ORIGINAL_ARTICLE
Cover for Volume.13, No.3
http://ijfs.usb.ac.ir/article_2627_ca230bc374d61c633116a51b3f3de2b6.pdf
2016-06-30T11:23:20
2017-09-20T11:23:20
0
10.22111/ijfs.2016.2627
ORIGINAL_ARTICLE
A PSO-based Optimization of a fuzzy-based MPPT controller for a photovoltaic pumping system used for irrigation of greenhouses
The main asset of this paper is among the uses of fuzzy logic in the engineering sector and especially in the renewable energies as a large alternate of fossil energies, in this paper a PSO-based optimization is used to find the optimal scaling parameters, of a fuzzy logic-based MPPT controller, that maximize the efficiency of a photovoltaic pumping system. The tuning of input and output parameters are of direct effect on the power that flows from the photovoltaic source to the load. In order to see concrete results, the PV system is used for irrigation of greenhouses in Laghouat, Algeria. The performances of the proposed PSO-based fuzzy controller are compared with those obtained using fuzzy logic and P&O controllers under variations of meteorological conditions. The simulation results proved a good robustness performance of the proposed Fuzzy based PSO controller over the other regarding the gained solar energy and the daily pumped water.
http://ijfs.usb.ac.ir/article_2426_19cf4facaa4c0c91f8603d066cf6790f.pdf
2016-06-29T11:23:20
2017-09-20T11:23:20
1
18
10.22111/ijfs.2016.2426
PSO-based optimization
Photovoltaic pumping system
MPPT controller
Fuzzy logic
Perturb and Observe (P&O)
aboubakeur
Hadjaissa
true
1
LACoSERE Laboratory, Amar Telidji University, BP 37G,
Ghardaia Road, Laghouat (03000), Algeria
LACoSERE Laboratory, Amar Telidji University, BP 37G,
Ghardaia Road, Laghouat (03000), Algeria
LACoSERE Laboratory, Amar Telidji University, BP 37G,
Ghardaia Road, Laghouat (03000), Algeria
LEAD_AUTHOR
Khaled
Ameur
true
2
LACoSERE Laboratory, Amar Telidji University, BP 37G, Ghardaia
Road, Laghouat (03000), Algeria
LACoSERE Laboratory, Amar Telidji University, BP 37G, Ghardaia
Road, Laghouat (03000), Algeria
LACoSERE Laboratory, Amar Telidji University, BP 37G, Ghardaia
Road, Laghouat (03000), Algeria
AUTHOR
Mohamed Salah
Ait-Cheikh
true
3
LDCCP Laboratory, Ecole nationale polytchnique, 10
avenue H. Badi BP 182 Harrach Algiers, Algeria
LDCCP Laboratory, Ecole nationale polytchnique, 10
avenue H. Badi BP 182 Harrach Algiers, Algeria
LDCCP Laboratory, Ecole nationale polytchnique, 10
avenue H. Badi BP 182 Harrach Algiers, Algeria
AUTHOR
Najib
Essounbouli
true
4
CReSTIC Laboratory, Reims University, 10026 Troyes CEDEX,
France
CReSTIC Laboratory, Reims University, 10026 Troyes CEDEX,
France
CReSTIC Laboratory, Reims University, 10026 Troyes CEDEX,
France
AUTHOR
[1] M. A. Eltawil and Z. Zhao, MPPT techniques for photovoltaic applications, Renewable and
1
Sustainable Energy Reviews, 25 (2013), 793-813.
2
[2] N. Gokmen, E. Karatepe, F. Ugranli and S. Silvestre, Voltage band based global MPPT
3
controller for photovoltaic systems, Solar Energy, 98 (2013), 322-334.
4
[3] O. Guenounou, B. Dahhou and F.Chabour, Adaptive fuzzy controller based MPPT for pho-
5
tovoltaic systems, Energy Conversion and Management, 78 (2014), 843-850.
6
[4] A. M. Kassem, MPPT control design and performance improvements of a PV generator
7
powered DC motor-pump system based on articial neural networksm, Electrical Power and
8
Energy Systems, 43 (2012), 90{98.
9
[5] L. K. Letting ,J. L. Munda and Y. Hamam, Optimization of a fuzzy logic controller for PV
10
grid inverter control using S-function based PSO, Solar Energy, 86 (2012), 1689-1700.
11
[6] T. Martire, C. Glaize, C. Joubert and B. Rouviere, A simplied but accurate prevision method
12
for along the sun PV pumping systems, Solar energy, 82 (2008), 1009-1020.
