ORIGINAL_ARTICLE
Cover Special Issue vol. 9, no. 6, December 2012
http://ijfs.usb.ac.ir/article_2806_bf0b8dbee5c9d7b98ae157ca9754c9e1.pdf
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10.22111/ijfs.2012.2806
ORIGINAL_ARTICLE
CREDIBILITY-BASED FUZZY PROGRAMMING MODELS TO
SOLVE THE BUDGET-CONSTRAINED FLEXIBLE
FLOW LINE PROBLEM
This paper addresses a new version of the exible ow line prob- lem, i.e., the budget constrained one, in order to determine the required num- ber of processors at each station along with the selection of the most eco- nomical process routes for products. Since a number of parameters, such as due dates, the amount of available budgets and the cost of opting particular routes, are imprecise (fuzzy) in practice, they are treated as fuzzy variables. Furthermore, to investigate the model behavior and to validate its attribute, we propose three fuzzy programming models based upon credibility measure, namely expected value model, chance-constrained programming model and dependent chance-constrained programming model, in order to transform the original mathematical model into a fuzzy environment. To solve these fuzzy models, a hybrid meta-heuristic algorithm is proposed in which a genetic al- gorithm is designed to compute the number of processors at each stage; and a particle swarm optimization (PSO) algorithm is applied to obtain the op- timal value of tardiness variables. Finally, computational results and some concluding remarks are provided.
http://ijfs.usb.ac.ir/article_110_4cdee35db4712858ef8408c9704bade8.pdf
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29
10.22111/ijfs.2012.110
Budget-constrained
exible
ow lines
Credibility-based fuzzy pro-
gramming
Meta-heuristic
Genetic Algorithm
particle swarm optimization
Ali
Ghodratnama
ghodratn@ut.ac.ir
true
1
Department of Industrial Engineering, College of Engineering,
University of Tehran, Tehran, Iran
Department of Industrial Engineering, College of Engineering,
University of Tehran, Tehran, Iran
Department of Industrial Engineering, College of Engineering,
University of Tehran, Tehran, Iran
AUTHOR
Seyed Ali
Torabi
satorabi@ut.ac.ir
true
2
Department of Industrial Engineering, College of Engineering,
University of Tehran, Tehran, Iran
Department of Industrial Engineering, College of Engineering,
University of Tehran, Tehran, Iran
Department of Industrial Engineering, College of Engineering,
University of Tehran, Tehran, Iran
LEAD_AUTHOR
Raza
Tavakkoli-Moghaddam
tavakoli@ut.ac.ir
true
3
Department of Industrial Engineering, College of En-
gineering, University of Tehran, Tehran, Iran
Department of Industrial Engineering, College of En-
gineering, University of Tehran, Tehran, Iran
Department of Industrial Engineering, College of En-
gineering, University of Tehran, Tehran, Iran
AUTHOR
[1] S. Abbasbandy and M. Alavi, A method for solving fuzzy linear systems, Iranian Journal of
1
Fuzzy Systems, 2(2) (2005),37-43.
2
[2] H. Allaoui and A. Artiba, Scheduling two-stage hybrid flow shop with availability constraints,
3
Computers and Operations Research, 33(5) (2006),1399-1419.
4
[3] V. A. Amentano and D. P. Ronconi, Tabu search for total tardiness minimization in flow
5
shop scheduling problems, Computers and Operations Research, 26(3) (1999), 219-235.
6
[4] M. Asano and H. Ohta, Single machine scheduling using dominance relation to minimize
7
earliness subject to ready and due times, Production Economics, 64(1-3) (1996), 101-111.
8
[5] V. Botta-Genoulaz, Hybrid flow-shop scheduling with precedence constrains and time legs to
9
minimize maximum lateness, Production Economics, 64(1-3) (2000), 101-111.
10
[6] J. M. Cadenas and J. L. Verdegay, A primer on fuzzy optimization models and methods,
11
Iranian Journal of Fuzzy Systems, 3(1) (2006), 1-21.
12
[7] J. Chang, W. Yan and H. Shao, Scheduling a two stage no wait hybrid flow shop with separated
13
setup and removal times, Proceedings of the American Control Conference, Boston, MA,
14
United states, 2(2) (2004), 1412-1416.
15
[8] R. C. Eberhart and J. Kennedy, A new optimizer using particle swarm theory, Proceedings
16
of the sixth International Symposium on Micromachine and Human Science, (1995), 9-43.
17
[9] M. B. Fakhrzad and M. Heydari, Flexible flow-lines model at m machine centers with fuzzy
18
total costs, Applied Sciences, 8(11) (2008), 2059-2066.
19
[10] M. Hapke and R. Slowinski, Fuzzy priority heuristic for project Scheduling, Fuzzy Sets and
20
Systems, 83(3) (1996),291-299.
21
[11] J. Holland, Adaptation in natural and artificial systems, University of Michigan Press, (1975),
22
Second Edition: MIT Press, 1992.
23
[12] J. Holland, Hierarchical descriptions, universal spaces, and adaptive systems, In: Arthur W.
24
Burks, Editor. Essays on Cellular Automata. University of Illinois Press, 1970.
25
[13] J. Holland, Iterative circuit computers, In: Proc. Western Joint Comp. Conf, (1960), 259-265.
26
[14] J. Holland, Outline for a logical theory of adaptive systems, JACM, 9(3) (1962), 279-314.
27
[15] X. Huang, Chance-constrained programming models for capital budgeting with NPV as fuzzy
28
parameters, Computational and Applied Mathematics, 198 (2007), 149-159.
29
[16] X. Huang, Metaheuristic approaches to the hybrid flow shop scheduling problem with a costrelated
30
criterion, Production Economics, 105(2) (2007), 407-424.
31
[17] Z. Jin, Z. Yang and T. Ito, Methaheuristics algorithms for the multi stage hybrid flow shop
32
scheduling problem, Production Economics, 100(2) (2006), 322-334.
33
[18] M. Kolonko, Methaheuristics algorithms for the multi stage hybrid flow shop scheduling problem
34
, European Journal of Operational Research, 113(1) (1999), 123-136.
35
[19] T. Konno and H. Ishii, An open shop scheduling problem with fuzzy allowable time and fuzzy
36
resource constraint, Fuzzy Sets and Systems, 109(1) (2000), 141-147.
37
[20] M. E. Kurz and R. G. Askin, Comparing scheduling rules for flexible flow lines, Production
38
Economics, 85(3) (2003), 371-388.
39
[21] G. J. Kyparisis and C. Koulamas, A note on weighted completion time minimization in a
40
flexible flow shop, Operation Research Letter, 29(1) (2001), 5-11.
41
[22] H. T. Lin and C. Liao, A case study in a two-stage hybrid flow-shop with set up time and
42
dedicated machines, Production Economics, 86(2) (2003), 133-143.
43
[23] M. Litoiu and R. Tadei, Real-time task scheduling with fuzzy deadlines and processing times,
44
Fuzzy Sets and Systems, 117(1) (2001), 34-45.
45
[24] B. Liu and K. Iwamura, Chance-constrained programming with fuzzy parameters, Fuzzy Sets
46
and Systems, 94 (1998), 227-237.
47
[25] B. Liu and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE
48
Transactions on Fuzzy Systems, 10 (2002), 445-450.
49
[26] B. Liu, Dependent-chance programming with fuzzy decisions, IEEE Transactions on Fuzzy
50
Systems, 7(3) (1999), 354-360.
51
[27] B. Liu, Uncertainty Theory: An Introduction to its Axiomatic Foundations, Springer, Berlin,
52
[28] C. Y. Liu and S. C. Chang, Scheduling flexible flow Shops with sequence-dependent set up
53
effects, IEEE Transactions. Robotics Automation, 16(1) (2000), 408-419.
54
[29] R. Logendran, S. Carson and E. Hanson, Group scheduling in flexible flow shops, Production
55
Economics, 96(2) (2005), 143-155.
56
[30] C. S. McCahon and E. S Lee, Job sequencing with fuzzy processing times, Computers Math-
57
ematics Application, 19(7) (1990), 31-41.
58
[31] E. Mehdizadeh, S. Sadi-Nezhad and R. Tavakkoli-Moghaddam, Optimization of fuzzy clustering
59
criteria by a hybrid pso and fuzzy c-means clustering algorithm, Iranian Journal of
60
Fuzzy Systems, 5(3) (2008), 1-14.
61
[32] H. Nezamabadi-Pour, S. Yazdani-Sharbabaki, M. M. Farsangi and M. Neyestani, A solution
62
to an economic dispatch problem by a fuzzy adaptive genetic algorithm, Iranian Journal of
63
Fuzzy Systems, 8(3) (2011), 1-21.
64
[33] E. C. Ozelkan and L. Duckstein, Optimal fuzzy counterparts of scheduling rules, European
65
Journal of Operational Research, 113(3) (1999), 593-609.
