ORIGINAL_ARTICLE
Cover vol.8,no.1- February 2011
http://ijfs.usb.ac.ir/article_2874_b146a1210c1b6737839b7a108b742ce0.pdf
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ORIGINAL_ARTICLE
FUZZY LOGISTIC REGRESSION: A NEW POSSIBILISTIC
MODEL AND ITS APPLICATION IN
CLINICAL VAGUE STATUS
Logistic regression models are frequently used in clinicalresearch and particularly for modeling disease status and patientsurvival. In practice, clinical studies have several limitationsFor instance, in the study of rare diseases or due ethical considerations, we can only have small sample sizes. In addition, the lack of suitable andadvanced measuring instruments lead to non-precise observations and disagreements among scientists in defining diseasecriteria have led to vague diagnosis. Also,specialists oftenreport their opinion in linguistic terms rather than numerically. Usually, because of these limitations, the assumptions of the statistical model do not hold and hence their use is questionable. We therefore need to develop new methods formodeling and analyzing the problem. In this study, a model called the `` fuzzy logistic model '' isproposed for the case when the explanatory variables arecrisp and the value of the binary response variable is reportedas a number between zero and one (indicating the possibility ofhaving the property). In this regard, the concept of `` possibilistic odds '' is alsointroduced. Then, the methodology and formulationof this model is explained in detail and a linear programming approach is use to estimate the model parameters. Some goodness-of-fit criteria are proposed and a numerical example is given as an example.
http://ijfs.usb.ac.ir/article_232_ab7ae3d9f840627e8888c9450131cbb6.pdf
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10.22111/ijfs.2011.232
Logistic Regression
Clinical research
Fuzzy logistic regression
Possibilistic
odds
Saeedeh
Pourahmad
pourahmad@sums.ac.ir
true
1
Department of Biostatistics, School of Medicine, Shiraz University
of Medical Sciences, Shiraz, 71345-1874, Iran
Department of Biostatistics, School of Medicine, Shiraz University
of Medical Sciences, Shiraz, 71345-1874, Iran
Department of Biostatistics, School of Medicine, Shiraz University
of Medical Sciences, Shiraz, 71345-1874, Iran
AUTHOR
S. Mohammad
Taghi Ayatollahi
ayatolahim@sums.ac.ir
true
2
Department of Biostatistics, School of Medicine,
Shiraz University of Medical Sciences, Shiraz, 71345-1874, Iran
Department of Biostatistics, School of Medicine,
Shiraz University of Medical Sciences, Shiraz, 71345-1874, Iran
Department of Biostatistics, School of Medicine,
Shiraz University of Medical Sciences, Shiraz, 71345-1874, Iran
LEAD_AUTHOR
S. Mahmoud
Taheri
sm_taheri@yahoo.com
true
3
Department of Mathematical Sciences, Isfahan University of
Technology, Isfahan, 84156-83111, Iran
Department of Mathematical Sciences, Isfahan University of
Technology, Isfahan, 84156-83111, Iran
Department of Mathematical Sciences, Isfahan University of
Technology, Isfahan, 84156-83111, Iran
AUTHOR
bibitem{Ag:cda}
1
A. Agresti, {it Categorical data analysis}, Wiley, New york,
2
bibitem{ArTa:Epflrm}
3
A. R. Arabpour and M. Tata, {it Estimating the parameters of a
4
fuzzy linear regression model}, Iranian Journal of Fuzzy Systems,
5
{bf 5} (2008), 1-19.
6
bibitem{BaWhGo:Lrmlsur}
7
S. C. Bagley, H. White and B. A. Golomb, {it Logistic regression
8
in the medical literature: standards for use and reporting with
9
particular attention to one medical domain}, Journal of Clinical
10
Epidemiology, {bf 54} (2001), 979-985.
11
bibitem{Cel:Lsmffvd}
12
A. Celmins, {it Least squares model fitting to fuzzy vector
13
data}, Fuzzy Sets and Systems, {bf 22} (1987), 260-269.
14
bibitem{CoDuGiSa:Lselrmfr}
15
R. Coppi, P. D'Urso, P. Giordani and A. Santoro, {it Least
16
squares estimation of a linear regression model with LR fuzzy
17
response}, Computational Statistics and Data Analysis, {bf
18
51} (2006), 267-286.
19
bibitem{Di:Lsfsfv}
20
P. Diamond, {it Least squares fitting of several fuzzy
21
variables}, Proc. of the Second IFSA Congress, Tokyo, (1987),
22
bibitem{DuKeMePr:Fia}
23
D. Dubois, E. Kerre, R. Mesiar and H. Prade, {it Fuzzy interval
24
analysis, In: D. Dubois, H. Prade, eds.}, Fundamentals of Fuzzy
25
Sets, Kluwer, 2000.
26
bibitem{FaBrKaHa:Haprinme}
27
A. S. Fauci, E. Braunwald, D. L. Kasper, S. L. Hauser, D. L.
28
Longo, J. L. Jameson and J. Loscalzo, {it Harrison's principals
29
of internal medicine}, Wiley, New York, {bf II} (2008), 2275-2279.
30
bibitem{GAMs:G}
31
GAMS (General Algebraic Modeling System), {it A high-level modeling
32
system for mathematical programming and optimization}, GAMS
33
Development Corporation, Washington, DC, USA, 2007.
34
bibitem{HaMaYa:Aeflr}
35
H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, {it A note on
36
evaluation of fuzzy linear regression models by comparing
37
membership functions}, Iranian Journal of Fuzzy Systems, {bf
38
6} (2009), 1-6.
39
bibitem{HoSoDo:Fulelireanus}
40
D. H. Hong, J. Song and H. Y. Do, {it Fuzzy least-squares linear
41
regression analysis using shape preserving operation}, Information
42
Sciences, {bf 138} (2001), 185-193.
43
bibitem{Lingo:A}
44
LINGO 8.0, {it A linear programming, integer programming, nonlinear
45
programming and global optimization solver}, Lindo System
46
Inc, 1415 North Dayton Str., Chicago, 2003.
47
bibitem{MATLAB:A}
48
MATLAB R., {it A technical computing environment for high-performance
49
numeric computation and Visualization}, The Math Works Inc.,
50
bibitem{MiTa:Plrlpa}
51
S. Mirzaei Yeganeh and S. M. Taheri, {it Possibilistic logistic
52
regression by linear programming approach}, Proc. of the 7th
53
Seminar on Probability and Stochastic Processes, Isfahan
54
University of Technology, Isfahan, Iran, (2009), 139-143.
55
bibitem{MoTa:Pedomodel}
56
J. Mohammadi and S. M. Taheri, {it Pedomodels fitting with fuzzy
57
least squares regression}, Iranian Journal of Fuzzy Systems, {bf
58
1} (2004), 45-61.
59
bibitem{Pe:Alfm}
60
G. Peters, {it A linear forecasting model and its application in
61
economic data}, Journal of Forecasting, {bf 20} (2001), 315-328.
62
bibitem{RoPe:Mtfgrfr}
63
S. Roychowdhury and W. Pedrycz, {it Modeling temporal functions
64
with granular regression and fuzzy rule}, Fuzzy Sets and Systems,
65
{bf 126} (2002), 377-387.
66
bibitem{SaGi:A}
67
B. Sadeghpour and D. Gien, {it A goodness of fit index to
68
reliability analysis in fuzzy model, In: A. Grmela, ed.,
69
Advances in Intelligent Systems, Fuzzy Systems, Evolutionary
70
Computation}, WSEAS Press, Greece, (2002), 78-83.
71
bibitem{Sh:Frm}
72
A. F. Shapiro, {it Fuzzy regression models}, ARC, 2005.
73
bibitem{TaHe:Amu}
74
B. D. Tabaei, and W. H. Herman, {it A multivariate logistic
75
regression equation to screen for Diabetes}, Diabetes Care, {bf
76
25} (2002), 1999-2003.
77
bibitem{Ta:Trends}
78
S. M. Taheri, {it Trends in fuzzy statistics}, Austrian Journal
79
of Statistics, {bf 32} (2003), 239-257.
80
bibitem{TaKe:Flar}
81
S. M. Taheri and M. Kelkinnama, {it Fuzzy least absolutes
82
regression}, Proc. of 4th International IEEE Conference on
83
Intelligent Systems, Varna, Bulgaria, {bf 11} (2008), 55-58.