13
[7] E. Mehdizadeh, S. Sadi-nezhad and R. Tavakkoli-moghaddam, Optimization of fuzzy clus-
14
tering criteria by a hybrid PSO and fuzzy c-means clustering algorithm, Iranian Journal of
15
Fuzzy Systems, 5(3) (2008), 1-14.
16
[8] P. Periasamy, N. K. Jain and I. P.Singh, A review on development of photovoltaic water
17
pumping system, Renewable and Sustainable Energy Reviews, 43 (2015), 918-925.
18
[9] H. Rezk and A. M. Eltamaly, A comprehensive comparison of dierent MPPT techniques
19
for photovoltaic systems, Solar energy, 112 (2015), 1-11.
20
ORIGINAL_ARTICLE
On minimal realization of IF-languages: A categorical approach
he purpose of this work is to introduce and study the concept of minimal deterministic automaton with IF-outputs which realizes the given IF-language. Among two methods for construction of such automaton presented here, one is based on Myhill-Nerode's theory while the other is based on derivatives of the given IF-language. Meanwhile, the categories of deterministic automata with IF-outputs and IF-languages alongwith a functorial relationship between them are introduced
http://ijfs.usb.ac.ir/article_2427_d4fba1c316d0e743973d31743874f79d.pdf
2016-06-30T11:23:20
2017-09-20T11:23:20
19
34
10.22111/ijfs.2016.2427
eterministic automaton
IF-output
IF-language
Minimal realization
Vijay K.
Yadav
true
1
Department of Mathematics, National Institute of Technology,
Jamshedpur-831014, Jharkhand, India
Department of Mathematics, National Institute of Technology,
Jamshedpur-831014, Jharkhand, India
Department of Mathematics, National Institute of Technology,
Jamshedpur-831014, Jharkhand, India
LEAD_AUTHOR
Vinay
Gautam
gautam.gautam181@gmail.com
true
2
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, Jharkhand, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, Jharkhand, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, Jharkhand, India
AUTHOR
S. P.
Tiwari
true
3
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, Jharkhand, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, Jharkhand, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, Jharkhand, India
AUTHOR
[1] M. A. Arbib and E. G. Manes, Machines in a category: An expository introduction, SIAM
1
Review, 16 (1974), 285{302.
2
[2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87{96.
3
[3] K. T. Atanassov, More on Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 33 (1989), 37{45.
4
[4] A. Choubey and K. M. Ravi, Minimization of deterministic nite automata with vague (nal)
5
states and intuitionistic fuzzy (nal) states, Iranian Journal of Fuzzy System, 10 (2013), 75{
6
[5] T. Y. Chen, H. P. Wang and J. C. Wang, Fuzzy automata based on Atanassov fuzzy sets
7
and applications on consumers, advertising involvement, African Journal of Business Man-
8
agement, 6 (2012), 865{880.
9
[6] T. Y. Chen and C. C. Chou, Fuzzy automata with Atanassov's intuitionstic fuzzy sets and
10
their applications to product involvement, Journal of the Chinese Institute of Industrial En-
11
gineers, 26 (2009), 245{254.
12
[7] D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade, Terminological diculties in
13
fuzzy set theory the case of intuitionistic fuzzy sets, Fuzzy Sets and Systems, 156 (2005),
14
[8] J. A. Goguen, Minimal realization of machines in closed categories, Bulletin of American
15
Mathematical Society, 78 (1972), 777{783.
16
[9] J. Ignjatovic, M. Ciric, S. Bogdanovic and T. Petkovic, Myhill-Nerode type theory for fuzzy
17
languages and automata, Fuzzy Sets and Systems, 161 (2010), 1288{1324.
18
[10] Y. B. Jun, Intuitionistic fuzzy nite state machines, Journal of Applied Mathematics and
19
Computing, 17 (2005), 109{120.
20
[11] Y. B. Jun, Quotient structures of intuitionistic fuzzy nite state machines, Information Sci-
21
ences, 177 (2007), 4977{4986.
22
[12] Y. H. Kim, J. G. Kim and S. J. Cho, Products of T-generalized state machines and T-
23
generalized transformation semigroups, Fuzzy Sets and Systems, 93 (1998), 87{97.
24
[13] H. V. Kumbhojkar and S. R. Chaudhri, On proper fuzzication of fuzzy nite state machines,
25
International Journal of Fuzzy Mathematics, 4 (2008), 1019{1027.
26
[14] E. T. Lee and L. A. Zadeh, Note on fuzzy languages, Information Sciences, 1 (1969), 421{434.
27
[15] F. Lin and H. Ying, Modeling and control of fuzzy discrete event systems, IEEE Transactions
28
on Systems, Man, and Cybernetics-Part B, 32 (2002), 408{415.