66
[34] D. Peidro and P. Vasant, Fuzzy Multi-Objective Transportation Planning with Modified
67
SCurve Membership Function, In Proceedings of Global Conference on Power Control and
68
Optimization, 35 (2009), 101-110.
69
[35] S. Pugazhendhi, S. Thiagarajan, C. Rejendran and N. Anantharaman, Generating nonpermutation
70
schedules in flow line based manufacturing systems with sequence-dependent
71
setup times of jobs: a heuristic approach, Applied Management and Technology, 23(1)
72
(2004), 64-78.
73
[36] Z. Qin and X. Ji, Logistics network design for product recovery in fuzzy environment, Euro-
74
pean Journal of Operational Research, 202(2) (2010), 479-490.
75
[37] S. Ramezanzadeh and A. Heydari, Optimal control with fuzzy chance constraints, Iranian
76
Journal of Fuzzy Systems, In press.
77
[38] R. Ruiz and C. Maroto, A genetic algorithm for hybrid flow shops with sequence dependent
78
setup times and machine eligibility, European Journal of Operational Research, 169(3)
79
(2006), 781-800.
80
[39] R. Ruiz, F. Svirikaya-Serifoglu and T. Urlings, Technical report, polytechnic university of
81
valencia, Department of Applied Statistics and Operating Research, Spain, 2006.
82
[40] M. R. Sa, H. R. Maleki and E. Zaeimazad, A note on zimmermann method for solving fuzzy
83
linear programming problems, Iranian Journal of Fuzzy Systems, 4(2) (2007), 31-45.
84
[41] M. Sakawa and R. Kubota, Fuzzy programming for multi objective job shop scheduling with
85
fuzzy processing time and fuzzy due date through genetic algorithms, European Journal of
86
Operational Research, 120(2) (2000), 393-407.
87
[42] J. Salerno, Using the particle swarm optimization technique to train a recurrent neural model,
88
IEEE Transactions, International Conference on Tools with Articial Intelligence, (1997), 45-
89
[43] T. Sawik, Mixed integer programming for scheduling flexible flow lines with limited intermediate
90
buffers, Mathematical and Computer Modelling, 31 (2000), 39-52.
91
[44] Y. Shi and R. Eberhart, Particle swarm optimization: development, applications and resources
92
, IEEE Transaction, 3(1) (2001), 81-86.
93
[45] E. Shivanian, E. Khorram and A. Ghodousian, Optimization of linear objective function subject
94
to fuzzy relation inequalities constraints with max-average composition, Iranian Journal
95
of Fuzzy Systems, 4(2) (2007), 15-29.
96
[46] H. Tanaka, H. Ichihashi and K. Asai, A formulation of fuzzy linear programming problem
97
bases on comparison of fuzzy numbers, Control and Cybernetics, 13 (1984), 185-194.
98
[47] S. A. Torabi and E. Hassini, An interactive possibilistic programming approach for multiple
99
objective supply chain master planning, Fuzzy Sets and Systems, 159 (2008), 193-214.
100
[48] S. A. Torabi and E. Hassini, Multi-site production planning integrating procurement and
101
distribution plans in multi-echelon supply chains: an interactive fuzzy goal programming
102
approach, International Journal of Production Research, 47(19) (2009), 5475-5499.
103
[49] S. A. Torabi, M. Ebadian and R. Tanha, Fuzzy hierarchical production planning (with a case
104
study), Fuzzy Sets and Systems, 161 (2010), 1511-1529.
105
[50] S. Vob and A. Witt, Hybrid flow shop scheduling as a multi-mode multi-project scheduling
106
problem with batching requirements: a real-world application, International Journal of
107
Production Economics, 105(2) (2007), 445-458.
108
[51] L. Zadeh,Fuzzy sets, Information and Control, 8 (1965), 338-353.
109
[52] H. Zimmermann, Fuzzy programming and linear programming with several objective functions
110
, Fuzzy Sets and Systems, 1(1) (1978), 45-56.
111
ORIGINAL_ARTICLE
AN ALGEBRAIC STRUCTURE FOR INTUITIONISTIC
FUZZY LOGIC
In this paper we extend the notion of degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove some theorems to demonstrate our goal.
http://ijfs.usb.ac.ir/article_111_92936ce87ae15b80c0c9d17ae0d847e8.pdf
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10.22111/ijfs.2012.111
Intuitionistic fuzzy logic
residuated lattice
Intuitionistic fuzzy
implication
Esfandiar
Eslami
esfandiar.eslami@uk.ac.ir
true
1
Department of Mathematics, Faculty of Mathematics and Com-
puter, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Mathematics, Faculty of Mathematics and Com-
puter, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Mathematics, Faculty of Mathematics and Com-
puter, Shahid Bahonar University of Kerman, Kerman, Iran
LEAD_AUTHOR
bibitem{1 } K. T. Atanassov, {it Intuitionistic fuzzy sets}, Fuzzy Sets and Systems, {bf20} (1986), 87-96.
1
bibitem{2 } K. T. Atanassov and S. Stoeva, {it Intuitionistic L - fuzzy sets}, In: R. Trappl, ed., Elsevier Science Publishers B.V., Noth Holland, 1984.
2
bibitem{3 } K. T. Atanassov and G. Gargov, {it Elements of intuitionistic fuzzy logic. part I}, Fuzzy Sets and Systems, {bf95} (1998), 39-52.
3
bibitem{4 } M. Baczynski, {it Residual implications revisited}, Fuzzy Sets and Systems, {bf 145} (2004), 267- 277.
4
bibitem{5} P. Burillo and H. Bustince, {it Intuitionistic fuzzy relations. effects of Atanassov's operators on the properties of intuitionistic fuzzy relations}, Mathware & Soft Computing, {bf2} (1995), 117- 148.
5
bibitem{6} R. Cignoli and F. Esteva, {it Commutative integral bounded residuated lattices with an added involution}, Annals of Pure and Applied Logic, {bf161} (2009), 150-160.
6
bibitem{7} P. Cintula, {it From fuzzy logic to fuzzy mathematics}, Ph.D. Thesis, Technical University, Prague, 2005.
7
bibitem{8} C. Cornelis, G. Deschrijver and E. E. Kerre, {it Classification on intuitionistic fuzzy implicators: an algebraic approach}, In Proceedings of the FT & T' 02, Durham, North Carolina, 105-108.
8
bibitem{9} G. Deschrijver, C. Cornelis and E. E. Kerre, {it Intuitionistic fuzzy connectives revisited}, In Proceedings of IPMU'02, July 1-5, 2002.
9
bibitem{10} J. A. Goguen, {it L - Fuzzy sets}, Journal of Math. Anal. And Applications, {bf18} (1967), 145-173.
10
bibitem{11} P. Hajek, {it Metamathematics of fuzzy logic}, Trends in Logic, Kluwer Acad.Publ., Drdrecht, {bf4} (1998).
11
bibitem{12} P. Hajek, {it What is mathematical fuzzy logic?}, Fuzzy Sets and Systems, {bf157} ( 2006), 597-603.
12
bibitem{13} Y. Hong, X. Ruiping and F. Xianwen, {it Characterizing ordered semigroups by means of intuitionistic fuzzy bi- ideals}, Mathware & Soft Computing, {bf14} (2007), 57-66.
13
bibitem{14} H. Ono, {it Subsructural logics and ResiduatedLattices-an introduction}, Trends in Logic, {bf20} (2003), 177-212.
14
bibitem{15} P. Smets and P. Magrez, {it Implications in fuzzy logic}, Int. J. of Approximate Reasoning, {bf1} (1987), 327-347.
15
bibitem{16} E. Szmidt and J. Kacprzyk, {it Intuitiinistic fuzzy sets in some medical applications, computational intelligence}, Theory and Applications, Lecture Notes in Computer Science, (2001), V. 2206/2001, 148-151.
16
bibitem{17} E. Szmidt and K. Marta, {it Atanassov's intuitionistic fuzzy sets in classification of imbalanced and overlapping classes}, Studies in Computational Intelligence (SCI), {bf109} (2008), 455- 471.
17
bibitem{18}A. Tepavcevic and M. G. Ranitovic, {it General form of lattice valued intuitionistic fuzzy sets}, Computational Intelligence, Theory and Applications, {bf14} (2006), 375-381.
18
bibitem{19}A. Tepavcevic and T. Gerstenkorn, {it Lattice valued intuitionistic fuzzy sets}, Central European Journal of Mathematics, {bf2(3)} (2004), 388-398.
19
bibitem{20} E. Turunen, {it Mathematics behind fuzzy logic}, Advances in Soft Computing, Physica-Verlag, Heidelberg, 1999.
20
bibitem{21} I. K. Vlachos and G. D. Sergiadis, {it Towards Intuitionistic fuzzy image processing}, Proceedings of the 2005 International Conference on Computational Intelligence for Modelling, Control and Automation.
21
22
bibitem{22}M. Ward and R. P. Dilworth, {it"Residuated lattices", Trans. Amer. Math. Soc.}, {bf45} (1939), 335-54, Reprinted in Bogart, K, Freese, R., and Kung, J., eds., 1990.