84
bibitem{TaUeAs:Lraw}
85
H. Tanaka, S. Uejima, K. Asai, {it Linear regression analysis
86
with fuzzy model}, IEEE Trans. Systems Man Cybernet., {bf
87
12} (1982), 903-907.
88
bibitem{VaBa:Fast}
89
E. Van Broekhoven and B. D. Baets, {it Fast and accurate of
90
gravity defuzzification of fuzzy systems outputs defined on
91
trapezoidsal fuzzy partitions}, Fuzzy Sets and Systems, {bf
92
157} (2006), 904-918.
93
bibitem{Za:Fs}
94
L. A. Zadeh, {it Fuzzy sets}, Information and Control, {bf
95
8} (1965), 338-353.
96
bibitem{Zimm:Fu}
97
H. J. Zimmermann, {it Fuzzy set theory and its applications}, 3rd
98
ed., Kluwer, Dodrecht, 1996.
99
ORIGINAL_ARTICLE
TOWARDS THE THEORY OF L-BORNOLOGICAL SPACES
The concept of an $L$-bornology is introduced and the theory of $L$-bornological spacesis being developed. In particular the lattice of all $L$-bornologies on a given set is studied and basic properties ofthe category of $L$-bornological spaces and bounded mappings are investigated.
http://ijfs.usb.ac.ir/article_233_1ad45ef27bcc863221cb4c71a4ff9e4b.pdf
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10.22111/ijfs.2011.233
Bornology
$L$-set
$L$-bornology
Fuzzy set
Fuzzy topology
mati
Abel
mati.abel@ut.ee
true
1
Institute of Pure Mathematics, University of Tartu, J.Liivi street 2,
EE-50409 Tartu, Estonia
Institute of Pure Mathematics, University of Tartu, J.Liivi street 2,
EE-50409 Tartu, Estonia
Institute of Pure Mathematics, University of Tartu, J.Liivi street 2,
EE-50409 Tartu, Estonia
AUTHOR
aleksandrs
ˇSostaks
true
2
Department of Mathematics, University of Latvia, Zellu street
8, LV-1002, Riga, Latvia and Institute of Mathematics and CS, University of Latvia,
Raina bulv. 29, LV-1586, Riga, Latvia
Department of Mathematics, University of Latvia, Zellu street
8, LV-1002, Riga, Latvia and Institute of Mathematics and CS, University of Latvia,
Raina bulv. 29, LV-1586, Riga, Latvia
Department of Mathematics, University of Latvia, Zellu street
8, LV-1002, Riga, Latvia and Institute of Mathematics and CS, University of Latvia,
Raina bulv. 29, LV-1586, Riga, Latvia
LEAD_AUTHOR
bibitem{AHS}J. Ad'amek, H. Herrlich and G. E. Strecker, {it Abstract and
1
concrete categories}, John Wiley & Sons, New York, 1990.
2
bibitem{Beer} G. Beer, {it Metric bornologies and Kuratowska-Painleve convergence to the empty set},
3
{Journal of Convex Analysis}, {bf 8} (2001), 273-289.
4
%bibitem{Beer_Levi} Gerald Beer, Levi
5
bibitem{Bir} G. Birkhoff, {it Lattice theory}, AMS Providence, RI,
6
bibitem{Ch68} C. L. Chang, {it Fuzzy topological spaces}, {J. Math. Anal.
7
Appl.}, {bf 24} (1968), 182-190.
8
bibitem{Gierz} G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, {it Continuous lattices and domains},
9
Cambridge University Press, Cambridge, 2003.
10
bibitem{Go67} J. A. Goguen, {it $L$-fuzzy sets}, {J. Math. Anal. Appl.}, {bf 18} (1967) 145-174.
11
bibitem{Go73} J. A. Goguen, {it The fuzzy Tychonoff theorem}, { J. Math. Anal. Appl.}, {bf 18} (1973), 734-742.
12
bibitem{HS} H. Herrlich and G. E. Strecker, { it Category theory}, Heldermann Verlag, Berlin, 1987.
13
bibitem{HN} H. Hogbe-Nlend, {it Bornology and functional analysis}, Math. Studies, North-Holland, Amsterdam, {bf 26} (1977).
14
bibitem{HoSo99} U. H"ohle and A. v{S}ostak, {it Axiomatics for fixed-based fuzzy topologies}, Chapter 3 in [8].
15
bibitem{HuS1} S. T. Hu, {it Boundedness in a topological space}, {it J. Math. Pures Appl.}, {bf 28} (1949), 287-320.
16
bibitem{HuS2} S. T. Hu, {it Introduction to general topology}, Holden-Day, San-Francisko, 1966.
17
bibitem{Hut} B. Hutton, {it Normality in fuzzy topologicl spaces}, {J. Math. Anal. Appl.}, {bf 50} (1975), 74-79.
18
bibitem{JiangYan} S. Q. Jiang and C. H. Yan, { it Fuzzy bounded sets and totally fuzzy bounded sets in I-topological vector spaces},
19
{ Iranian Journal of Fuzzy Systems}, {bf 6(3)} (2009), 73-90.
20
bibitem{MFS} U. H"ohle and S. E. Rodabaugh, eds., {it Mathematics of fuzzy sets: logic, topology and
21
measure theory}, Handbook Series, Kluwer Acad. Publ., {bf3} (1999).
22
bibitem{NVT} A. Narayaanan, S. Vijayabalaji and N. Thillaigovitidan, {it Intuitionistic fuzzy linear bounded operators},
23
{Iranian Journal of Fuzzy Systems}, {bf 4(1)} (2007), 89-93.
24
bibitem{NR} C. V. Negoita and D. A. Ralescu, { it Application of fuzzy sets to system analysis}, John Wiley & Sons,
25
New York, 1975.
26
bibitem{Ro99} S. E. Rodabaugh, {it Powerset operator foundations for poslat fuzzy set theories and topologies},
27
Chapter 2 in
28
cite{MFS}.
29
bibitem{Za} L. Zadeh, {it Fuzzy sets}, {Information and Control}, {bf 8} (1965), 338-353.
30
ORIGINAL_ARTICLE
ORDERED INTUITIONISTIC FUZZY SOFT
MODEL OF FLOOD ALARM
A flood warning system is a non-structural measure for flood mitigation. Several parameters are responsible for flood related disasters. This work illustrates an ordered intuitionistic fuzzy analysis that has the capability to simulate the unknown relations between a set of meteorological and hydrological parameters. In this paper, we first define ordered intuitionistic fuzzy soft sets and establish some results on them. Then, we define similarity measures between ordered intuitionistic fuzzy soft (OIFS) sets and apply these similarity measures to five selected sites of Kerala, India to predict potential flood.
http://ijfs.usb.ac.ir/article_234_35cde19badb331cea8f2e50565ae547a.pdf
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10.22111/ijfs.2011.234
rainfall
Intuitionistic fuzzy soft set
Flood
Simulation
Sunny Joseph
Kalayathankal
sunnyjose2000@yahoo.com
true
1
Department of Mathematics, K.E.College, Mannanam,
Kottayam, 686561, Kerala, India
Department of Mathematics, K.E.College, Mannanam,
Kottayam, 686561, Kerala, India
Department of Mathematics, K.E.College, Mannanam,
Kottayam, 686561, Kerala, India
LEAD_AUTHOR
G. Suresh
Singh
true
2
Department of Mathematics, University of Kerala, Trivandrum,
695581, Kerala, India
Department of Mathematics, University of Kerala, Trivandrum,
695581, Kerala, India
Department of Mathematics, University of Kerala, Trivandrum,
695581, Kerala, India
AUTHOR
P. B.
Vinodkumar
true
3
Department of Mathematics, Rajagiri School of Engineering &
Technology, Cochin, Kerala, India
Department of Mathematics, Rajagiri School of Engineering &
Technology, Cochin, Kerala, India
Department of Mathematics, Rajagiri School of Engineering &
Technology, Cochin, Kerala, India
AUTHOR
Sabu
Joseph
true
4
Department of Environmental Science, University of Kerala, Trivan-
drum, Kerala, India
Department of Environmental Science, University of Kerala, Trivan-
drum, Kerala, India
Department of Environmental Science, University of Kerala, Trivan-
drum, Kerala, India
AUTHOR
Jobin
Thomas
true
5
Department of Environmental Science, University of Kerala, Trivan-
drum, Kerala, India
Department of Environmental Science, University of Kerala, Trivan-
drum, Kerala, India
Department of Environmental Science, University of Kerala, Trivan-
drum, Kerala, India
AUTHOR
bibitem{at} K. Atanassov, emph{Intuitionistic fuzzy sets}, Fuzzy sets and Systems, {bf20} (1986), 87-96.