29
[16] D. S. Malik, J. N. Mordeson and M. K. Sen, Submachines of fuzzy nite state machine,
30
Journal of Fuzzy Mathematics, 2 (1994), 781{792.
31
[17] D. S. Malik and J. N. Mordeson, Fuzzy automata and languages: theory and applications,
32
Chapman Hall, CRC Boca Raton, 2002.
33
[18] D. Qiu, Supervisory control of fuzzy discrete event systems: A formal approach, IEEE Trans-
34
actions on Systems, Man, and Cybernetics-Part B, 35 (2005), 72{88.
35
[19] D. Qiu and F. Liu, Fuzzy discrete event systems under fuzzy observability and a test-
36
algorithm, IEEE Transactions on Fuzzy Systems, 17 (2009), 578{589.
37
[20] E. S. Santos, Maximin automata, Information and Control, 12 (1968), 367{377.
38
[21] A. K. Srivastava and S. P. Tiwari, IF-topologies and IF-automata, Soft Computing, 14 (2010),
39
[22] S. P. Tiwari and Anupam K. Singh, On bijective correspondence between IF-preorders and
40
saturated IF-topologies, International Journal of Machine Learning and Cybernetics, 4 (2013),
41
[23] S. P. Tiwari and Anupam K. Singh, IF-preorder, IF-topology and IF-automata, International
42
Journal of Machine Learning and Cybernetics, 6 (2015), 205{211.
43
[24] M. G. Thomason and P. N. Marinos, Deterministic acceptors of regular fuzzy languages,
44
IEEE Transactions Systems Man Cybernetics, 4 (1974), 228{230.
45
[25] W. G.Wee, On generalizations of adaptive algorithm and application of the fuzzy sets concept
46
to pattern classication, Ph. D. Thesis, Purdue University, Lafayette, IN 1967.
47
[26] L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338{353.
48
[27] L. A. Zadeh, Fuzzy languages and their relation to human and machine intelligence, Electrn.
49
Research Laboratory University California, Berkeley, CA,Technical Report 1971.
50
[28] X. Zhang and Y. Li, Intuitionistic fuzzy recognizers and intuitionistic fuzzy nite automata,
51
Soft Computing, 13 (2009), 611{616.
52
ORIGINAL_ARTICLE
Power and Velocity Control of Wind Turbines by Adaptive Fuzzy Controller during Full Load Operation
Research on wind turbine technologies have focused primarily on power cost reduction. Generally, this aim has been achieved by increasing power output while maintaining the structural load at a reasonable level. However, disturbances, such as wind speed, affect the performance of wind turbines, and as a result, the use of various types of controller becomes crucial.This paper deals with two adaptive fuzzy controllers at full load operation. The first controller uses the generated power, and the second one uses the angular velocity as feedback signals. These feedback signals act to control the load torque on the generator and blade pitch angle. Adaptive rules, derived from the fuzzy controller, are defined based on the differences between state variables of the power and angular velocity of the generator and their nominal values.The results, which are compared with verified results of reference controller, show that the proposed adaptive fuzzy controller in full load operation has a higher efficiency than that of reference ones, insensitive to fast wind speed variation that is considered as disturbance.
http://ijfs.usb.ac.ir/article_2428_308f6f0e85ce1f925dc3c630db3c4b78.pdf
2016-06-30T11:23:20
2017-09-20T11:23:20
35
48
10.22111/ijfs.2016.2428
Adaptive fuzzy controller
Control strategy
Full load region
Wind turbine model
Hamed
Habibi
hamed28160@gmail.com
true
1
PhD, Faculty of Science and Engineering, School of Civil and Me-
chanical Engineering, Curtin University, Perth, Australia
PhD, Faculty of Science and Engineering, School of Civil and Me-
chanical Engineering, Curtin University, Perth, Australia
PhD, Faculty of Science and Engineering, School of Civil and Me-
chanical Engineering, Curtin University, Perth, Australia
LEAD_AUTHOR
Aghil
Yousefi Koma
aykoma@ut.ac.ir
true
2
Professor, Center of Advanced Systems and Technologies
(CAST), School of Mechanical Engineering, College of Engineering, University of
Tehran, Tehran, Iran
Professor, Center of Advanced Systems and Technologies
(CAST), School of Mechanical Engineering, College of Engineering, University of
Tehran, Tehran, Iran
Professor, Center of Advanced Systems and Technologies
(CAST), School of Mechanical Engineering, College of Engineering, University of
Tehran, Tehran, Iran
AUTHOR
Ahmad
Sharifian
true
3
Computational Engineering and Science Research Centre (CESRC),
Faculty of Health, Engineering and Science, University of Southern Queensland, Toow-
oomba, Australia
Computational Engineering and Science Research Centre (CESRC),
Faculty of Health, Engineering and Science, University of Southern Queensland, Toow-
oomba, Australia
Computational Engineering and Science Research Centre (CESRC),
Faculty of Health, Engineering and Science, University of Southern Queensland, Toow-
oomba, Australia
AUTHOR
[1] A. G. Aissaoui, A. Tahour, N. Essounbouli, F. Nollet, M. Abid, and M. I. Chergui, A Fuzzy-PI
1
control to extract an optimal power from wind turbine, Energy Conversion and Management,
2
65(1) (2013), 688{696.