23
24
bibitem{23} L. A. Zadeh, {it Fuzzy sets}, Information and Control, {bf8(3)} (1965), 338-353.
25
26
bibitem{24} L. A. Zadeh, {it Fuzzy sets, fuzzy logic and fuzzy systems}, Selected papers by Lotfi A. Zadeh, Editors George J. Klir and Bo Yuan, World Scientific, 1996.
27
ORIGINAL_ARTICLE
FUZZY GRADE OF THE COMPLETE HYPERGROUPS
This paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. The classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. Finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number
http://ijfs.usb.ac.ir/article_112_0ff69d8d879db7c0ac75b78249b3499f.pdf
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10.22111/ijfs.2012.112
Complete hypergroup
Join space
Fuzzy set
Fuzzy grade
Carmen
Angheluta
floryangheluta@yahoo.com
true
1
Faculty of Mathematics and Computer Science, University of
Bucharest, Str. Academiei 14, 010014 Bucharest, Romania
Faculty of Mathematics and Computer Science, University of
Bucharest, Str. Academiei 14, 010014 Bucharest, Romania
Faculty of Mathematics and Computer Science, University of
Bucharest, Str. Academiei 14, 010014 Bucharest, Romania
AUTHOR
Irina
Cristea
irinacri@yahoo.co.uk
true
2
Center for Systems and Information Technologies, University of
Nova Gorica, Vipavska 13, SI-5000, Nova Gorica, Slovenia
Center for Systems and Information Technologies, University of
Nova Gorica, Vipavska 13, SI-5000, Nova Gorica, Slovenia
Center for Systems and Information Technologies, University of
Nova Gorica, Vipavska 13, SI-5000, Nova Gorica, Slovenia
AUTHOR
[1] R. Ameri and M. M. Zahedi,typergroup and join space induced by a fuzzy subset, PU.M.A.,8(1997).
1
[2] R. Ameri and O. R. Dehghan,Dimension of fuzzy hypervector spaces, Iranian Journal of Fuzzy Systems,8(5) (2011), 149-166.
2
[3] C. Angheluta and I. Cristea,On Atanassov's intuitionistic fuzzy grade of complete hyper-groups, J. Mult.-Valued Logic Soft Comput., 20 (2013), 55-74.
3
[4] P. Corsini,Prolegomena of Hypergroups Theory, Aviani Editore, Tricesimo, 1993.
4
[5] P. Corsini,Join spaces, power sets, fuzzy sets , Proc. Fifth International Congress on A.H.A.,1993, Iasi, Romania, Hadronic Press, (1994), 45-52.
5
[6] P. Corsini,A new connection between hypergroups and fuzzy sets, Southeast Asian Bull.Math.,27(2003), 221-229.
6
[7] P. Corsini and I. Cristea,Fuzzy grade of i.p.s. hypergroups of order 7, Iranian Journal of Fuzzy Systems,1(2) (2004), 15-32.
7
[8] P. Corsini and I. Cristea,Fuzzy sets and non complete 1-hypergroups, An. St. Univ. vidiusConstanta,13(1)(2005), 27-54.
8
[9] P. Corsini and V. Leoreanu,Join spaces associated with fuzzy sets, J. Combin. Inform. Syst.Sci.,20(1-4) 1995), 293-303.
9
[10] P. Corsini and V. Leoreanu,Applications of hyperstructure theory, Kluwer Academic Pub-lishers, Advances in Mathematics, 2003.
10
[11] P. Corsini and V. Leoreanu-Fotea,On the grade of a sequence of fuzzy sets and join spacesdetermined by a hypergraph, Southeast Asian Bull. Math., 34(2) (2010), 231-242.
11
[12] P. Corsini, V. Leoreanu-Fotea and A. Iranmanesh,On the sequence of hypergroups and mem-bership functions determined by a hypergraph, J. Mult.-Valued Logic Soft Comput., 14(6)(2008), 565-577.
12
[13] P. Corsini and R. Mahjoob,Multivalued functions, fuzzy subsets and join spaces, Ratio Math.,20(2010), 1-41.
13
[14] I. Cristea,Complete hypergroups, 1-Hypergroups and fuzzy sets, An. St. Univ. Ovidius Constanta,10(2) (2002), 25-38.
14
[15] I. Cristea,A property of the connection between fuzzy sets and hypergroupoids, Ital. J. Pure Appl. Math.,21 (2007), 73-82.
15
[16] I. Cristea,About the fuzzy grade of the direct product of two hypergroupoids, Iranian Journal of Fuzzy Systems,7(2) (2010), 95-108.
16
[17] I. Cristea and B. Davvaz,Atanassov's intuitionistic fuzzy grade of hypergroups, Information Sciences,180 (2010), 1506-1517.
17
[18] I. Cristea, M. Jafarpour and S. S. Mousavi,On fuzzy preordered structures and (fuzzy) hy-perstructures, Acta Math. Sin. (Engl. Ser.), 28(9) (2012), 1787-1798.
18
[19] B. Davvaz and M. Karimian,On the n-complete hypergroups, European J. Combin., 28(1)(2007), 86-93.[20] B. Davvaz and M. Karimian,On the n-complete hypergroups and K(H) hypergroups, ActaMath. Sin. (Engl. Ser.),24(11) (2008), 1901-1908.
19
[21] B. Davvaz, E. Hassani Sadrabadi and I. Cristea,Atanassov's intuitionistic fuzzy grade of the complete hypergroups of order less than or equal to6, submitted.
20
[22] B. Davvaz, E. Hassani Sadrabadi and I. Cristea,Atanassov's intuitionistic fuzzy grade of i.p.s. pergroups of order less than or equal to6, Iranian Journal of Fuzzy Systems,9(4)(2012), 71-97.
21
[23] B. Davvaz, E. Hassani Sadrabadi and I. Cristea,Atanassov's intuitionistic fuzzy grade of i.p.s.hypergroups of order7, J. Mult.-Valued Logic Soft Comput., accepted.
22
[24] H. Hedayati,Generalized fuzzy k-ideals of semirings with interval-valued membership func-tions, Bull.Malays.Math.Sci.Soc., 32(3) (2009), 409-424.
23
[25] J. Jantosciak,Homomorphism, equivalence and reductions in hypergroups, Riv. Mat. PuraAppl.,9(1991), 23-47.
24
[26] V. Leoreanu Fotea,t hypermodules, Comput. Math. Appl., 57(3) (2009), 466-47.
25
[27] V. Leoreanu Fotea and B. Davvaz,Fuzzy hyperrings, Fuzzy Sets and Systems, 160(16)(2009), 2366-2378.[28] F. Marty,Sur une generalization de la notion de groupe, Eight Congress Math. Scandenaves,Stockholm, (1934), 45-49.
26
[29] R. Migliorato,On the complete hypergroups, Riv. Mat. Pura Appl., 14 (1994), 21-31.
27
[30] W. Prenowits and J. Jantosciak,Geometries and join spaces, J. Reind und Angew Math.,257(1972), 100-128.
28
[31] A. Rosenfeld,Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
29
[32] M. Shabir, Y. B. Yun and M. Bano,On prime fuzzy bi-ideals of semigroups, Iranian Journal of Fuzzy Systems,7(3) (2010), 115-128.
30
[33] M. Stefanescu and I. Cristeon the fuzzy grade of the hypergroup, Fuzzy Sets and System159((2008), 1097-1106.
31
[34] Y. Yin, J. Zhan and X. Huang,A new way to fuzzy h-ideals of hemirings, Iranian Journal of Fuzzy Systems,8(5) (2011), 81-101.
32
[35] L. A. Zadeh,Fuzzy sets, Information and Control, 8 (1965), 338-353.
33
[36] J. Zhan and B. Davvaz,Study of fuzzy algebraic hypersystems from a general viewpoint, Int.J. Fuzzy Syst.,12(1) (2010), 73-79.
34
ORIGINAL_ARTICLE
DEFUZZIFICATION METHOD FOR RANKING FUZZY
NUMBERS BASED ON CENTER OF GRAVITY
Ranking fuzzy numbers plays a very important role in decision making and some other fuzzy application systems. Many different methods have been proposed to deal with ranking fuzzy numbers. Constructing ranking indexes based on the centroid of fuzzy numbers is an important case. But some weaknesses are found in these indexes. The purpose of this paper is to give a new ranking index to rank various fuzzy numbers effectively. Finally, several numerical examples following the procedure indicate the ranking results to be valid.
http://ijfs.usb.ac.ir/article_113_80aeb7a1e681279f864e912e3a6e965f.pdf
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10.22111/ijfs.2012.113
Ranking
Fuzzy numbers
Centroid point
Defuzzification
Tofigh
Allahviranloo
allahviranloo@yahoo.com
true
1
Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran
Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran
Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran
LEAD_AUTHOR
Rahim
Saneifard
srsaneeifard@yahoo.com
true
2
Department of Mathematics, Science and Research Branch, Islamic
Azad University, Tehran, Iran
Department of Mathematics, Science and Research Branch, Islamic
Azad University, Tehran, Iran
Department of Mathematics, Science and Research Branch, Islamic
Azad University, Tehran, Iran
AUTHOR
[1] S. Abbasbandy and B. Asady,Ranking of fuzzy numbers by sign distance, Information Sciences,176(2006), 2405-2416.