1
bibitem{bu} J. J. Buckley, K. D. Reilly and L. J. Jowers, emph{Simulating continuous fuzzy systems}, Iranian Journal of fuzzy systems, {bf 2(1)} (2005), 1-18.
2
bibitem{ca}J. M. Cadenas and J. L. Verdegay, emph{A primer on fuzzy optimization models and methods}, Iranian Journal of fuzzy systems, {bf 3(1)} (2006), 1-21.
3
bibitem{shu}S. L. Chen, emph{The application of comprehensive fuzzy judgement in the interpretation of water-flooded reservoirs}, The Journal of Fuzzy Mathematics, {bf9(3)} (2001), 739-743.
4
bibitem{ch} S. M. Chen, S. M. Yeh and P. H. Hasiao, emph{A comparison of similarity measures of fuzzy values}, Fuzzy sets and Systems, {bf72} (1995), 79-89.
5
bibitem{su} S. Joseph Kalayathankal and S. Singh, emph{Need and significance of fuzzy modeling of rainfall}, In: Proceedings of the National Seminar on Mathematical Modeling and Simulation, Department of Mathematics, K. E. College, Mannanam, Kerala, India, (2007), 27-35.
6
bibitem{sun}S. Joseph Kalayathankal, G. Suresh Singh and P. B. Vinodkumar, emph{OIIF model of flood alarm}, Global Journal of Mathematical Sciences: Theory and Practical, {bf1(1)} (2009), 1-8.
7
bibitem{sunn}S. Joseph Kalayathankal and G. Suresh Singh, emph{IFS model of flood alarm}, Global Journal of Pure and Applied Mathematics, {bf9} (2009), 15-22.
8
bibitem{suy} S. Joseph Kalayathankal and G. Suresh Singh, emph{A fuzzy soft flood alarm model}, Mathematics and Computers in Simulation, {bf80} (2010), 887-893.
9
bibitem{sunm}S. Joseph Kalayathankal, G. Suresh Singh and P. B. Vinodkumar, emph{MADM models using ordered ideal intuitionistic fuzzy sets}, Advances in Fuzzy Mathematics, {bf4(2)} (2009), 101-106.
10
bibitem{pa}P. Kumar Maji, R. Biswas and A. Ranjan Roy, emph{Intuitionistic fuzzy soft sets}, The Journal of Fuzzy Mathematics, {bf9(3)} (2001) 677-692.
11
bibitem{pab}P. Kumar Maji, R. Biswas and A. Ranjan Roy, emph{Fuzzy soft sets}, The Journal of Fuzzy Mathematics, {bf9(3)} (2001), 589-602.
12
bibitem{mo} D. Molodtsov, emph{Soft set theory-first results}, Computers and Mathematics with Applications, {bf37} (1999), 19-31.
13
bibitem{pc} P. C. Nayak, K. P. Sudheer and K. S. Ramasastri, emph{Fuzzy computing based rainfall-runoff model for real time flood forecasting}, Hydrological Processes, {bf19} (2005), 955-968.
14
bibitem{ped} W. Pedrycz, emph{Distributed and collaborative fuzzy modeling}, Iranian Journal of fuzzy systems, {bf 4(1)} (2007), 1-19.
15
bibitem{to}E. Toth, A. Brath and A. Montanari, emph{Comparison of short-term rainfall prediction models for real-time flood forecasting}, Journal of Hydrology, {bf239} (2000), 132-147.
16
bibitem{xu} Z. S. Xu and J. Chen, emph{An overview of distance and similarity measures of intuitionistic fuzzy sets}, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, {bf16(4)} (2008), 529-555.
17
bibitem{zes}Z. Xu, emph{Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making}, Fuzzy Optim. Decis. Making, {bf6} (2007), 109-121.
18
ORIGINAL_ARTICLE
DISCRETE TOMOGRAPHY AND FUZZY INTEGER
PROGRAMMING
We study the problem of reconstructing binary images from four projections data in a fuzzy environment. Given the uncertainly projections,w e want to find a binary image that respects as best as possible these projections. We provide an iterative algorithm based on fuzzy integer programming and linear membership functions.
http://ijfs.usb.ac.ir/article_235_665d416a9509a1786df4be6c203977f0.pdf
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10.22111/ijfs.2011.235
Discrete tomography
F uzzy integer programming
Image
reconstruction
Fethi
Jarray
fethi.jarray@cnam.fr
true
1
Laboratoire CEDRIC-CNAM, 292 rue St-Martin, 75003 Paris, France,
Gabes University of Sciences, 6072 Gabes, Tunisia
Laboratoire CEDRIC-CNAM, 292 rue St-Martin, 75003 Paris, France,
Gabes University of Sciences, 6072 Gabes, Tunisia
Laboratoire CEDRIC-CNAM, 292 rue St-Martin, 75003 Paris, France,
Gabes University of Sciences, 6072 Gabes, Tunisia
LEAD_AUTHOR
[1] T. Allahviranloo,K. Shamsolkotabi, N. A. Kiani and L. Alizadeh, Fuzzy integer linear programming
1
problems,In t. J. Contemp. Math. Sciences, 2(4) (2007),167- 181.
2
[2] M. G. Bailey and B. E. Gillett, Parametric integer programming analysis: A contraction
3
approach,Jour nal of the Operational Research Society, 31 (1980),253- 262.
4
[3] K. J. Batenburg, Network flow algorithms for discrete tomography,A dvances in Discrete
5
Tomography and its Applications,Bi rkh¨auser,Bos ton, (2007), 175-205.
6
[4] J. J. Buckley and L. J. Jowers, Monte carlo methods in fuzzy optimization,Studi es in Fuzziness
7
and Soft Computig, 222 (2008),223- 226.
8
[5] J. M. Cadenas and J. L. Verdegay, A primer on fuzzy optimization models and methods,
9
Iranian Journal of Fuzzy Systems, 3(1) (2006),1- 21.
10
[6] R. J. Gardner,P . Gritzmann and D. Prangenberg, The computational complexity of reconstructing
11
lattice sets from their X-rays,D iscrete Math., 202 (1999),45- 71.
12
[7] F. Herrera and J. L. Verdegay, Three models of fuzzy integer linear programming,Eur opean
13
Journal of Operational Research, 83 (1995),581- 593.
14
[8] F. Jarray, Solving problems of discrete tomography: applications in workforce scheduling,
15
Ph.D. Thesis,U niversity of CNAM,P aris, 2004.
16
[9] F. Jarray,M . C. Costa and C. Picouleau, Complexity results for the horizontal bar packing
17
problem,I nformation Processing Letters, 108(6) (2008),356- 359.
18
[10] N. Javadian,Y . Maali and N. Mahdavi-Amiri, Fuzzy linear programming with grades of
19
satisfaction in constraints,Ir anian Journal of Fuzzy Systems, 6(3) (2009),17- 35.
20
[11] A. Mitsos and P. I. Barton, Parametric mixed-integer 0-1 linear programming: the general
21
case for a single parameter,Eur opean Journal of Operational Research, 194 (2009),663- 686.
22
[12] S. A. Orlovski, On programming with fuzzy constraint sets,K ybernetes, 6 (1977),197- 201.
23
[13] M. S. Osman,O . M. Saad and A. G. Hasan, Solving a special class of Large-Scale fuzzy
24
multiobjective integer linear programming problems,F uzzy sets and systems, 107 (1999),
25
[14] H. J. Ryser, Combinatorial properties of matrices of zeros and ones,Canad. J. Math, 9
26
(1957),371- 377.
27
[15] E. Shivantian,E. Khorram and A. Ghodousian, Optimization of linear objective function subject
28
to fuzzy relation inequalities constraints with max-average composition,Ir anian Journal
29
of Fuzzy Systems, 4(2) (2007),15- 29.
30
[16] J. L. Verdegay, Fuzzy mathematical programming,In M. M. Gupta and E. Sanchez,Eds .,
31
Fuzzy Information and Decision Processes,N orth-Holland,(1982), 231-236.
32
[17] S. Weber,T. Schule,J. Hornegger and C. Schnorr, Binary tomography by iterating linear
33
programs from noisy projections,LNCS, 233 (2004),38- 51.
34
[18] H. J. Zimmermann, Description and optimization of fuzzy systems,In ternational Journal
35
General Systems, 2 (1976),209- 215.