3
[2] R. Ata and Y. Kocyigit, An adaptive neuro-fuzzy inference system approach for prediction of
4
tip speed ratio in wind turbines, Expert Systems with Applications, 37(7) (2010), 5454{5460.
5
[3] K. Bedoud, M. Ali-rachedi, T. Bahi, and R. Lakel, Adaptive Fuzzy Gain Scheduling of PI
6
Controller for control of the Wind Energy Conversion Systems, Energy Procedia, 74(8)
7
(2015), 211-225.
8
[4] F. D. Bianchi, H. De Battista and R. J. Mantz, Wind turbine control systems: principles,
9
modelling and gain scheduling design, Springer Science and Business Media, (2006).
10
[5] S. Bououden, M. Chadli, S. Filali, and A. El Hajjaji, Fuzzy model based multivariable pre-
11
dictive control of a variable speed wind turbine: LMI approach, Renewable Energy, 37(1)
12
(2012), 434{439.
13
[6] S. Bououden, M. Chadli and H. R. Karimi, Robust Predictive Control of a variable speed wind
14
turbine using the LMI formalism, European Control Conference (ECC), France, (2014), 820{
15
[7] A. L. Elshafei and M. A. Azzouz, Adaptive fuzzy regulation of the DC-bus capacitor voltage in
16
a wind energy conversion system (WECS), Expert Systems with Applications, 38(5) (2011),
17
5500{5506.
18
[8] T. Esbensen, B. Jensen, M. Niss, C. Sloth and J. Stoustrup, Joint power and speed control
19
of wind turbines, Aalborg University, Denmark, 2008.
20
[9] G. Feng, X. Daping and L. Yuegang, Pitch-control for large-scale wind turbines based on
21
feed forward fuzzy-PI, 7th World Congress on Intelligent Control and Automation (WCICA),
22
China, (2008), 2277{2282.
23
[10] S. Heier, Grid integration of wind energy conversion systems, Wiley, 1998.
24
[11] G. Hou, L. Hu and J. Zhang, Variable universe adaptive fuzzy PI control used in VSCF
25
wind power generator system, 8th World Congress on Intelligent Control and Automation
26
(WCICA), China, (2010), 4870-4874.
27
[12] X. Jian-Jun, X. Li-Mei, Q. Xiao-Ning, J. Chun-Lei and W. Jian-Ren, Study of variable-pitch
28
wind turbine based on fuzzy control, 2nd International Conference on Future Computer and
29
Communication (ICFCC), China, (2010), V1-235{V1-239.
30
[13] K. E. Johnson, L. Y. Pao, M. J. Balas and L. J. Fingersh, Control of variable-speed wind
31
turbines: standard and adaptive techniques for maximizing energy capture, Control Systems,
32
26(3) (2006), 70{81.
33
[14] M. Mohandes, S. Rehman and S. M. Rahman, Estimation of wind speed prole using adaptive
34
neuro-fuzzy inference system (ANFIS), Applied Energy, 88(11) (2011), 4024{4032.
35
[15] Y. Qi and Q. Meng, The application of fuzzy PID control in pitch wind turbine, Energy
36
Procedia, 16(Part C) (2012), 1635{1641.
37
[16] S. Shamshirband, D. Petkovi, . ojbai, V. Nikoli, N. B. Anuar, N. L. Mohd Shuib, et al.,
38
Adaptive neuro-fuzzy optimization of wind farm project net prot, Energy Conversion and
39
Management, 80(4) (2014), 229{237.
40
[17] S. Simani and P. Castaldi, Data-driven and adaptive control applications to a wind turbine
41
benchmark model, Control Engineering Practice, 21(12) (2013), 1678{1693.
42
[18] C. Sloth, T. Esbensen, M. Niss, J. Stoustrup and P. F. Odgaard, Robust LMI-based control
43
of wind turbines with parametric uncertainties, IEEE International Conference on Control
44
Applications (CCA) part of the IEEE Multi-Conference on Systems and Control (MSC),
45
Russia, (2009), 776{781.