1
[2] T. Allahviranloo and M. Afshar,Numerical methods for fuzzy linear partial differential equationsunder new ition for derivative, Iranian Journal of Fuzzy Systems, 7 (2010), 33-50.
2
[3] T. Allahviranloo, S. Abbasbandy and R. Saneifard,A method for ranking fuzzy numbers using new weighted distance , Mathematical and Computational Applications, 2 (2011), 359-369.
3
[4] T. Allahviranloo, S. Abbasbandy and R. Saneifard,An approximation approach for ranking fuzzy numbers based on weighted interval-value, Mathematical and Computational Applications,3(2011), 588-597.
4
[5] I. Altun,Some fixed point theorems for single and multi valued mappings on ordered nonarchimedean fuzzy metric spaces , Iranian Journal of Fuzzy Systems, 1 (2010), 91-96.
5
[6] J. F. Baldwin and N. C. Guild,Comparison of fuzzy sets on the same decision space, Fuzzy Sets and Systems,2 (1979), 213-231.
6
[7] S. M. Bass and H. Kwakernaak,Rating and ranking of multiple aspect alternatives using fuzzy sets Automatica, 13 (1977), 47-58.
7
[8] W. Chang,Ranking of fuzzy utilities with triangular membership function , Proceeding of the International conference on policy analysis information system,105 (1981), 263-272.
8
[9] S. H. Chen,Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and Systems,17 985), 113-129.
9
[10] L. H. Chen and H. W. Lu,An approximate approach for ranking fuzzy numbers based on left and right dominance, Comput Math Appl., 41(2001), 1589-1602.
10
[11] C. H. Cheng,A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems,95 998), 307-317.
11
[12] C. H. Cheng,Ranking alternatives with fuzzy weights using maximizing set and minimizing set, Fuzzy Sets and Systems, 105 (1999), 365-375.
12
[13] T. Chu and C. Tsao,Ranking fuzzy numbers with an area between the centroid point andoriginal point, Comput. Math. Appl., 43 (2002), 111-117.
13
[14] D. Dubois and H. Prade,Operation on fuzzy numbers, Internat. J. Syst. Sci., 9 (1978),613-626.
14
[15] R. Ezatti and R. Saneifard,A new approach for ranking of fuzzy numbers with continuousweighted quasi-arithmetic means, Mathematical Sciences, 4 (2010), 143-158.
15
[16] R. Ezzati and R. Saneifard,Defuzzification through a novel approach, Proc.10th Iranian Conference on Fuzzy Systems, (2010), 343-348.
16
[17] E. C. Lee and R. L. Li,Comparison of fuzzy numbers based on the probability measure of fuzzy events , Comput Math Appl., 105 (1988), 887-896.
17
[18] F. Merghadi and A. Alioughe,A related fixed point theorem in n fuzzy metric spaces, Iranian Journal of Fuzzy Systems,3 (2010), 73-86.
18
[19] E. Pasha, A. Saiedfar and B. Asady,The percentiles of fuzzy numbers and their applications,Iranian Journal of Fuzzy Systems,6 (2009), 27-44.
19
[20] R. Saneiafard,Some properties of neural networks in designing fuzzy systems, Neural Computing and Applications, doi:10.1007/s00521-011-0777-1, 2011.
20
[21] R. Saneifard,A method for defuzzification by weighted distance, Int. J. Industrial Mathematics,3(2010), 209-217.
21
[22] R. Saneiafrd,Designing an algorithm for evaluating decision-making units based on neuralweighted function, Neural Computing and Applications, doi:10.1007/s00521-012-0878-5, 2012.
22
[23] R. Saneifard,Ranking L-R fuzzy numbers with weighted averaging based on levels, Int. J.Industrial Mathematics,2(2009), 163-173.
23
[24] Rahim Saneiafrd and Rasoul Saneifard,A new effect of radius of gyration with neural networks,Neural Computing and Applications, doi:10.1007/s00521-012-1067-2, 2012.
24
[25] R. Saneifard and R. Ezzati,Defuzzification through a bi-Symmetrical weighted function, Aust.J. Basic appl. sci.,10 (2009), 4976-4984.
25
[26] R. Saneifard and T. Allahviranloo,A comparative study of ranking fuzzy numbers based on regular weighted function, Fuzzy Information and Engineering, 3 (2012), 235-248.
26
[27] R. Saneifard, T. Allahviranloo, F. Hosseinzadeh and N. Mikaeilvand,Euclidean ranking DMUs with fuzzy data in DEA, Applied Mathematical Sciences, 60 (2007), 2989-2998.
27
[28] T. Y. Tseng and C. M. Klein,New algorithm for the ranking procedure in fuzzy decision making, IEEE Trans Syst Man Cybernet SMC., 19 (1989), 1289-1296.
28
[29] X. Wang and E. E. Kerre,Reasonable properties for the ordering of fuzzy quantities (I),Fuzzy Sets and Systems,118 (2001), 378-405.
29
[30] Y. M. Wang, J. B. Yang, D. L. Xu and K. S. Chin,On the centroids of fuzzy numbers, FuzzySets and Systems,157 (2006), 919-926.
30
[31] R. R. Yager and D. P. Filev,On the issue of defuzzification and selection based on a fuzzy set, Fuzzy Sets and Systems, 55 (2006), 255-272.
31
[32] J. Zhao and Q. S. Liu,Ranking fuzzy numbers based on the centroid of fuzzy numbers, Fuzzy Systems and Mathematics,22 (2008), 142-146.
32
ORIGINAL_ARTICLE
A FUZZY DIFFERENCE BASED EDGE DETECTOR
In this paper, a new algorithm for edge detection based on fuzzyconcept is suggested. The proposed approach defines dynamic membershipfunctions for different groups of pixels in a 3 by 3 neighborhood of the centralpixel. Then, fuzzy distance and -cut theory are applied to detect the edgemap by following a simple heuristic thresholding rule to produce a thin edgeimage. A large number of experiments are employed to confirm the robustnessof the proposed algorithm. In the experiments different cases such as normalimages, images corrupted by Gaussian noise, and uneven lightening imagesare involved. The results obtained are compared with some famous algorithmssuch as Canny and Sobel operators, a competitive fuzzy edge detector, and astatistical based edge detector. The visual and quantitative comparisons showthe effectiveness of the proposed algorithm even for those images that werecorrupted by strong noise.
http://ijfs.usb.ac.ir/article_114_04f71f0b2f0662f7763880565a251dae.pdf
2012-12-02T11:23:20
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69
85
10.22111/ijfs.2012.114
Edge detection
Fuzzy edge detection
Dynamic membership function
Fuzzy dierence
Noisy images
M. A.
Nikouei Mahani
nikouei@mahani.info
true
1
Electrical Engineering Department, Shahid Bahonar Univer-
sity of Kerman, Kerman, Iran
Electrical Engineering Department, Shahid Bahonar Univer-
sity of Kerman, Kerman, Iran
Electrical Engineering Department, Shahid Bahonar Univer-
sity of Kerman, Kerman, Iran
AUTHOR
Mohamad
Koohi Moghadam
m koohi m@comp.iust.ac.ir
true
2
School of Computer Engineering, Iran University of
Science and Technology, Tehran, Iran
School of Computer Engineering, Iran University of
Science and Technology, Tehran, Iran
School of Computer Engineering, Iran University of
Science and Technology, Tehran, Iran
AUTHOR
Hosein
Nezamabadi-pour
nezam@mail.uk.ac.ir
true
3
Electrical Engineering Department, Shahid Bahonar Uni-
versity of Kerman, Kerman, Iran
Electrical Engineering Department, Shahid Bahonar Uni-
versity of Kerman, Kerman, Iran
Electrical Engineering Department, Shahid Bahonar Uni-
versity of Kerman, Kerman, Iran
AUTHOR
[1] O. AbuAarqob, N. Shawagfeh and O. AbuGhneim, Functions dened on fuzzy real numbers
1
according to zadehs extension, International Mathematical Forum, (2008), 763-776.
2
[2] A. J. Baddeley, An error metric for binary images, Robust Computer Vision-Quality of
3
Vision Algorithms, (1992), 59-78.
4
[3] M. Basu, Gaussian-based edge-detection methodsa survey, IEEE Transactions on Systems
5
Man, and CyberneticsPart C, 32(3) (2002), 252-260.
6
[4] J. C. Bezdek, R. Chandrasekhar and Y. Attikiouzel, A geometric approach to edge detection,
7
IEEE Transaction on Fuzzy Systems, 6(1) (1998), 52-75.