36
[19] H. J. Zimmermann, Fuzzy programming and linear programming with several objective functions,
37
F uzzy Sets and Systems, 1 (1978),45- 55.
38
ORIGINAL_ARTICLE
MODIFIED K-STEP METHOD FOR SOLVING FUZZY INITIAL
VALUE PROBLEMS
We are concerned with the development of a K−step method for the numerical solution of fuzzy initial value problems. Convergence and stability of the method are also proved in detail. Moreover, a specific method of order 4 is found. The numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.
http://ijfs.usb.ac.ir/article_236_a45147c5661d20b5db9030a06ea49fe5.pdf
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10.22111/ijfs.2011.236
Fuzzy numbers
Fuzzy differential equations
Modified k-step method
Omid
Solaymani Fard
osfard@du.ac.ir, omidsfard@gmail.com
true
1
School of Mathematics and Computer Science, Damghan
University, Damghan, Iran
School of Mathematics and Computer Science, Damghan
University, Damghan, Iran
School of Mathematics and Computer Science, Damghan
University, Damghan, Iran
LEAD_AUTHOR
Ali
Vahidian Kamyad
avkamyad@math.um.ac.ir
true
2
Department of Mathematics, Ferdowsi University of Mashhad,
Mashhad, Iran
Department of Mathematics, Ferdowsi University of Mashhad,
Mashhad, Iran
Department of Mathematics, Ferdowsi University of Mashhad,
Mashhad, Iran
AUTHOR
bibitem{abb1} S. Abbasbandy, J. J. Nieto and M. Alavi, {it Tuning of reachable set in one dimensional fuzzy differential inclusions}, Chaos, Solitons Fractals, {bf 26} (2005), 1337-1341.
1
bibitem{abb2} S. Abbasbandy, T. Allahviranloo, O. López-Pouso and J. J. Nieto, {it Numerical methods for fuzzy differential inclusions}, Comput. Math. Appl., {bf 48} (2004), 1633-1641.
2
bibitem{abb3} S. Abbasbandy and T. Allahviranloo, {it Numerical solutions of fuzzy differential equations by Taylor method}, , Journal of Computational Methods in Applied Mathematics, {bf 2} (2002), 113-124.
3
bibitem{alh1} T. Allahviranloo, N. Ahmady and E. Ahmady, {it Numerical solution of fuzzy differential equations by predictor-–corrector method}, Information Sciences, {bf 177} (2007), 1633-1647.
4
bibitem{alh2} T. Allahviranloo, N. Ahmady and E. Ahmady, {it Improved predictor–corrector method for solving fuzzy initial
5
value problems}, Information Sciences, {bf 179} (2009), 945-955.
6
bibitem{bede1} B. Bede, {it Note on "Numerical solutions of fuzzy differential equations by predictor-–corrector method"}, Information Sciences, {bf 178} (2008), 1917-1922.
7
bibitem{bede2} B. Bede and S. G. Gal, {it Generalizations of the differentiability of fuzzy umber valued functions with applications to fuzzy differential equation}, Fuzzy Sets and Systems, {bf 151} (2005), 581-599.
8
bibitem{bede3} B. Bede, J. Imre, C. Rudas and L. Attila, {it First order linear fuzzy differential equations under generalized differentiability}, Information Sciences, {bf 177} (2007), 3627-3635.
9
bibitem{buk1} J. J. Buckley and T. Feuring, {it Fuzzy differential equations}, Fuzzy Sets and Systems, {bf 110} (2000), 43-54.
10
bibitem{can1} Y. Chalco-Cano and H. Roman-Flores, {it On new solutions of fuzzy differential equations}, Chaos, Solitons and Fractals, {bf 38} (2008), 112-119.
11
bibitem{can2} Y. Chalco-Cano, H. Roman-Flores, M. A. Rojas-Medar, O. Saavedra and M. Jiménez-Gamero, {it The extension principle and a decomposition of
12
fuzzy sets}, Information Sciences, {bf 177} (2007), 5394-5403.
13
bibitem{chen1} C. K. Chen and S. H. Ho, {it Solving partial differential equations by two-dimensional differential transform method}, Applied Mathematics and Computation, {bf 106} (1999), 171-179.
14
bibitem{cho} Y. J. Cho and H. Y. Lan, {it The existence of solutions for the nonlinear first order fuzzy differential equations with discontinuous conditions}, Dynamics Continuous Discrete Inpulsive Systems Ser. AMath. Anal., {bf 14} (2007), 873-884.
15
bibitem{con} W. Congxin and S. Shiji, {it Exitance theorem to the Cauchy problem of fuzzy differential equations under compactance-type conditions}, Information Sciences, {bf 108} (1993), 123-134.
16
bibitem{dia1} P. Diamond, {it Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations}, IEEE Trans. Fuzzy Systems, {bf 7} (1999), 734-740.
17
bibitem{dia2} P. Diamond, {it Brief note on the variation of constants formula for fuzzy differential equations}, Fuzzy Sets and Systems, {bf 129} (2002), 65-71.
18
bibitem{ding} Z. Ding, M. Ma and A. Kandel, {it Existence of solutions of fuzzy differential equations with parameters}, Information Sciences, {bf 99} (1997), 205-217.
19
bibitem{dub} D. Dubois and H. Prade, {it Towards fuzzy differential calculus: part 3, differentiation}, Fuzzy Sets and Systems, {bf 8} (1982), 225-233.
20
bibitem{fei} W. Fei, {it Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients}, Information Sciences, {bf 177} (2007), 329-4337.
21
bibitem{geo1} R. Goetschel and W. Voxman, {it Topological properties of fuzzy number}, Fuzzy Sets and Systems, {bf 10} (1983), 87-99.
22
bibitem{geo2} R. Goetschel and W. Voxman, {it Elementary fuzzy calculus}, Fuzzy sets and Systems, {bf 18} (1986), 31-43.
23
bibitem{ijfs1} M. S. Hashemi, M. K. Mirnia and S. Shahmorad, {it Solving fuzzy linear systems by using the Schur complement when coefficient matrix is an M-matrix}, Iranian Journal of Fuzzy Systems, {bf 5}textbf{(3)} (2008), 15-30.
24
bibitem{ijfs2}H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, {it A note on evaluation of fuzzy linear regression models by comparing membership functions}, Iranian Journal of Fuzzy Systems, {bf 6}textbf{(2)} (2009), 1-8.
25
bibitem{hen} P. Henrici, {it Discrete vatiablr methods in ordinary differential equations}, Wiley, New York, 1962.
26
bibitem{jang} M. J. Jang, C. L. Chen and Y. C. Liy, {it On solving the initial-value problems using the differential transformation method}, Applied Mathematics and Computation, {bf 115} (2000), 145-160.
27
bibitem{kal1} O. Kaleva, {it Fuzzy differential equations}, Fuzzy Sets and Systems, {bf 24} (1987), 301-317.
28
bibitem{kal2} O. Kaleva, {it The Cauchy problem for fuzzy differential equations}, Fuzzy Sets and Systems, {bf 35} (1990), 389-396.
29
bibitem{kal3} O. Kaleva, {it A note on fuzzy differential equations}, Nonlinear Analysis, {bf 64} (2006), 895-900.
30
bibitem{lak} V. Lakshmikantham and S. Leela, {it Differential and integral inequalities}, Academic Press, New York, {bf1} (1969).
31
bibitem{lo1} R. R. Lopez, {it Comparison results for fuzzy differential equations}, Information Sciences, {bf 178} (2008), 1756-1779.
32
bibitem{ma} M. Ma, M. Friedman and A. Kandel, {it Numerical solutions of fuzzy differential equations}, Fuzzy Sets and Systems, {bf 105} (1999) 133–-138.
33
bibitem{ma1} M. Ma, M. Friedman and A. Kandel, {it A new approach for defuzzification}, Fuzzy Sets and Systems, {bf 111} (2000), 351-356.
34
bibitem{org} D. '{O}Regan, V. Lakshmikantham and J. Nieto, {it Initial and boundary value problems for fuzzy differential equations}, Nonlinear Anal., {bf 54} (2003), 405-415.
35
bibitem{miz} M. T. Mizukoshi, L. C. Barros, Y. Chalco-Cano, H. Roman-Flores and R. C. Bassanezi, {it Fuzzy differential equations and the extension principle}, Information Sciences, {bf 177} (2007), 3627-3635.
36
bibitem{pall} S. C. Palligkinis, G. Stefanidou and P. Efraimidi, {it Runge-Kutta methods for fuzzy differential equations}, Applied Mathematics and Computation, {bf 209} (2009), 97-105.