46
[19] Y. Xiyun and L. Xinran, Integral variable structure fuzzy adaptive control for variable speed
47
wind power system, International Conference on Logistics Systems and Intelligent Manage-
48
ment, China, (2010), 1247{1250.
49
ORIGINAL_ARTICLE
Intuitionistic Fuzzy Information Measures with Application in Rating of Township Development
Predominantly in the faltering atmosphere, the precise value of some factors is difficult to measure. Though, it can be easily approximated by intuitionistic fuzzy linguistic term in the real-life world problem. To deal with such situations, in this paper two information measures based on trigonometric function for intuitionistic fuzzy sets, which are a generalized version of the fuzzy information measures are introduced. Based on it new trigonometric similarity measure is developed. Mathematical illustration displays reasonability and effectiveness of the information measures for IFSs by comparing it with the existing information measures. Corresponding to information and similarity measures for IFSs, two new methods: (1) Intuitionistic Fuzzy Similarity Measure Weighted Average Operator (IFSMWAO) method for township development and (2) TOPSIS method for multiple criteria decision making (MCDM) (investment policies) problems have been developed. In the existing methods the authors have assumed the weight vectors, while in the proposed method it has been calculated using intuitionistic fuzzy information measure. This enhances the authenticity of the proposed method.
http://ijfs.usb.ac.ir/article_2429_0a20ccdc49e7f2ba01b140e7ce8033a0.pdf
2016-06-30T11:23:20
2017-09-20T11:23:20
49
70
10.22111/ijfs.2016.2429
Intuitionistic fuzzy set
Intuitionistic fuzzy information
Similarity measure
Township development
TOPSIS
Arunodaya Raj
Mishra
true
1
Department of Mathematics, ITM University, Gwalior-474001,
M. P., India
Department of Mathematics, ITM University, Gwalior-474001,
M. P., India
Department of Mathematics, ITM University, Gwalior-474001,
M. P., India
LEAD_AUTHOR
[1] K. T. Atanassov and G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and
1
Systems, 31 (1989), 343{349.
2
[2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87{96.
3
[3] K. T. Atanassov, Intuitionistic fuzzy sets, Springer Physica-Verlag Heidelberg, Germany,
4
[4] P. Burillo and H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy
5
sets, Fuzzy Sets and Systems, 78 (1996), 305{316.
6
[5] H. Bustince and P. Burillo, Vague sets are intuitionistic fuzzy sets, Fuzzy sets and systems,
7
79 (1996), 403{405.
8
[6] J. Chachi and S. M. Taheri, A unied approach to similarity measures between intuitionistic
9
fuzzy sets, International Journal of Intelligent Systems, 28 (2013), 669{685.
10
[7] T. Y. Chen and C. H. Li, Determining objective weights with intuitionistic fuzzy entropy
11
measures: A comparative analysis, Information Sciences, 180 (2010), 4207{4222.
12
[8] C. Cornelis, K. T. Atanassov and E. E. Kerre, Intuitionistic fuzzy sets and interval-valued
13
fuzzy sets: a critical comparison, In: Proceedings of the 3rd Conference of the European
14
Society for Fuzzy Logic and Technology (EUSFLAT '03), Zittau, Germany, (2003), 159-163.
15
[9] A. De Luca and S. Termini, A denition of non-probabilistic entropy in the setting of fuzzy
16
set theory, Inform. Control, 20 (1972), 301{312.
17
[10] G. Deschrijver and E. E. Kerre, On the relationship between some extensions of fuzzy set
18
theory, Fuzzy Sets and Systems, 133 (2003), 227{235.
19
[11] B. Farhadinia, A theoretical development on the entropy of interval-valued fuzzy sets based
20
on the intuitionistic distance and its relationship with similarity measure, Knowledge-Based
21
Systems, 39 (2013), 79{84.
22
[12] W. L. Gau and D.J. Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cyber-
23
netics, 23 (1993), 610{614.
24
[13] P. Grzegorzewski and E. Mrowka, Some notes on (Atanassov's) intuitionistic fuzzy sets,
25
Fuzzy sets and systems, 156 (2005), 492{495.
26
[14] D. S. Hooda and A. R. Mishra, On trigonometric fuzzy information measures, ARPN Journal
27
of Science and Technology, 05 (2015), 145{152.
28
[15] C. Hung and L. H. Chen, A fuzzy TOPSIS decision making model with entropy under intu-
29
itionistic fuzzy environment, In: Proceedings of the international multi- conference of engi-
30
neers and computer scientists (IMECS), 01 (2009), 01{04.
31
[16] W. L. Hung and M. S. Yang, Fuzzy entropy on intuitionistic fuzzy sets, International Journal
32
of Intelligent Systems, 21 (2006), 443{451.