8
[5] V. Boskovitz and H. Guterman, An adaptive neuro-fuzzy system for automatic image seg-
9
mentation and edge detection, IEEE Transactions on Fuzzy Systems, 10 (2002), 247-262.
10
[6] D. Brzakovic and L. Hong, Road edge detection for mobile robot navigation, In Proceedings
11
of IEEE International Conference on Robotics and Automation, Scottsdale, AZ , USA, 2
12
(1989), 1143-1147.
13
[7] S. M. Chen, New methods for subjective mental workload assessment and fuzzy risk analysis,
14
Cybernetics and Systems, 27 (1996), 449-472.
15
[8] K. David A. and B. James C, Edge detection using a fuzzy neural network, Science of Articial
16
Neural Networks, 1710 (1992), 510-521.
17
[9] C. Ducottet, T. Fournel and C. Barat, Scale-adaptive detection and local characterization of
18
edges based on wavelet transform, Signal Processing, 84(11) (2004), 2115-2137.
19
[10] T. Hou and W. Kuo, A new edge detection method for automatic visual inspection, The
20
International Journal of Advanced Manufacturing Technology, 13 (1997), 407-412.
21
[11] J. S. R. Jang, C. T. Sun and E. Mizutani, Neuro-fuzzy and soft computing- a computational
22
approach to learning and machine intelligence, Prentice-Hall of India Pvt. Ltd., New Delhi,
23
[12] S. Karungaru, M. Fukumi, N. Akamatsu and T. Akashi, A simple 3D edge template for pose
24
invariant face detection, Lecture Notes in Computer Science, 4253 (2006), 692-698.
25
[13] H. Kim, J. Lee, D. Kim, H. Yoon and S. Chi, Motion and natural hand detection for gesture
26
recognition, SICE-ICASE,International Joint Conference, Busan,Korea, (2006), 313-316.
27
[14] T. Law, H. Itoh and H. Seki, Image ltering, edge detection, and edge tracing using fuzzy
28
reasoning, IEEE Transactions on Pattern Analysis and Machine Intelligence, 18 (1996), 481-
29
[15] L. R. Liang and C. G. Looney, Competitive fuzzy edge detection, Applied Soft Computing, 3
30
(2003), 123-137.
31
[16] D. H. Lim, Robust edge detection in noisy images, Computational Statistics and Data Anal-
32
ysis, 50 (2006), 803-812.
33
[17] C. Lopez-Molina, H. Bustince, J. Fernandez, P. Couto and B. De Baets, A gravitational
34
approach to edge detection based on triangular norms, Pattern Recognition, 43(11) (2010),
35
3730-3741.
36
[18] S. Lu, Z.Wang and J. Shen, Neuro-fuzzy synergism to the intelligent system for edge detection
37
and enhancement, Pattern Recognition, 36 (2003), 2395-2409.
38
[19] D. Marr and E. Hildreth, Theory of edge detection, Proceedings Royal Soc.London, 207
39
(1980), 187-217.
40
[20] A. Maturo, On some structures of fuzzy numbers, Iranian Journal of Fuzzy Systems, 6 (2009),
41
[21] R. Medina-Carnicer, A. Carmona-Poyato, R. Muoz-Salinas and F. J. Madrid-Cuevas, Deter-
42
mining hysteresis thresholds for edge detection by combiningthe advantages and disadvantages
43
of thresholding methods, IEEE Transactionson Image Processing, 19(1) (2010), 165-173.
44
[22] R. Medina-Carnicer, F. Madrid-Cuevas, A. Carmona-Poyato and R. M. noz Salinas, On
45
candidates selection for hysteresis thresholds in edge detection, PatternRecognition, 42(7)
46
(2009), 1284-1296.
47
[23] R. Medina-Carnicer and F. Madrid-Cuevas, Unimodal thresholding for edgeDetection, Pattern
48
Recognition, 41(7) (2008), 2337-2346.
49
[24] R. Medina-Carnicer, F. Madrid-Cuevas, R. Muoz-Salinas and A. Carmona-Poyato, Solving
50
the process of hysteresis without determining the optimal thresholds, Pattern Recognition,
51
43(4) (2010), 1224-1232.
52
[25] H. Meng, M. Freeman, N. Pears and C. Bailey, Real-time human action recognition on an em-
53
bedded, recongurable video processing architecture, Journal of Real-Time Image Processing,
54
3 (2008), 163-176.
55
[26] S. Morillas, V. Gregori and Antonio. Hervs, Fuzzy peer groups for reducing mixed gaussian-
56
impulse noise from color images, IEEE Transaction on Image Processing, 18(7) (2009),
57
1452-1466.
58
[27] J. Musevi-Niya and A. Aghagolzadeh, Adaptive directional wavelet-based edge detection, 2nd
59
International Symposium on Telecommunications (IST2003), Isfahan, Iran, (2003), 191-195.
60
[28] H. Nezamabadi-pour, S. Saryazdi and E. Rashedi, Edge detection using ant algorithms, Soft
61
Computing, 10 (2005), 623-628.
62
[29] E. Pasha, A. Saiedifar and B. Asady, The percentiles of fuzzy numbers and their applications,
63
Iranian Journal of Fuzzy Systems, 6 (2009), 27-44.
64
[30] W. K. Pratt, Digital image processing, John Wiley and Sons, 2001.
65
[31] G. Roy Jun and W. Voxman, Topological properties of fuzzy numbers, Fuzzy Sets and Systems,
66
10(1-3) (1983), 87-99.
67
[32] X. Ruoning, A linear regression model in fuzzy environment, Adv. Modelling Simulation, 27
68
(1991), 31-40.
69
[33] F. Russo and G. Ramponi, Edge extraction by FIRE operators , in IEEE World Congress on
70
Computational Intelligence, 1 (1994), 249-253.
71
[34] J. I. Siddigue and K. E.Barner, Wavelet-based multi-resolution edge detection utilizing gray
72
level edge maps, International Conference on Image Processing (ICIP 98), (1998), 550-554.
73
[35] B. Sridevi and R. Nadarajan, Fuzzy similarity measure for generalized fuzzy numbers, Inter-
74
national Journal of Open Problems in Computer Science and Mathematics, 2 (2009), 240-253.
75
[36] P. Terry and D. Vu, Edge detection using neural networks, In IEEE Proceedings of 27th
76
Asilomar Conference on Signals, Systems and Computers, (1993), 391-395.
77
[37] V. Torre and T. Poggio, On edge detection, Massachusetts Institute of Technology-Articial
78
Intelligence Laboratory, 1984.
79
[38] D. Van De Ville, M. Nachtegael, D. Van Der Weken, E. Kerre, W. Philips and I. Lemahieu,
80
Noise reduction by fuzzy image ltering, IEEE Transactions on Fuzzy Systems, 11 (2003),
81
[39] J. Wu, Z. Yin and Y. Xiong, The fast multilevel fuzzy edge detection of blurry images, IEEE
82
Signal Processing Letters, 14 (2007), 344-347.
83
[40] R. Xu and C. Li, Multidimensional least-squares tting with a fuzzy model, Fuzzy Sets and
84
Systems, 119 (2001), 215-223.
85
[41] F. Yang, S. Wan and Y. Chang, Improved method for gradient-threshold edge detector based
86
on HVS, Lecture Notes in Computer Science, 3801 (2005), 1051-1056.
87
[42] S. Yi, D. Labate, G. R. Easley and H. Krim, A shearlet approach to edge analysis and
88
detection, Trans. Image Proc,18(15) (2009), 1057-7149.
89
[43] X. Zong and W. Liu, Fuzzy edge detection based on wavelets transform, Machine Learning
90
and Cybernetics, International Conference, (2008), 2869-2873.
91
ORIGINAL_ARTICLE
SYMMETRIC TRIANGULAR AND INTERVAL
APPROXIMATIONS OF FUZZY SOLUTION TO
LINEAR FREDHOLM FUZZY INTEGRAL
EQUATIONS OF THE SECOND KIND
In this paper a linear Fuzzy Fredholm Integral Equation(FFIE) with arbitrary Fuzzy Function input and symmetric triangular (Fuzzy Interval) output is considered. For each variable, output is the nearest triangular fuzzy number (fuzzy interval) to the exact fuzzy solution of (FFIE).
http://ijfs.usb.ac.ir/article_115_4867dc5fc41055bc015b22cd768c5f10.pdf
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87
99
10.22111/ijfs.2012.115
Fuzzy number
Expected interval
Fuzzy integral equations
Symmetric
fuzzy number
Nystrom method
Majid
Alavi
M-alavi@Iau-arak.ac.ir
true
1
Department of Mathematics, Islamic Azad University, Arak Branch,
Arak, Iran
Department of Mathematics, Islamic Azad University, Arak Branch,
Arak, Iran
Department of Mathematics, Islamic Azad University, Arak Branch,
Arak, Iran
AUTHOR
Babak
Asady
B-asay@Iau-arak.ac.ir
true
2
Department of Mathematics, Islamic Azad University, Arak Branch,
Arak, Iran
Department of Mathematics, Islamic Azad University, Arak Branch,
Arak, Iran
Department of Mathematics, Islamic Azad University, Arak Branch,
Arak, Iran
AUTHOR
[1] S. Abbasbandy and T. Allahviranloo, Numerical solution of fuzzy dierential equation by
1
runge-Kutta method, Nonlinear Stud, 11 (2004), 117-129.
