups,
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J. Korean Math. Soc., 29 (1992), 1-8.
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[10] D. S. Malik, and J. N. Mordeson, R-primary representation of L-ideals, Inform, Sci., 88
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(1996), 227-246.
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[11] J. N. Mordeson, L-subspaces and L-subfield, Centre for Research in Fuzzy Mathematics
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and Computer Science, Creighton University, USA. 1996.
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[12] J. N. Mordeson and D. S. Malik, Fuzzy commutative algebra, World Scientific Publishing
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Co. USA. 1998.
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[13] A. S. Prajapati and N. Ajmal, Maximal ideals of L-subring, The Journal of Fuzzy
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Mathematics (preprint).
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[14] A. S. Prajapati and N. Ajmal, Maximal ideals of L-subring II, The Journal of Fuzzy
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Mathematics (preprint).
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[15] A. S. Prajapati and N. Ajmal, Prime ideal, Semiprime ideal and Primary ideal of an
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L-subring, Communicated.
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[16] G. Szasz, Introduction to lattice theory, Academic Press, New York and London, 1963.
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[17] Y. Yandong, J. N. Mordeson and S.-C. Cheng, Elements of L-algebra, Lecture notes in
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Fuzzy Mathematics and Computer Science 1, Center for Research in Fuzzy Mathematics
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and Computer Science, Creighton University, USA. 1994.
31
ORIGINAL_ARTICLE
SOME PROPERTIES OF NEAR SR-COMPACTNESS
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.
http://ijfs.usb.ac.ir/article_379_273713dcd904c068e3e93be78892c8b4.pdf
2007-10-09T11:23:20
2017-09-23T11:23:20
83
87
10.22111/ijfs.2007.379
L-topology
SS-remote neighborhood family
-net
Compactness
Near SR-compact L-subset
Shi-Zhong
Bai
shizhongbai@yahoo.com
true
1
Department of Mathematics, Wuyi University, Guangdong 529020,
P.R.China
Department of Mathematics, Wuyi University, Guangdong 529020,
P.R.China
Department of Mathematics, Wuyi University, Guangdong 529020,
P.R.China
AUTHOR
[1] S. Z. Bai, Fuzzy strongly semiopen sets and fuzzy strong semicontinuity, Fuzzy Sets and
1
Systems, 52 (1992), 345-351.
2
[2] S. Z. Bai, The SR-compactness in L-fuzzy topological spaces, Fuzzy Sets and Systems, 87
3
(1997), 219-225.
4
[3] C. L. Chang, Fuzzy topological spaces, J.Math.Anal.Appl., 24 (1968), 182-190.
5
[4] S. G. Li, S. Z. Bai and N. Liu, The near SR-compactness axiom in L-topological spaces, Fuzzy
6
Sets and Systems, 174 (2004), 307-316.
7
[5] Y. M. Liu and M. K. Luo, Fuzzy topology, World Scientific Publishing, Singapore, 1998.
8
[6] R. Lowen, A comparison of different compactness notions in fuzzy topological spaces, J. Math.
9
Anal. Appl., 64 (1978), 446-454.
10
[7] G. J. Wang, A new fuzzy compactness defined by fuzzy nets, J. Math. Anal. Appl., 94 (1983),
11
[8] G. J. Wang, Theory of L-fuzzy topological spaces, Shaanxi Normal University, Xian, 1988.
12
[9] D. S. Zhao, The N-compactness in L-fuzzy topological spaces, J. Math. Anal. Appl., 128
13
(1987), 64-79.
14
ORIGINAL_ARTICLE
COUNTABLY NEAR PS-COMPACTNESS IN L-TOPOLOGICAL SPACES
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.
http://ijfs.usb.ac.ir/article_381_a1cab2ee2db813cfbf1b688858d2b558.pdf
2007-10-09T11:23:20
2017-09-23T11:23:20
89
94
10.22111/ijfs.2007.381
L-topology
Pre-semiclosed set
Remote-neighborhood
Countably
near PS-compact set
Shi-Zhong
Bai
shizhongbai@yahoo.com
true
1
Department of Mathematics, Wuyi University, Guangdong 529020,
P.R.China
Department of Mathematics, Wuyi University, Guangdong 529020,
P.R.China
Department of Mathematics, Wuyi University, Guangdong 529020,
P.R.China
AUTHOR
[1] S. Z. Bai, The SR-compactness in L-fuzzy topological spaces, Fuzzy Sets and Systems, 87
1
(1997), 219-225.
2
[2] S. Z. Bai, L-fuzzy PS-compactness, IJUFKS, 10 (2002), 201-209.
3
[3] S. Z. Bai, Near PS-compact L-subsets, Information Sciences, 115 (2003), 111-118.
4
[4] S. Z. Bai, Pre-semiclosed sets and PS-convergence in L-fuzzy topological spaces, J. Fuzzy
5
Math. 9 (2001), 497-509.
6
[5] C. L. Chang, Fuzzy topological spaces, J.Math.Anal.Appl. 24 (1968), 182-190.
7
[6] B. Hutton, Products of fuzzy topological spaces, Topology Appl. 11 (1980), 59-67.
8
[7] Y. M. Liu and M. K. Luo, Induced spaces and fuzzy Stone-Cech compactifications, Scientia
9
Sinica (A), 30 (1987), 1034-1044.
10
[8] Y. M. Liu and M. K. Luo, Fuzzy topology, World Scientific Publishing, Singapore, 1998.
11
[9] R. Lowen, Fuzzy topological spaces and fuzzy compactness, J.Math.Anal.Appl. 56 (1976),
12
[10] F. G. Shi, Countable compactness and Lindeloff property of L-fuzzy sets, Iranian journal of
13
fuzzy systems, 1 (2004), 79-88.
14
[11] B. M. Pu and Y. M. Liu, Fuzzy topological,I.Neighborhood structure of a fuzzy point and
15
Moore-Smith convergence0, J. Math. Anal. Appl. 76 (1980), 571-599.
16
[12] G. J. Wang, A new fuzzy compactness defined by fuzzy nets, J.Math.Anal.Appl. 94 (1983),
17
[13] G. J. Wang, Theory of L-fuzzy topological spaces, Shaanxi Normal University, Xian, 1988.
18
[14] D. S. Zhao, The N-compactness in L-fuzzy topological spaces, J. Math. Anal. Appl. 128
19
(1987), 64-79.
20
ORIGINAL_ARTICLE
Persian-translation Vol.4 No.2, October 2007
http://ijfs.usb.ac.ir/article_2909_61412a1a0bcf35f7346eb24d362cbd77.pdf
2007-10-30T11:23:20
2017-09-23T11:23:20
97
104
10.22111/ijfs.2007.2909