33
[17] C. L. Hwang and K. S. Yoon, Multiple attribute decision making: Methods and applications,
34
Berlin: Springer-Verlag, 1981.
35
[18] Y. Jiang, Y. Tang, H. Liu and Z. Chen, Entropy on intuitionistic fuzzy soft sets and on
36
interval-valued fuzzy soft sets, Information Sciences, 240 (2013), 95{114.
37
[19] D. Joshi and S. Kumar, Intuitionistic fuzzy entropy and distance measure based TOPSIS
38
method for multi-criteria decision making, Egyptian informatics journal, 15 (2014), 97{104.
39
[20] A. Kauman, Fuzzy subsets-Fundamental theoretical elements, Academic Press, New York,
40
[21] D. F. Li and C. T. Cheng, New similarity measure of intuitionistic fuzzy sets and application
41
to pattern recognitions, Pattern Recognition Letters, 23 (2002), 221{225.
42
[22] J. Li, D. Deng, H. Li and W. Zeng, The relationship between similarity measure and entropy
43
of intuitionistic fuzzy sets, Information Science, 188 (2012), 314{321.
44
[23] F. Li, Z. H. Lu and L. J. Cai, The entropy of vague sets based on fuzzy sets, J. Huazhong
45
Univ. Sci. Tech., 31 (2003), 24{25.
46
[24] Z. Z. Liang and P. F. Shi, Similarity measures on intuitionistic fuzzy sets, Pattern Recognition
47
Letters, 24 (2003), 2687{2693.
48
[25] L. Lin, X. H. Yuan and Z. Q. Xia, Multicriteria fuzzy decision-making methods based on
49
intuitionistic fuzzy sets, J. Comp Syst. Sci., 73 (2007), 84{88.
50
[26] H. W. Liu and G. J. Wang, Multi-criteria decision-making methods based on intuitionistic
51
fuzzy sets, European Journal of Operational Research, 179 (2007), 220{233.
52
[27] P. D. Liu and Y. M. Wang, Multiple attribute group decision making methods based on
53
intuitionistic linguistic power generalized aggregation operators, Applied Soft Computing
54
Journal,17 (2014), 90{104.
55
[28] P. Liu, Some hamacher aggregation operators based on the interval-valued intuitionistic fuzzy
56
numbers and their application to group decision making, IEEE Transactions on Fuzzy Sys-
57
tems, 22 (2014), 83{97.
58
[29] A. R. Mishra, D. S. Hooda and D. Jain, Weighted trigonometric and hyperbolic fuzzy infor-
59
mation measures and their applications in optimization principles, International Journal of
60
Computer and Mathematical Sciences, 03 (2014), 62{68.
61
[30] A. R. Mishra, D. Jain and D. S. Hooda, Exponential intuitionistic fuzzy information measure
62
with assessment of service quality, International journal of fuzzy systems, accepted.
63
[31] H. B. Mitchell, On the Dengfeng-Chuntian similarity measure and its application to pattern
64
recognition, Pattern Recognition Letters, 24 (2003), 3101{3104.
65
[32] E. Szmidt and J. Kacprzyk, A concept of similarity for intuitionistic fuzzy sets and its
66
application in group decision making, In: Proceedings of International Joint Conference on
67
Neural Networks & IEEE International Conference on Fuzzy Systems, Budapest, Hungary,
68
(2004), 25{29.
69
[33] E. Szmidt and J. Kacprzyk, A new concept of a similarity measure for intuitionistic fuzzy
70
sets and its use in group decision making, In: V. Torra, Y. Narukawa, S. Miyamoto (Eds.),
71
Modelling Decision for Articial Intelligence, LNAI 3558, Springer, (2005), 272{282.
72
[34] E. Szmidt and J. Kacprzyk, Entropy for intuitionistic fuzzy sets, Fuzzy Sets and Systems,
73
118 (2001), 467{477.
74
[35] I. K. Vlachos and G. D. Sergiadis, Inner product based entropy in the intuitionistic fuzzy
75
setting, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 14
76
(2006), 351{366.
77
[36] I. K. Vlachos and G. D. Sergiadis, Intuitionistic fuzzy information-application to pattern
78
recognition, Pattern Recognition Letters, 28 (2007), 197{206.
79
[37] P.Z.Wang, Fuzzy sets and its applications, Shanghai Science and Technology Press, Shanghai,
80
[38] X. Z. Wang, B. D. Baets and E. E. Kerre, A comparative study of similarity measures, Fuzzy
81
Sets and Systems, 73 (1995), 259{268.