37
bibitem{pap} G. Papaschinopoulos, G. Stefanidou and P. Efraimidi, {it Existence uniqueness and asymptotic behavior of the solutions of a fuzzy differential equation with piecewise constant argument}, Information Sciences, {bf 177} (2007), 3855-3870.
38
bibitem{pur} M. L. Puri and D. A. Ralescu, {it Differentials of fuzzy functions}, Journal of Mathematical Analysis and Applications, {bf 91} (1983), 552-558.
39
bibitem{ijfs3} R. Saadati, S. Sedghi and H. Zhou, {it A common fixed point theorem for $psi$-weakly commuting maps in L-fuzzy metric spaces}, Iranian Journal of Fuzzy Systems, {bf 5}textbf{(1)} (2008), 47-54.
40
bibitem{ijfs4} M. R. Safi, H. R. Maleki and E. Zaeimazad, {it A note on Zimmermann method for solving fuzzy linear programming problems}, Iranian Journal of Fuzzy Systems, {bf 4}textbf{(2)} (2007), 31-46.
41
bibitem{sei} S. Seikkala, {it On the fuzzy initial value problem}, Fuzzy Sets and Systems, {bf 24} (1987), 319-330.
42
bibitem{ijfs5} A. K. Shaymal and M. Pal, {it Triangular fuzzy matrices}, Iranian Journal of Fuzzy Systems, {bf 4}textbf{(1)} (2007), 75-87.
43
bibitem{song} S. Song, L. Guo and C. Feng, {it Global existence of solutions to fuzzy differential equations}, Fuzzy Sets and Systems, {bf 115} (2000), 371-376.
44
ORIGINAL_ARTICLE
On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism
http://ijfs.usb.ac.ir/article_237_ea23a937b8bfe7d93a4e7c3e69a6bbc5.pdf
2011-02-12T11:23:20
2017-09-21T11:23:20
65
76
10.22111/ijfs.2011.237
Hypergroup
$n$-ary hypergroup
Fuzzy set
$n$-ary sub-hypergroup
Fuzzy $n$-ary sub-hypergroup
$n$-ary homomorphism
O.
Kazancı
kazancio@yahoo.com
true
1
Department of Mathematics, Karadeniz Technical University,61080,
Trabzon, Turkey
Department of Mathematics, Karadeniz Technical University,61080,
Trabzon, Turkey
Department of Mathematics, Karadeniz Technical University,61080,
Trabzon, Turkey
LEAD_AUTHOR
S.
Yamak
syamak@ktu.edu.tr
true
2
Department of Mathematics, Karadeniz Technical University,61080, Trabzon,
Turkey
Department of Mathematics, Karadeniz Technical University,61080, Trabzon,
Turkey
Department of Mathematics, Karadeniz Technical University,61080, Trabzon,
Turkey
AUTHOR
B.
Davvaz
davvaz@yazduni.ac.ir
true
3
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
AUTHOR
bibitem{1} N. Ajmal, {it Homomorphism of fuzzy groups, correspondence theorem and fuzzy quotient groups},
1
Fuzzy Sets and Systems, {bf 61} (1994), 329-339.
2
bibitem{2} R. Ameri and M. M. Zahedi, {it Hyperalgebraic system}, Italian J. Pure Appl. Math., {bf 6} (1999), 21-32.
3
bibitem{3} M. Bakhshi and R. A. Borzooei, {it Lattice structure on fuzzy congruence relations of a hypergroupoid},
4
Information Sciences, {bf 177} (2007), 3305-3313.
5
bibitem{4} A. B. Chakraborty and S. S. Khare, {it Fuzzy homomorphism and algebraic structures},
6
Fuzzy Sets and Systems, {bf 59} (1993), 211-221.
7
bibitem{5} P. Corsini, {it Prolegomena of hypergroup theory}, Second edition, Aviani Editor, 1993.
8
bibitem{6} P. Corsini, {it Join spaces, power sets, fuzzy sets}, Proc. 5th Internat.
9
Congress, Algebraic Hyperstructures and Appl., Iasi, Romani, 1993, Hadronic Press, (1994),45-52.
10
bibitem{7} P. Corsini and V. Leoreanu, {it Applications of hyperstructures theory}, Advanced
11
in Mathematics, Kluwer Academic Publisher, 2003.
12
bibitem{8} P. Corsini and I. Tofan, {it On fuzzy hypergroups}, Pure Math. Appl., {bf 8} (1997), 29-37.
13
bibitem{9} P. S. Das, {it Fuzzy groups and level subgroups}, J. Math. Anal. Apple., {bf 85} (1981), 264-269.
14
bibitem{10} B. Davvaz, {it Fuzzy $H_v$-groups}, Fuzzy Sets and
15
Systems, {bf 101} (1999), 191-195.
16
bibitem{11} B. Davvaz, {it On connection between uncertainty algebraic hypersystems and probability
17
spaces}, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems, {bf 13(3)} (2005), 337-345.
18
bibitem{12} B. Davvaz, {it Approximations in $n$-ary algebraic systems}, Soft Computing, {bf 12} (2008), 409-418.
19
bibitem{13} B. Davvaz, {it On $H_v$-groups and fuzzy homomorphism}, The Journal of Fuzzy Mathematics
20
{bf 9(2)} (2001), 271-278.
21
bibitem{14} B. Davvaz, {it A brief survey of the theory of $H_v$-structures},
22
Proc. 8th INT. Congress on AHA, Greece, 2002, Spanidis Press, (2003), 39-70.
23
bibitem{15} B. Davvaz and T. Vougiouklis, {it $n$-ary hypergroups},
24
Iranian Journal of Science and Technology, Transaction A, {bf 30(A2)} (2006), 165-174.
25
bibitem{16} B. Davvaz and P. Corsini, {it Fuzzy $n$-ary hypergroups}, Journal of Intelligent and Fuzzy
26
Systems, {bf 18(4)} (2007), 377-382.
27
bibitem{17} B. Davvaz and W. A. Dudek, {it Fuzzy $n$-ary groups as a generalization of Rosenfeld's fuzzy groups},
28
Journal of Multiple-Valued Logic and Soft Computing, {bf 15(5-6)} (2009), 451-469.
29
bibitem{18} W. D{"o}rnte, {it Unterschungen uber einen verallgemeinerten gruppenbegriff}, Math.Z.,
30
{bf 6} (1929), 1-19.
31
bibitem{19} W. A. Dudek, {it Fuzzification of $n$-ary groupoids},
32
Quasigroups and Related Systems, {bf 7} (2000), 45-66.
33
bibitem{20} W. A. Dudek, {it Idempotents in $n$-ary semigroups}, Southeast Asian Bull. Math.,
34
{bf 25} (2001), 97-104.
35
bibitem{21} F. Jin-Xuan, {it Fuzzy homomorphism and fuzzy isomorphism}, Fuzzy Sets
36
and Systems, {bf 63} (1994), 237-242.
37
bibitem{22} E. Kasner, {it An extension of the group concept}
38
(reported by L. G. Weld), Bull. Amer. Math. Soc., {bf 10 }(1904), 290-291.
39
bibitem{23} M. Koskas, {it Groupoides, Demi-hypergroupes et hypergroupes}, J. Math. Pures et Appl., {bf 49} (1970),
40
155--192.
41
bibitem{24} V. Leoreanu, {it About hyperstructures associated with fuzzy sets of type 2},
42
Italian J. Pure Appl. Math., {bf 17} (2005), 127-136.
43
bibitem{25} V. Leoreanu-Fotea and B. Davvaz, {it $n$-hypergroups and
44
binary relations}, European Journal of Combinatorics, {bf 29} (2008), 1207-1218.
45
bibitem{26} S. Y. Li, D. G. Chen, W. X. Gu and H. Wang, {it Fuzzy homomorphisms},
46
Fuzzy Sets and Systems, {bf 79} (1996), 235-238.
47
bibitem{27} F. Marty, {it Sur une generalization de la notion de group}, 8th Congress Math.
48
Scandenaves, Stockholm, (1934), 45-49.
49
bibitem{28} P. P. Ming and Y. M. Ming, {it Fuzzy topology I, neighborhood structure of a fuzzy point and Moors-Smith
50
convergence}, J. Math. Anal., {bf 76} (1980), 571-599.
51
bibitem{29} A. Rosenfeld, {it Fuzzy groups}, J. Math. Anal. Appl., {bf 35} (1971), 512-517.