2
[2] S. Abbasbandy and B. Asady, The nearest trapezoidal fuzzy number to a fuzzy quantity, Appl
3
Math Comput, 156 (2004), 381-386.
4
[3] S. Abbasbandy, E. Babolian and M. Alavi, Numerical method for solving linear Fredholm
5
fuzzy integral equations of the second kind, Chaos, Soliton and Fractals, 31 (2007), 138-146.
6
[4] T. Allahviranloo and M. Otadi, Gaussian quadratures for approximate of fuzzy integrals,
7
Applied Mathematics and Computation, 170 (2005), 874-885.
8
[5] K. Atkinson, A survey of numerical methods for solving nonlinear integral equations, J. of
9
Integral Equat. and Appl., 4 (1992), 15-46.
10
[6] E. Babolian, H. Sadeghi Goghary and S. Abbasbandy, Numerical solution of linear Fredholm
11
fuzzy integral equations of the second kind by Adomian method, Applied Mathematics and
12
Computation, 161 (2005), 733-744
13
[7] E. Babolian, H. Sadeghi and S. Javadi, Numerically solution of fuzzy dierential equations
14
by Adomian method, Appl. Math. Comput., 149 (2004), 547-557.
15
[8] K. Balachandran and K. Kanagarajan, Existence of solutions of general nonlinear fuzzy
16
Voltera-Feredholm integral equations, J. Appl. Math. Stochastic Anal, 3 (2005), 333-343.
17
[9] K. Balachandran and P. Prakash, Existence of solution of nonlinear fuzzy Voltera-Feredholm
18
integral equations, Indian J. Pure Appl. Math, 333 (2002), 329-343.
19
[10] B. Bede and S. G. Gal, Quadrature rules for integral of fuzzy-number-valued functions, Fuzzy
20
Sets and Systems, 145 (2004), 359-380.
21
[11] A. M. Bica, Error estimation in the Approximation of the solution of nonlinear fuzzy Fered-
22
holm integral equations, Information Sciences, 174 (2008), 1279-1292.
23
[12] J. J. Buckley and T. Furing, Fuzzy integral equations, J. Fuzzy Math, 10 (2002), 1011-1024.
24
[13] S. S. L. Chang and L. Zadeh, On fuzzy mapping and control, IEEE Trans System Man
25
Cybernet, 2 (1972), 30-34.
26
[14] W. Cingxin and M. Ming, On embedding problem of fuzzy number spaces: part I, Fuzzy Sets
27
and Systems, 44 (1991), 33-38.
28
[15] W. Cingxin and M. Ming, On embedding problem of fuzzy number spaces: part II, Fuzzy Sets
29
and Systems, 45 (1992), 189-202.
30
[16] W. Cingxin and M. Ming, On embedding problem of fuzzy number spaces: part III, Fuzzy
31
Sets and Systems, 44 (1992), 281-286.
32
[17] W. Congxin and M. Ming, On the integrals. series and integral equations of fuzzy set-valued
33
functions, J. Harbin Inst Technol, 21 (1990), 11-19.
34
[18] L. M. Delves and J. L. Mohemed, Computational methods for bntegral equations, Cambridge
35
University Press, Cambridge, 1985.
36
[19] K. Deimling, Multivalued dierential equations, Walter de Gruyter, New York, 1992.
37
[20] P. Diamond, Stability and periodicity in fuzzy dierential equations, IEEE Trans. Fuzzy Syst,
38
8 (2000), 583-590.
39
[21] D. Dubois and H. prade, Towards fuzzy dierential calculus, Fuzzy Sets and System, 8 (1982),
40
[22] M. Friedman, M. Ma and A. Kandel, Numerical solutions of fuzzy dierential and integral
41
equations, Fuzzy Sets and Systems, 106 (1999), 35-48.
42
[23] M. Fridman, M. Ma and A. Kandel, On fuzzy integral equations, Fundam. Inform, 37 (1999),
43
[24] M. Fridman, M. Ming and A. Kandel, Solution to fuzzy integral equations with arbitrary
44
kernels, Internat. J. Approx. Reason, 20 (1999), 249-262.
45
[25] D. N. Georgion and I. E. Kougias, Bounded solutions for fuzzy integral equations, Int. j.
46
Math.sci, 312 (2002), 109 114.
47
[26] D. N. Georgion and I. E. Kougias, On fuzzy fredholm and Voltera integral equations, J. Fuzzy
48
Math, 94 (2001), 943-951.
49
[27] R. Goetschel and W. Voxman, Elementary calculus, Fuzzy Sets and Systems, 18 (1986),
50
[28] P. Grzegorzewski, Metricsand orders in space of fuzzy numbers, Fuzzy Sets and Systems, 97
51
(1987), 83-94
52
[29] P. Grzegorzewski, Nearst interval approximation of a fuzzy number, Fuzzy Sets ans Systems,
53
130 (2002), 321-330.
54
[30] P. Grzegorzewski, Trapezoidal approximations of fuzzy numbers preserving the expected in-
55
terval -algorithms and properties, Fuzzy Sets and Systems, 159 (2008), 1354-1364.
56
[31] H. Hochstadt, Integral equations, Wiley, New York, 1973.
57
[32] O. Kaleva, Fuzzy dierential equations, Fuzzy Sets and Systems, 24 (1987), 301-317.
58
[33] W. V. Lovitt, Linear integral equation, Dover, New York, 1950.
59
[34] M. Ma, M. Friedman and A. Kandel, Numerical solution of fuzzy dierential equations, Fuzzy
60
Sets and Systems, 105 (1999), 133-138.
61
[35] M. Matloka, On fuzzy integrals Proc, 2nd Polish Symp. on Interval and Fuzzy Mathematics,
62
Politechnika Poznnsk, (1987), 167-170.
63
[36] A. Maturo, On some structure of fuzzy numbers, Iranian Journal of Fuzzy Systems, 6 (2009),
64
[37] A. Molabahrami, A. Shidfar and A. Ghyasi, An analytical method for solving linear Feredholm
65
fuzzy integral equations of the second kind, Computers and Mathematics with Applications,
66
61 (2011), 2754-2761.
67
[38] J. Mordeson and W. Newman, Fuzzy integral equations, Information Sciences, 814 (1995),
68
[39] J. J. Nieto and R. Rodriguez-Lopaz, Bounded solution for fuzzy dierential and integral
69
equations, Choas Solitons and Fractals, 275 (2006), 1376-1386.
70
[40] N. Parandin and M. A. Fariborzi Araghi, The approximate solution of linear fuzzy Fered-
71
holm integral equations of the second kind by using iterative interpolation, Word Academy
72
of science, Engineering and Technology, 49 (2009), 425-431.
73
[41] E. Pasha, A. saiedifar and B. Asady, The presentation on fuzzy numbers and their applica-
74
tions, Iranian Journal of Fuzzy Systems, 6 (2009), 27-44.
75
[42] J. Y. Perk and J. U. Jeong, On the existence and uniquenes of solutions of fuzzy Voltera-
76
Feredholm, integral equations, Fuzzy Sets and Systems, 115 (2000), 425-431.
77
[43] O. Solaymani and A. Vahidian kamyad, Modied K-step method for solving fuzzy initial value
78
problems, Iranian Journal of Fuzzy Systems, 8 (2011), 49-59.