82
[39] C. P. Wei and Y. Zhang, Entropy measures for interval-valued intuitionistic fuzzy sets and
83
their application in group decision making, Mathematical Problems in Engineering, 2015
84
(2015), 01{13.
85
[40] C. P. Wei, P. Wang and Y. Zhang, Entropy, similarity measure of interval-valued intuition-
86
istic fuzzy sets and their applications, Information Sciences, 181 (2011), 4273{4286.
87
[41] P. Wei, Z. H. Gao and T. T. Guo, An intuitionistic fuzzy entropy measure based on the
88
trigonometric function, Control and Decision, 27(2012), 571{574.
89
[42] G. Wei, X. Zhao and R. Lin, Some hesitant interval-valued fuzzy aggregation operators
90
and their applications to multiple attribute decision making, Knowledge-Based Systems, 46
91
(2013), 43{53.
92
[43] M. M. Xia and Z. S. Xu, Entropy/cross entropy-based group decision making under intu-
93
itionistic fuzzy environment, Information Fusion, 13 (2012), 31{47.
94
[44] Z. S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Transactions on Fuzzy Systems,
95
15 (2007), 1179{1187.
96
[45] Z. S. Xu, On similarity measures of interval-valued intuitionistic fuzzy sets and their appli-
97
cation to pattern recognitions, Journal of Southeast University(English Edition), 23 (2007),
98
[46] R. R. Yager, On the measure of fuzziness and negation, part I: membership in unit interval,
99
International Journal of General Systems, 05 (1979), 221{229.
100
[47] J. Ye, Two eective measures of intuitionistic fuzzy entropy, Computing, 87 (2010), 55{62.
101
[48] Z. Yue, Extension of TOPSIS to determine weight of decision maker for group decision
102
making problems with uncertain information, Exp. Syst. Appl., 39 (2012), 6343{6350.
103
[49] L. A. Zadeh, Fuzzy sets, Information and Computation, 08 (1965), 338{353.
104
[50] W. Zeng and P. Guo, Normalized distance, similarity measure, inclusion measure and entropy
105
of interval-valued fuzzy sets and their relationship, Information Sciences, 178 (2008), 1334{
106
[51] W. Zeng and H. Li, Inclusion measures, similarity measures, and the fuzziness of fuzzy sets
107
and their relations, International Journal of Intelligent Systems, 21 (2006), 639{653.
108
[52] W. Zeng and H. Li, Relationship between similarity measure and entropy of interval valued
109
fuzzy sets, Fuzzy Sets and Systems, 157 (2006), 1477{1484.
110
[53] H. Zhang, W. Zhang and C. Mei, Entropy of interval-valued fuzzy sets based on distance and
111
its relationship with similarity measure, Knowledge-Based Systems, 22 (2009), 449{454.
112
[54] Q. S. Zhang and S. Y. Jiang, A note on information entropy measures for vague sets and its
113
applications, Information Sciences, 178 (2008), 4184{4191.
114
ORIGINAL_ARTICLE
Solving fuzzy differential equations by using Picard method
In this paper, The Picard method is proposed to solve the system of first-order fuzzy differential equations $(FDEs)$ with fuzzy initial conditions under generalized $H$-differentiability. Theexistence and uniqueness of the solution and convergence of theproposed method are proved in details. Finally, the method is illustrated by solving some examples.
http://ijfs.usb.ac.ir/article_2430_46f79676ff400d760887de75aa5b914a.pdf
2016-06-30T11:23:20
2017-09-20T11:23:20
71
81
10.22111/ijfs.2016.2430
First order fuzzy differential equations
Fuzzy number
Fuzzy-valued function
$h$-difference
Generalized differentiability
Picard method
S. S.
Behzadi
true
1
Department of Mathematics, Islamic Azad University, Qazvin Branch
Qazvin Iran
Department of Mathematics, Islamic Azad University, Qazvin Branch
Qazvin Iran
Department of Mathematics, Islamic Azad University, Qazvin Branch
Qazvin Iran
LEAD_AUTHOR
T.
Allahviranloo
true
2
Department of Mathematics, Islamic Azad University, Science and
Research Branch, Tehran Iran
Department of Mathematics, Islamic Azad University, Science and
Research Branch, Tehran Iran
Department of Mathematics, Islamic Azad University, Science and
Research Branch, Tehran Iran
AUTHOR
[1] S. Abbasbandy and T. Allahviranloo, Numerical solutions of fuzzy dierential equations by
1
Taylor method, J. Comput. Meth. Appl. Math., 2 (2002), 113-124.
2
[2] S. Abbasbandy, T. Allahviranloo, O. Lopez-Pouso and J. J. Nieto, Numerical methods for
3
fuzzy dierential inclusions, Comput. Math. Appl., 48 (2004), 1633-1641.