52
bibitem{30} B. K. Sarma and T. Ali, {it Weak and strong fuzzy homomorphisms of groups},
53
J. Fuzzy Math., {bf 12} (2004), 357-368.
54
bibitem{31} S. Sebastian and S. Babu Sunder, {it Fuzzy groups and group homomorphisms},
55
Fuzzy Sets and Systems, {bf 81} (1996), 397-401.
56
bibitem{32} T. Vougiouklis, {it Hyperstructures and their representations}, Hadronic Press, Inc,
57
115, Palm Harber, USA, 1994.
58
bibitem{33} T. Vougiouklis, {it The fundamental relation in hyperrings. The
59
general hyperfield}, Proc. Fourth Int. Congress on Algebraic Hyperstructures
60
and Applications (AHA 1990), World Scientific, (1991), 203-211.
61
bibitem{34} L. A. Zadeh, {it Fuzzy sets}, Information and Control, {bf 8} (1965), 338-353.
62
bibitem{35} M. Mashinchi and M. M. Zahedi, {it A counter-example of P. S. Das's paper},
63
Journal of Mathematical Analysis and Applications, {bf 153(2)} (1990), 591-592.
64
bibitem{36} M. M. Zahedi, M. Bolurian and A. Hasankhani, {it On
65
polygroups and fuzzy subpolygroups}, J. Fuzzy Math., {bf 3} (1995), 1-15.
66
ORIGINAL_ARTICLE
FUZZIFYING CLOSURE SYSTEMS AND CLOSURE
OPERATORS
In this paper, we propose the concepts of fuzzifying closure systems and Birkhoff fuzzifying closure operators. In the framework of fuzzifying mathematics, we find that there still exists a one to one correspondence between fuzzifying closure systems and Birkhoff fuzzifying closure operators as in the case of classical mathematics. In the aspect of category theory, we prove that the category of fuzzifying closure system spaces is isomorphic to the category of Birkhoff fuzzifying closure spaces. In addition, we obtain an important result that the category of fuzzifying closure spaces and that of fuzzifying closure system spaces can be both embedded in the category of Birkhoff 𝐼 -closure spaces. Finally, using fuzzifying closure systems of the paper, we introduce a set of separation axioms in fuzzifying closure system spaces, which offer a try how to research the properties of spaces by fuzzifying closure systems.
http://ijfs.usb.ac.ir/article_239_4b07e5de579748d34a7d4f9ffee36621.pdf
2011-02-13T11:23:20
2017-09-21T11:23:20
77
94
10.22111/ijfs.2011.239
Fuzzifying closure operator
Fuzzifying closure system
Isomorphism
of categories
Embedding of categories
Fuzzifying remote neighborhood system
Separation axioms
Xiaoli
Luo
luosixi@yahoo.cn
true
1
Department of Mathematics, Ocean University of China, Qingdao 266071,
People’s Republic of China
Department of Mathematics, Ocean University of China, Qingdao 266071,
People’s Republic of China
Department of Mathematics, Ocean University of China, Qingdao 266071,
People’s Republic of China
LEAD_AUTHOR
Jinming
Fang
jinming-fang@163.com
true
2
Department of Mathematics, Ocean University of China, Qingdao
266071, People’s Republic of China
Department of Mathematics, Ocean University of China, Qingdao
266071, People’s Republic of China
Department of Mathematics, Ocean University of China, Qingdao
266071, People’s Republic of China
AUTHOR
[1] J. Ad´𝑎mek, H. Herrlich and G. E. Srreker, Abstract and concrete categories, Wiley, New York,
1
[2] R. Bˇelohl´avek, Fuzzy closure operators, J. Math. Anal. Appl., 262 (2001), 473-489.
2
[3] M. ´Ciri´c, J. Ignjatovi´c and S. Bogdanovi´c, Fuzzy equivalence relations and their equivalence
3
classes, Fuzzy Sets and Systems, 158 (2007), 1259-1313.
4
[4] J. Fang, 𝐼-fuzzy Alexandrov topologies and specialization orders, Fuzzy Sets and Systems, 158
5
(2007), 2359-2374.
6
[5] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, Continuous
7
lattices and domains, Cambridge University Press, 2003.
8
[6] B. Hutton and I. Reilly, Separation axioms in fuzzy topological spaces, Fuzzy Sets and Systems,
9
3 (1980), 93-104.
10
[7] F. H. Khedr, F. M. Zeyada and O. R. Sayed, On separation axioms in fuzzifying topology,
11
Fuzzy Sets and Systems, 119 (2001), 439-458.
12
[8] R. Lowen and L. Xu, Alternative characterizations of FNCS, Fuzzy Sets and Systems, 104
13
(1999), 381-391.
14
[9] A. S. Mashhour and M. H. Ghanim, Fuzzy closure spaces, J. Math. Anal. Appl., 106 (1985),
15
[10] J. Shen, Separation axioms in fuzzifying topology, Fuzzy Sets and Systems, 57 (1993), 111-
16
[11] S. P. Sinha, Separation axioms in fuzzy topological spaces, Fuzzy Sets and Systems, 45 (1992),
17
[12] R. Srivastava, A. K. Srivastava and A. Choubey, Fuzzy closure spaces, J. Fuzzy Math., 2
18
(1994), 525-534.
19
[13] R. Srivastava and M. Srivastava, On 𝑇0- and 𝑇1-fuzzy closure spaces, Fuzzy Sets and Systems,
20
109 (2000), 263-269.
21
[14] M. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems, 39 (1991), 303-321.
22
[15] Y. Yue and J. Fang, On separation axioms in 𝐼-fuzzy topological spaces, Fuzzy Sets and
23
Systems, 157 (2006), 780-793.
24
[16] W. Zhou, Generalization of 𝐿-closure spaces, Fuzzy Sets and Systems, 149 (2005), 415-432.
25
ORIGINAL_ARTICLE
SEMISIMPLE SEMIHYPERGROUPS IN TERMS OF
HYPERIDEALS AND FUZZY HYPERIDEALS
In this paper, we define prime (semiprime) hyperideals and prime(semiprime) fuzzy hyperideals of semihypergroups. We characterize semihypergroupsin terms of their prime (semiprime) hyperideals and prime (semiprime)fuzzyh yperideals.
http://ijfs.usb.ac.ir/article_255_bb68e07ae3f0a44c6e035530baa661f9.pdf
2011-02-15T11:23:20
2017-09-21T11:23:20
95
111
10.22111/ijfs.2011.255
Semihypergroups
Prime (semiprime) hyperideals of semihypergroups
Prime (semiprime) fuzzy hyperideals of semihypergroups
Semisimple semihypergroups
Piergiulio
Corsini
piergiulio.corsini@uniud.it, corsini2002@yahoo.com
true
1
Department of Civil Engineering and Architecture, Via delle
Scienze 206, 33100 Udine, Italy
Department of Civil Engineering and Architecture, Via delle
Scienze 206, 33100 Udine, Italy
Department of Civil Engineering and Architecture, Via delle
Scienze 206, 33100 Udine, Italy
LEAD_AUTHOR
Muhammad
Shabir
mshabirbhatti@yahoo.co.uk
true
2
Department of Mathematics, Quaid-i-Azam University, Islamabad-
45320, Pakistan
Department of Mathematics, Quaid-i-Azam University, Islamabad-
45320, Pakistan
Department of Mathematics, Quaid-i-Azam University, Islamabad-
45320, Pakistan
AUTHOR
Tariq
Mahmood
tmhn3367@gmail.com
true
3
Department of Mathematics, Quaid-i-Azam University, Islamabad-
45320, Pakistan
Department of Mathematics, Quaid-i-Azam University, Islamabad-
45320, Pakistan
Department of Mathematics, Quaid-i-Azam University, Islamabad-
45320, Pakistan
AUTHOR
[1] J. Ahsan, K. Saifullah and M. F. Khan, Semigroups characterized by thier fuzzy ideals, Fuzzy
1
systems and Math., 9 (1995) 29-32.
2
[2] A. H. Clifford and G. B. Preston, The algebraic theory of semigroups, AMS, Math., Surveys,
3
Providence, R. I., 1&2(7) (1961/67).
4
[3] P. Corsini, Join spaces, power sets, fuzzy sets, Proceedings of the 5th International Congress
5
on Aigebraic Hyperstructures and Applications 1993, Isai, Romania, Hadronic Press, 1994.