79
[44] J. Vrba, A note on inverse in arithwith fuzzy numbers, Fuzzy Sets and Systems, 50 (1992),
80
ORIGINAL_ARTICLE
THE RELATIONSHIP BETWEEN L-FUZZY PROXIMITIES AND
L-FUZZY QUASI-UNIFORMITIES
In this paper, we investigate the L-fuzzy proximities and the relationships betweenL-fuzzy topologies, L-fuzzy topogenous order and L-fuzzy uniformity. First, we show that the category of-fuzzy topological spaces can be embedded in the category of L-fuzzy quasi-proximity spaces as a coreective full subcategory. Second, we show that the category of L -fuzzy proximity spaces is isomorphic to the category of L-fuzzy topogenous order spaces. Finally,we obtain that the category of L-fuzzy proximity spaces can be embeddedin the category of L-fuzzy uniform spaces as a bireective full subcategory.
http://ijfs.usb.ac.ir/article_120_e9a1f2dafb8bbda298f95ab61533e4c2.pdf
2012-12-02T11:23:20
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101
111
10.22111/ijfs.2012.120
L-Fuzzy topology
L-fuzzy proximity
L-fuzzy uniformity
L-fuzzy
topogenous order
Fuzzy remote neighborhood systems
Eun-Seok
Kim
manmunje@hanmail.net
true
1
Department of Mathematics, Chonnam National University, 300 Yongbong-
dong, Bukgu, 500-757, Gwangju, Korea
Department of Mathematics, Chonnam National University, 300 Yongbong-
dong, Bukgu, 500-757, Gwangju, Korea
Department of Mathematics, Chonnam National University, 300 Yongbong-
dong, Bukgu, 500-757, Gwangju, Korea
AUTHOR
Seung-Ho
Ahn
shahn@chonnam.ac.kr
true
2
Department of Mathematics, Chonnam National University, 300 Yongbong-
dong, Bukgu, 500-757, GwangJu, Korea
Department of Mathematics, Chonnam National University, 300 Yongbong-
dong, Bukgu, 500-757, GwangJu, Korea
Department of Mathematics, Chonnam National University, 300 Yongbong-
dong, Bukgu, 500-757, GwangJu, Korea
AUTHOR
Dae Heui
Park
dhpark3331@chonnam.ac.kr
true
3
Department of Mathematics, Chonnam National University, 300 Yongbong-
dong, Bukgu, 500-757, GwangJu, Korea
Department of Mathematics, Chonnam National University, 300 Yongbong-
dong, Bukgu, 500-757, GwangJu, Korea
Department of Mathematics, Chonnam National University, 300 Yongbong-
dong, Bukgu, 500-757, GwangJu, Korea
AUTHOR
[1] J. Adamek J, H. Herrlich and G. E. Strecker, Abstract and concrete categories, J. Wiley and
1
Sons, New York, 1990.
2
[2] G. Artico and R. Moresco, Fuzzy proximities and totally bounded fuzzy uniformities, J. Math.
3
Anal. Appl., 9 (1984), 320-1337.
4
[3] G. Artico and R. Moresco, Fuzzy proximities compatible with Lowen uniformities, Fuzzy Sets
5
and Systems, 21 (1987), 85-99.
6
[4] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182-190.
7
[5] A. Csaszar, Foundations of general topology, Pergamon Press, 1963.
8
[6] D. Dzajanbajev and A. Sostak, On a fuzzy uniform structure, Acta Comm. Univ. Tartu, 940
9
(1992), 31-36.
10
[7] J. M. Fang and Y. L. Yue, Base and subbase in I-fuzzy topological spaces, J. Math. Res.
11
Expositon, 26 (2006), 89-95.
12
[8] M. H. Ghanim, O. A. Tantawy and F. M. Selim, On S-fuzzy quasi-proximity spaces, Fuzzy
13
Sets and Systems, 109 (2000), 285-290.
14
[9] F. Gierz, et al., A compendium of continuous lattices, Berlin: Springer Verlag, 1980.
15
[10] J. Gutierrez Garcia, M. A. de Prada Vicente and A. Sostak, A unied approach to the
16
concept of fuzzy L-uniform space, In: Topological and Algebraic Strutures in Fuzzy Sets,
17
A Handbook of Recent Developments in the Mathematics of Fuzzy Sets, S. E. Rodabaugh
18
and E. P. Klement eds. Kluwer Acad. Publ., Dordrecht, Boston, London, Chapter 3, (2003),
19
[11] U. Hohle, Upper semicontinuous fuzzy sets and applications, J. Math. Anal. Appl., 78 (1980),
20
[12] B. Hutton, Uniformities on fuzzy topological spaces, J. Math. Anal. Appl., 58 (1977), 557-571.
21
[13] A. K. Katsaras, On fuzzy syntopogenous structures, J. Math. Anal. Appl., 99 (1983), 219-236.
22
[14] A. K. Katsaras, On fuzzy uniform spaces, J. Math. Anal. Appl., 101 (1984), 97-114.
23
[15] T. Kubiak, On fuzzy topologies, PhD Thesis, Adam Mickiewicz, Poznan (Poland), 1985.
24
[16] W. J. Liu, Fuzzy proximity spaces redened, Fuzzy Sets and Systems, 15 (1985), 241-248.
25
[17] Y. M. Liu and M. K. Luo, Fuzzy topology, Singapore: World Scientic Press, 1997.
26
[18] S. Markin and A.Sostak , Another approach to the concept of a fuzzy proximity, Suppl. Rend.
27
Mat. Palermo, 29 (1992), 530-551.
28
[19] G. Preuss, Theory of topological structures: an approch to categorical topology, D. Reidel
29
Publishing Company, 1987.
30
[20] F. G. Shi, The category of pointwise S-proximity spaces, Fuzzy Sets and Systems, 152 (2005),
31
[21] A. Sostak, On a fuzzy topological structure, Rend. Cire. Matem. Palermo, Ser. II, 11 (1985),
32
[22] A. Sostak, Basic structures of fuzzy topology, J. Math. Sciences, 78 (1996), 662-697.
33
[23] A. Sostak, Fuzzy syntopogenous structures, Quaestiones Math., 20 (1997), 431-461.
34
[24] Y. Yue and J. Fang, Categories isomorphic to the Kubiak-Sostak extension of TML, Fuzzy
35
Sets and Systems, 157 (2006), 832-842.
36
[25] Y. Yue and F. G. Shi, Generalized quasi-proximities, Fuzzy Sets and Systems, 158 (2007),
37
ORIGINAL_ARTICLE
Uniquely Remotal Sets in $c_0$-sums and $ell^infty$-sums of Fuzzy Normed Spaces
Let $(X, N)$ be a fuzzy normed space and $A$ be a fuzzy boundedsubset of $X$. We define fuzzy $ell^infty$-sums and fuzzy $c_0$-sums offuzzy normed spaces. Then we will show that in these spaces, all fuzzyuniquely remotal sets are singletons.
http://ijfs.usb.ac.ir/article_121_ff6e9553bb02f301be1760cab42930a1.pdf
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10.22111/ijfs.2012.121
Fuzzy normed spaces
Fuzzy remotal set
Alireza
Kamel Mirmostafaee
mirmostafaei@ferdowsi.um.ac.ir
true
1
Center of Excellence in Analysis on Algebraic Struc-
tures, Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box
1159, Mashhad 91775, Mashhad, Iran
Center of Excellence in Analysis on Algebraic Struc-
tures, Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box
1159, Mashhad 91775, Mashhad, Iran
Center of Excellence in Analysis on Algebraic Struc-
tures, Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box
1159, Mashhad 91775, Mashhad, Iran
AUTHOR
Madjid
Mirzavaziri
mirzavaziri@gmail.com
true
2
Center of Excellence in Analysis on Algebraic Structures, De-
partment of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mash-
had 91775, Mashhad, Iran
Center of Excellence in Analysis on Algebraic Structures, De-
partment of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mash-
had 91775, Mashhad, Iran
Center of Excellence in Analysis on Algebraic Structures, De-
partment of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box 1159, Mash-
had 91775, Mashhad, Iran
AUTHOR
bibitem{asplund} E. Asplund, {it Sets with unique farthest
1
points}, Israel J. Math., {bf5} (1967), 201-209.
2
bibitem{bs1} T. Bag and S. K. Samanta, textit{Finite dimensional fuzzy normed linear spaces},
3
J. Fuzzy Math., textbf{11(3)} (2003), 687-705.
4
bibitem{bs2} T. Bag and S. K. Samanta, textit{Fuzzy bounded linear operators},
5
Fuzzy Sets and Systems, textbf{151} (2005), 513-547.
6
bibitem{b}M. V. Balashov and G. E. Ivanov, {it On farthest points of
7
sets}, Mathematical Notes, {bf80(1-2)} (2006), 159-166.
8
bibitem{pa}M. Baronti and P. L. Papini, textit{Remotal sets
9
revisited}, Taiwanese J. Math., {bf5(2)} (2001), 367-373.
10
bibitem{blat} J. Blatter, {it Weiteste punkte und nachste
11
punkte}, Ren. Poum. Math. Pures Appl., {bf14} (1969), 615-621.
12
bibitem{bor} R. A. Borzooei and M. Bakhshi, emph{T-fuzzy congruences and T-fuzzy filters of a BL-algebras,} Iranian Journal of Fuzzy Systems, {bf6(4)} (2009), 37-47.
13
bibitem{cm} S. C. Chang and J. N. Mordeson, {it Fuzzy linear
14
operators and fuzzy normed linear spaces}, Bull. Cal. Math. Soc.,
15
{bf86} (2004), 429-436.
16
bibitem{cob}S. Cobzas, {it Geometric properties of Banach
17
spaces and the existence of nearest and farthest points}, Abstr.
18
Appl. Anal., {bf3} (2005), 259-285.
19
bibitem{fb}C. Feblin, {it The completion of a fuzzy normed
20
space}, J. Math. Anal. Appl., {bf174} (1993), 428-440.
21
bibitem{h}S. B. Hosseini, D. Oï¿½regan and R. Saadati, emph{Some results on intuitonistic fuzzy spaces,} Iranian Journal of Fuzzy Systems, {bf4(1)} (2007), 53-64.
22
bibitem{Iv}G. E. Ivanov, emph{Farthest points and the strong convexity of sets,} (Russian) Mat. Zametki, {bf87(3)} (2010), 382-395.
23
bibitem{ka} A. K. Katsaras, {it Fuzzy topological vector space
24
II }, Fuzzy sets and Systems, {bf12} (1984), 143-154.
25
bibitem{klee} L. Klee, {it Convexity of Chebyshev sets}, Math.
26
Ann., {bf142} (1961), 292-304.
27
bibitem{kr} I. Kramosil and J. Michalek, {it Fuzzy metric and
28
statistical metric spaces}, Kybernetica, {bf11} (1975), 326-334.
29
bibitem{mir1} A. K. Mirmostafaee, emph{Perturbation of generalized derivations in fuzzy Menger normed algebras,} Fuzzy sets and systems,
30
doi:10.1016/j.fss.2011.10.015.
31
bibitem{mirmirza} A. K. Mirmostafaee and M. Mirzavaziri, emph{Closability of farthest point maps in fuzzy normed spaces}, Bull. Math. Anal., {bf2(4)} (2010), 140-145.
32
bibitem{mir} A. K. Mirmostafaee and A. Niknam, {it A remark on
33
uniquely remotal sets}, Indian J. Pure Appl. Math., {bf 29(8)} (1998), 849-854.
34
bibitem{narang1}T. D. Narang, {it A study of farthest points},
35
Nieuw Arch. Wisk., {bf25} (1977), 54-79.
36
bibitem{narang3}T. D. Narang, {it On farthest points in metric
37
spaces}, J. Korea Soc. Math. Educ. Ser B Pure Appl. Math., {bf9} (2002), 1-7.
38
bibitem{narang2}T. D. Narang, {it Uniquely remotal sets are sigletons},
39
Nieuw Arch. Wisk., {bf4(9)} (1991), 1-12.
40
bibitem{va} S. M. Vaezpour and F. Karimi, emph{$t$-best approximation in fuzzy normed spaces}, Iranian Journal of Fuzzy Systems, {bf5(2)} (2008), 93-99.
41
bibitem{z} L. A. Zadeh, {it Fuzzy sets}, Information and
42
Control, {bf8} (1965), 338-353.
43
ORIGINAL_ARTICLE
(IC)LM-FUZZY TOPOLOGICAL SPACES
The aim of the present paper is to define and study (IC)$LM$-fuzzytopological spaces, a generalization of (weakly) induced $LM$-fuzzytopological spaces. We discuss the basic properties of(IC)$LM$-fuzzy topological spaces, and introduce the notions ofinterior (IC)-fication and exterior (IC)-fication of $LM$-fuzzytopologies and prove that {bf ICLM-FTop} (the category of(IC)$LM$-fuzzy topological spaces) is an isomorphism-closed fullproper subcategory of {bf LM-FTop} (the category of $LM$-fuzzytopological spaces) and {bf ICLM-FTop} is a simultaneouslybireflective and bicoreflective full subcategory of {bf LM-FTop}.
http://ijfs.usb.ac.ir/article_124_a929db0f489a56ad82899d80d76f5f06.pdf
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10.22111/ijfs.2012.124
LM-fuzzy topology
(IC) LM-fuzzy topological spaces
(IC)-fication
of LM-fuzzy topology
Category
Hai-Yang
Li
fplihiayang@126.com
true
1
School of Science, Xi'an Polytechnic University, Xi'an 710048, P. R.
China
School of Science, Xi'an Polytechnic University, Xi'an 710048, P. R.
China
School of Science, Xi'an Polytechnic University, Xi'an 710048, P. R.
China
AUTHOR
bibitem{AHS:Abstract}
1
J. Ad'{a}mek, H. Herrlich and G. E. Strecker, {it Abstract and concrete
2
categories}, John Wiley & Sons, New York, 1990.
3
bibitem{Chang:Fuzzy}
4
C. L. Chang, {it Fuzzy topological spaces}, J. Math. Anal. Appl., {bf 24} (1968), 182-190.
5
bibitem{FY:Base}
6
J. Fang and Y. Yue, {it Base and subbase in $I$-fuzzy
7
topological space}, J. Math. Res. Exposition, {bf 26} (2006), 89-95.
8
bibitem{GHKL:Cont}
9
G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislowe and
10
D. S. Scott, {it Continuous lattices and domains}, Cambridge University Press, Cambridge, 2003.
11
bibitem{GHK:Comp}
12
G. Gierz, K. H. Hofmann, K. Keimel and et al., {it A compendium
13
of continuous lattices}, Springer, Berlin, 1980.
14
bibitem{Hh:Upper}
15
U. H"{o}hle, {it Upper semicontinuous fuzzy sets and
16
applications}, J. Math. Anal. Appl., {bf 78} (1980), 659-673.
17
bibitem{HhSo:Afff}
18
U. H"{o}hle and A. P. v{S}ostak, {it Axiomatic
19
foundations of fixed-basis fuzzy topology}, In: U. H"{o}hle, S. E.
20
Rodabaugh, eds., Mathematic of Fuzzy Sets-Logic, Topology and
21
Measure Theory, Kluwer Academic Publishers, Boston/Dordrecht/London,
22
(1999), 123-272.
23
bibitem{Kub:ft}
24
T. Kubiak, {it On fuzzy topologies}, Ph.D. Thesis, Adam
25
Mickiewicz, Poznan, Poland, 1985.
26
bibitem{LSG:Con}
27
S. G. Li, {it Connectedness and local connectedness in Lowen spaces},
28
Fuzzy Sets and Systems, {bf 158} (2007), 85-98.
29
bibitem{LLF:IC}
30
S. G. Li, H. Y. Li and W. Q. Fu, {it (IC)$L$-cotopological
31
spaces}, Fuzzy Sets and Systems, {bf 158} (2007), 1226-1236.
32
bibitem{Low:Fts}
33
R. Lowen, {it Fuzzy topological spaces and fuzzy compactness},
34
J. Math. Anal. Appl., {bf 56} (1976), 621-633.
35
bibitem{Macl:Categ}
36
S. Maclane, {it Categories for working mathematicians}, Springer, Berlin, 1971.
37
bibitem{Mar:Weakly}
38
H. W. Martin, {it Weakly induced fuzzy topological spaces},
39
J. Math. Anal. Appl., {bf 78} (1980), 634-639.
40
bibitem{rodab:Pofft}
41
S. E. Rodabaugh, {it Powerset operator foundations for poslat fuzzy
42
set theories and topologies}, In: U. H"{o}hle, S. E. Rodabaugh,
43
eds., Mathematics of Fuzzy Sets: Logic, Topology and Measure
44
Theory, The Handbooks of Fuzzy Sets Series,
45
Kluwer Academic Publishers, Dordrecht, Chapter 2, {bf 3} (1999), 91-116.
46
bibitem{Rodab;Cafft}
47
S. E. Rodabaugh, {it Categrical foundations of
48
variable-basis fuzzy topology}, In: U. H"{o}hle, S.
49
E. Rodabaugh, eds., Mathematic of Fuzzy Sets-Logic, Topology and
50
Measure Theory, Kluwer Academic Publishers, Boston/Dordrecht/London, Chapter 4,
51
(1999), 273-388.
52
bibitem{So:Bsft}
53
A. P. v{S}ostak, {it Basic structures of fuzzy topology}, J. Math. Sciences, {bf 78} (1996), 662-701.
54
bibitem{So:Fts}
55
A. P. v{S}ostak, {it On a fuzzy topological
56
structure}, Rend. Ciecolo Mat. Palermo (Suppl.Ser.II), {bf 11} (1985), 89-103.
57
bibitem{So:Tdft}A. P. v{S}ostak, {it Two decades of fuzzy topology: basic ideas, notions and results}, Russian Math. Surveys,
58
{bf 44} (1989), 125-186.
59
bibitem{Wei:Fixed}
60
M. D. Weiss, {it Fixed points, separation and induced topologies
61
for fuzzy sets}, J. Math. Anal. Appl., {bf 50} (1975), 142-150.
62
bibitem{Yao;Net}
63
W. Yao, {it Net-theoretical $L$-generalized convergence spaces}, Iranian Journal of Fuzzy Systems, {bf 8} (2011), 121-131.
64
bibitem{Yue:Ind}
65
Y. Yue, {it Lattice-valued induced fuzzy topological spaces}, Fuzzy Sets
66
and Systems, {bf 158} (2007), 1461-1471.
67
bibitem{Zh:Lft}
68
D. Zhang, {it $L$-fuzzifying topologies as $L$-topologies},
69
Fuzzy Sets and Systems, {bf 125} (2002), 135-144.
70
ORIGINAL_ARTICLE
Persian-translation Vol.9, No.6
http://ijfs.usb.ac.ir/article_2807_82664d9575be6d31f502231085f96bf9.pdf
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10.22111/ijfs.2012.2807