6
[4] P. Corsini, New themes of research on hyperstructures associated with fuzzy sets., J. of Basic
7
Science, Mazandaran, Iran, 2(2) (2003), 25-36.
8
[5] P. Corsini, A new connection between hypergroups and fuzzy sets., Southeast Bul. of Math.,
9
27 (2003), 221-229.
10
[6] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publishers,
11
Dordrecht, Hardbound, 2003.
12
[7] I. Cristea, Hyperstructures and fuzzy sets endowed with two membership functions, Fuzzy
13
Sets and Systems, 160 (2009), 1114-1124.
14
[8] I. Cristea, About the fuzzy grade of the direct product of two hypergroupoids, Iranian Journal
15
of FuzzySy stems, 7(2) (2010), 95-108.
16
[9] B. Davvaz, Fuzzy hyperideals in semihypergroups, Italian J. Pure and Appl. Math., 8 (2000),
17
[10] B. Davvaz, Strong regularity and fuzzy strong regularity in semihypergroups., Korean J. Comput.
18
& Appl. Math., 7(1) (2000), 205-213.
19
[11] A. Hasankhani, Ideals in a semihypergroup and Green’s relations., Ratio Mathematica, 13
20
(1999), 29-36.
21
[12] A. Kehagias, Lattice-fuzzy meet and join hyperoperations, Proceedings of the 8th International
22
Congress on AHA and Appl., Samothraki, Greece, (2003), 171-182.
23
[13] N. Kuroki, Fuzzy bi-ideals in semigroups, Comment. Math. Univ. St. Paul., 28 (1979) 17-21.
24
[14] V. Leoreanu, About hyperstructures associated with fuzzy sets of type 2., Italian J. of Pure
25
and Appl. Math., 17 (2005), 127-136.
26
[15] F. Marty, Sur une generalization de la notion de groupe, 8𝑖𝑒𝑚 Congress Math. Scandinaves,
27
Stockholm, (1934), 45-49.
28
[16] J. N. Mordeson, D. S. Malik and N. Kuroki, Fuzzy semigroups, Springer, 2003.
29
[17] M. Stefanescu and I. Cristea, On the fuzzy grade of hypergroups, FuzzySets and Systems,
30
159(9) (2008), 1097-1106
31
[18] I. Tofan and A. C. Volf, On some connections between hyperstructures and fuzzy sets, Italian
32
J. of Pure and Appl. Math., 7 (2000), 63-68.
33
[19] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
34
ORIGINAL_ARTICLE
SOME HYPER K-ALGEBRAIC STRUCTURES INDUCED BY
MAX-MIN GENERAL FUZZY AUTOMATA
We present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. First, we introduce a hyper BCK-algebra induced by a max-min general fuzzy automaton. Then, we study the properties of this hyper BCK-algebra. Particularly, some theorems and results for hyper BCK-algebra are proved. For example, it is shown that this structure consists of different types of (positive implicative) commutative hyper K-ideals. As a generalization, we extend the definition of this hyper BCK-algebra to a bounded hyper K-algebra and obtain relative results.
http://ijfs.usb.ac.ir/article_256_71305226c332631bc2f1b6569fe5e508.pdf
2011-02-16T11:23:20
2017-09-21T11:23:20
113
134
10.22111/ijfs.2011.256
(Positive implicative) Commutative hyper K-ideal
(Bounded) Hyper
BCK-algebra
Hyper BCK-ideal
Max-min general fuzzy automata
khadijeh
Abolpour
abolpor kh@yahoo.com
true
1
Department of Mathematics, Islamic Azad University, Kerman
Branch, Kerman, Iran
Department of Mathematics, Islamic Azad University, Kerman
Branch, Kerman, Iran
Department of Mathematics, Islamic Azad University, Kerman
Branch, Kerman, Iran
LEAD_AUTHOR
Mohammad Mehdi
Zahedi
zahedi mm@modares.ac.ir
true
2
Department of Mathematics, Tarbiat Modares University,
Tehran, Iran
Department of Mathematics, Tarbiat Modares University,
Tehran, Iran
Department of Mathematics, Tarbiat Modares University,
Tehran, Iran
AUTHOR
Masoome
Golmohamadian
true
3
Department of Mathematics, Tarbiat Modares University,
Tehran, Iran
Department of Mathematics, Tarbiat Modares University,
Tehran, Iran
Department of Mathematics, Tarbiat Modares University,
Tehran, Iran
AUTHOR
[1] M. A. Arbib, From automata theory to brain theory, Int. J. Man-Machine Stud., 7(3) (1975),
1
[2] W. R. Ashby, Design for a brain, Chapman and Hall, London, 1954.
2
[3] R. A. Borzooei, Hyper BCK and K-algebras, Ph.D. Thesis, Department of Mathematics,
3
Shahid Bahonar University of Kerman, Iran, 2000.
4
[4] R. A. Borzooei, A. Hasankhani, M. M. Zahedi and Y. B. Jun, On hyper K-algebras, Scientiae
5
Mathematicae Japonica, 52(1) (2000), 113-121.
6
[5] A. W. Burks, Logic, biology and automata-some historical reflections, Int. J. Man-Machine
7
Stud., 7(3) (1975), 297-312.
8
[6] P. Corsini, Prolegomena of hyper group theory, Avian Editor, Italy, 1993.
9
[7] P. Corsini and V. Leoreanu, Applications of hyper structure theory, Advances in Mathematics,
10
Kluwer Academic Publishers, 5 (2003).
11
[8] M. Doostfatemeh and S. C. Kremer, New directions in fuzzy automata, International Journal
12
of Approximate Reasoning, 38 (2005), 175-214.
13
[9] J. E. Hopcroft, R. Motwani and J. D. Ullman, Introduction to automata theory, languages
14
and computation, seconded, Addison-Wesley, Reading, MA, 2001.
15
[10] M. Horry and M. M. Zahedi, Uniform and semi-uniform topology on general fuzzy automata,
16
Iranian Journal of Fuzzy Systems, 6(2) (2009), 19-29.
17
[11] M. Horry and M. M. Zahedi, Hypergroups and general fuzzy automata, Iranian Journal of
18
Fuzzy Systems, 6(2) (2009), 61-74.
19
[12] Y. Imai and K. Iseki, On axiom systems of propositional calculi, XIV Proc. Japan Academy,
20
42 (1966), 19-22.
21
[13] D. S. Malik and J. N. Mordeson, Fuzzy discrete structures, Physica-Verlag, NewY ork, 2000.
22
[14] F. Marty, Sur une generalization de la notion de groups, 8th Congress Math. Scand naves,
23
Stockholm, (1934), 45-49.
24
[15] W. S. McCulloch and W. Pitts, A logical calculus of the ideas immanent in nervous activity,
25
Bull. Math. Biophysics., 5 (1943), 115-133.
26
[16] J. Meng and Y. B. Jun, BCK-algebra, Kyung Moons, Co., Seoul, 1994.
27
[17] M. L. Minsky, Computation: finite and infinite machines, Prentice-Hall, Englewood Cliffs,
28
NJ, Chapter 3, (1967), 32-66.
29
[18] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages, theory and applications,
30
Chapman and Hall/CRC, London/Boca Raton, FL, 2002.
31
[19] M. A. Nasr Azadani and M. M. Zahedi, S-absorbing set and (P)-decomposition in hyper
32
K-algebras, Italian Journal of Pure and Applied Mathematics, to appear.
33
[20] W. Omlin, K. K. Giles and K. K. Thornber, Equivalence in knowledge representation: automata,
34
runs, and dynamicfuzzy systems, Proc. IEEE, 87(9) (1999), 1623-1640.
35
[21] W. Omlin, K. K. Thornber and K. K. Giles, Fuzzy finite-state automata can be deterministically
36
encoded into recurrent neural networks, IEEE Trans. Fuzzy Systems, 5(1) (1998),
37
[22] T. Roodbari, Positive implicative and commutative hyper K-ideals, Ph.D. Thesis, Department
38
of Mathematics, Shahid Bahonar University of Kerman, Iran, 2008.
39
[23] T. Roodbari, L. Torkzadeh and M. M. Zahedi, Normal hyper K-algebras, Sciatica Mathematical
40
Japonica, 68(2) (2008), 265-278.
41
[24] T. Roodbari and M. M. Zahedi, Positive implicative hyper K-ideals II, Scientiae Mathematicae
42
Japonica, 66(3) (2007), 391-404.
43
[25] L. Torkzadeh, Dual positive implicative and commutative hyper K-ideals, Ph.D. Thesis, Department
44
of Mathematics, Shahid Bahonar University of Kerman, Iran, 2005.
45
[26] L. Torkzadeh, T. Roodbari and M. M. Zahedi, Hyper stabilizers and normal hyper BCKalgebras,
46
Set-Valued Mathematics and Applications, to appear.
47
[27] A. Turing, On computable numbers, with an application to the entscheidungs problem, Proc.
48
London Math. Soc., 42 (1936-37), 220-265.
49
[28] J. Von Neumann, Theory of self-reproducing automata, University of Illinois Press, Urbana,
50
[29] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept
51
to pattern classification, Ph.D. Thesis, Purdue University, Lafayette, IN, 1967.
52
[30] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
53
[31] M. M. Zahedi, R. A. Borzooei and H. Rezaei, Some classifications of hyper K-algebra of order
54
3, Math. Japon., (2001), 133-142.
55
[32] M. M. Zahedi, M. Horry and K. Abolpor, Bifuzzy (general) topology on max-min general
56
fuzzy automata , Advances in Fuzzy Mathematics, 3(1) (2008), 51-68.
57
ORIGINAL_ARTICLE
NORM AND INNER PRODUCT ON FUZZY LINEAR SPACES
OVER FUZZY FIELDS
In this paper, we introduce the concepts of norm and inner prod- uct on fuzzy linear spaces over fuzzy elds and discuss some fundamental properties.
http://ijfs.usb.ac.ir/article_257_86f80c9af851736ee66c2d110c3055f3.pdf
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10.22111/ijfs.2011.257
Fuzzy fields
Fuzzy linear spaces
Norm on fuzzy linear spaces
Inner
product on fuzzy linear spaces
C. P.
Santhosh
santhoshcpchu@yahoo.co.in
true
1
Department of Mathematical Sciences, Kannur University, Man-
gattuparamba, Kannur, Kerala, 670 567, India.
Department of Mathematical Sciences, Kannur University, Man-
gattuparamba, Kannur, Kerala, 670 567, India.
Department of Mathematical Sciences, Kannur University, Man-
gattuparamba, Kannur, Kerala, 670 567, India.
LEAD_AUTHOR
T. V.
Ramakrishnan
ramakrishnantv@rediffmail.com
true
2
Department of Mathematical Sciences, Kannur University, Man-
gattuparamba, Kannur, Kerala, 670 567, India.
Department of Mathematical Sciences, Kannur University, Man-
gattuparamba, Kannur, Kerala, 670 567, India.
Department of Mathematical Sciences, Kannur University, Man-
gattuparamba, Kannur, Kerala, 670 567, India.
AUTHOR
[1] T. Bang and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math.,
1
11(3) (2003), 687-705.
2
[2] R. Biswas, Fuzzy inner product spaces and fuzzy norm functions, Information Sciences, 53
3
(1991), 185-190.
4
[3] S. C. Cheng and J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces,
5
Bull. Calcutta Math. Soc., 86(5) (1994), 429-436.
6
[4] A. M. El-Abyad and H. M. El-Hamouly, Fuzzy inner product spaces, Fuzzy Sets and Systems,
7
44(2) (1991), 309-326.
8
[5] C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48(2)
9
(1992), 239-248.
10
[6] C. Felbin, Finite dimensional fuzzy normed linear space. II, Journal of Analysis, 7 (1999),
11
[7] M. Goudarzi and S. M. Vaezpour, On the denition of fuzzy Hilbert spaces and its application,
12
J. Nonlinear Sci. Appl., 2(1) (2009), 46-59.
13
[8] A. K. Katsaras, Fuzzy topological vector spaces. II, Fuzzy Sets and Systems, 12(2) (1984),
14
[9] G. J. Klir and B. Yuan, Fuzzy sets and fuzzy logic: theory and applications, Prentice-Hall of
15
India, New Delhi, 2002.
16
[10] J. K. Kohli and R. Kumar, On fuzzy inner product spaces and fuzzy co-inner product spaces,
17
Fuzzy Sets and Systems, 53(2) (1993), 227-232.
18
[11] S. V. Krishna and K. K. M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets and
19
Systems, 63(2) (1994), 207-217.
20
[12] R. Saadati and S. M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math. and
21
Computing, 17 (2005), 475-484.
22
[13] S. M. Vaezpour and F. Karimi, t-best approximation in fuzzy normed spaces, Iranian Journal
23
of Fuzzy Systems, 5(2) (2008), 93-99.
24
[14] G. Wenxiang and L. Tu, Fuzzy linear spaces, Fuzzy Sets and Systems, 49 (1992), 377-380.
25
[15] C. Wu and J. Fang, Fuzzy generalization of Kolmogoros theorem, J. Harbin Inst. Technol.,
26
1 (1984), 1-7.
27
[16] J. Xiao and X. Zhu, On linearly topological structure and property of fuzzy normed linear
28
space, Fuzzy Sets and Systems, 125(2) (2002), 153-161.
29
[17] H. J. Zimmermann, Fuzzy set theory and its applications (second revised edition), Allied
30
Publishers Limited, New Delhi, 1996.
31
ORIGINAL_ARTICLE
VAGUE RINGS AND VAGUE IDEALS
In this paper, various elementary properties of vague rings are obtained. Furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.
http://ijfs.usb.ac.ir/article_258_c7c6d1457f353b46765c5eee7dd0ef9b.pdf
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10.22111/ijfs.2011.258
Vague group
Generalized vague subgroup
Vague ring
Vague subring
Vague ideal
Vague prime ideal
Vague maximal ideal
Sevda
Sezer
sevdasezer@yahoo.com , sevdasezer@akdeniz.edu.tr
true
1
Faculty of Education, Akdeniz University, 07058, Antalya, Turkey
Faculty of Education, Akdeniz University, 07058, Antalya, Turkey
Faculty of Education, Akdeniz University, 07058, Antalya, Turkey
LEAD_AUTHOR
[1] M. Demirci, Fuzzy functions and their fundamental properties, Fuzzy Sets and Systems, 106
1
(1999), 239-246.
2
[2] M. Demirci, Vague groups, J. Math. Anal. Appl., 230 (1999), 142-156.
3
[3] M. Demirci, Fundamentals of M-vague algebra and M-vague arithmetic operations, Int. J.
4
Uncertain. Fuzziness Knowl.-Based Syst., 10 (2002), 25-75.
5
[4] M. Demirci, Foundations of fuzzy functions and vague algebra based on many-valued equivalence
6
relations, part I: fuzzy functions and their applications, Int. J.Gen. Syst., 32(2) (2003),
7
[5] M. Demirci, Foundations of fuzzy functions and vague algebra based on many-valued equivalence
8
relations, part II: vague algebraic notions, Int. J. Gen. Syst., 32(2) (2003), 157-175.
9
[6] M. Demirci, Foundations of fuzzy functions and vague algebra based on many-valued equivalence
10
relations, part III: constructions of vague algebraic notions and vague arithmetic
11
operations, Int. J. Gen. Syst., 32(2) (2003), 177-201.
12
[7] M. Demirci and D. Coker, Remarks on vague groups, J. Fuzzy Math., 10 (2002), 657-668.
13
[8] M. Demirci and J. Recasens, Fuzzy groups, fuzzy functions and fuzzy equvalence relation,
14
Fuzzy Sets ans Systems, 144 (2004), 441-458.
15
[9] P. Dheena and S. Coumaressane, Characterization of regular Γ-semigroups through fuzzy
16
ideals, Iranian Journal of Fuzzy Systems, 4(2) (2007), 57-68.
17
[10] Y. B. Jun and C. H. Park, Ideals of pseudo MV-algebras based on vague set theory, Iranian
18
Journal of Fuzzy Systems, 6(2) (2009), 31-45.
19
[11] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
20
[12] S. Sezer, Vague subgroups, 15th Turkish National Mathematical Symposium Procedings-
21
Mersin University/Turkey (in Turkish), (2004), 119-133 .
22
[13] S. Sezer, Vague groups and generalized vague subgroups on the basis of ([0, 1],≤,∧), Information
23
Sciences, 174 (2005), 123-142.
24
[14] S. Sezer, Vague normal subgroups, J. Fuzzy Math., 16(3) (2008).
25
ORIGINAL_ARTICLE
Persian-translation vol.8,no.1- February 2011
http://ijfs.usb.ac.ir/article_2875_306b1941e5189f522993186d670bc66f.pdf
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10.22111/ijfs.2011.2875