4
[3] S. Abbasbandy, J. J. Nieto and M. Alavi, Tuning of reachable set in one dimensional fuzzy
5
dierential inclusions, Chaos Soliton and Fractals., 26 (2005), 1337-1345.
6
[4] T. Allahviranloo, N. Ahmady and E. Ahmady, Numerical solution of fuzzy dierential equa-
7
tions by predictorcorrector method, Inform. Sci., 177 (2007), 1633-1647.
8
[5] B. Bede, Note on Numerical solutions of fuzzy dierential equations by predictorcorrector
9
method, Inform. Sci., 178 (2008), 1917-1922.
10
[6] B. Bede and S. G. Gal, Generalizations of the dierentiability of fuzzy number valued func-
11
tions with applications to fuzzy dierential equation, Fuzzy Set.Syst., 151 (2005), 581-599.
12
[7] B. Bede, J. Imre, C. Rudas and L. Attila, First order linear fuzzy dierential equations under
13
generalized dierentiability, Inform. Sci., 177 (2007), 3627-3635.
14
[8] J. J. Buckley and T. Feuring, Fuzzy dierential equations, Fuzzy Set. Syst., 110 (2000),
15
[9] J.J. Buckley, T. Feuring and Y. Hayashi, Linear systems of rst order ordinary dierential
16
equations: fuzzy initial conditions, Soft Comput., 6 (2002), 415-421.
17
[10] J. J. Buckley and L. J. Jowers, Simulating Continuous Fuzzy Systems, Springer-Verlag, Berlin
18
Heidelberg, 2006.
19
[11] Y. Chalco-Cano and H. Romn-Flores,On new solutions of fuzzy dierential equations, Chaos
20
Soliton and Fractals., 45 (2006), 1016-1043.
21
[12] Y. Chalco-Cano, Romn-Flores, M. A. Rojas-Medar, O. Saavedra and M. Jimnez-Gamero, The
22
extension principle and a decomposition of fuzzy sets, Inform. Sci., 177 (2007), 5394-5403.
23
[13] C. K. Chen and S. H. Ho,Solving partial dierential equations by two-dimensional dierential
24
transform method, Appl. Math. Comput., 106 (1999), 171-179.
25
[14] Y. J. Cho and H. Y. Lan, The existence of solutions for the nonlinear rst order fuzzy
26
dierential equations with discontinuous conditions, Dyn. Contin.Discrete., 14 (2007) , 873-
27
[15] W. Congxin and S. Shiji,Exitance theorem to the Cauchy problem of fuzzy dierential equa-
28
tions under compactance-type conditions, Inform. Sci., 108 (1993), 123-134.
29
[16] P. Diamond, Time-dependent dierential inclusions, cocycle attractors and fuzzy dierential
30
equations, IEEE Trans. Fuzzy Syst., 7 (1999), 734-740.
31
[17] P. Diamond, Brief note on the variation of constants formula for fuzzy dierential equations,
32
Fuzzy Set. Syst., 129 (2002), 65-71.
33
[18] Z. Ding, M. Ma and A. Kandel, Existence of solutions of fuzzy dierential equations with
34
parameters, Inform. Sci., 99 (1997), 205-217.
35
[19] D. Dubois and H. Prade, Towards fuzzy dierential calculus: Part 3, dierentiation, Fuzzy
36
Set. Syst., 8 (1982), 225-233.
37
[20] O. S. Fard, Z. Hadi, N. Ghal-Eh and A. H. Borzabadi,A note on iterative method for solving
38
fuzzy initial value problems, J. Adv. Res. Sci. Comput., 1 (2009), 22-33.
39
[21] O. S. Fard, A numerical scheme for fuzzy cauchy problems, J. Uncertain Syst., 3 (2009),
40
[22] O. S. Fard, An iterative scheme for the solution of generalized system of linear fuzzy dier-
41
ential equations, World Appl. Sci. J., 7 (2009), 1597-1604.
42
[23] O. S. Fard and A. V. Kamyad, Modied k-step method for solving fuzzy initial value problems,
43
Iranian Journal of Fuzzy Systems, 8(1) (2011), 49-63.
44
[24] O. S. Fard, T. A. Bidgoli and A. H. Borzabadi, Approximate-analytical approach to nonlinear
45
FDEs under generalized dierentiability, J. Adv. Res. Dyn. Control Syst., 2 (2010), 56-74.
46
[25] W. Fei,Existence and uniqueness of solution for fuzzy random dierential equations with
47
non-Lipschitz coecients, Inform. Sci., 177 (2007), 329-4337.
48
[26] M. J. Jang and C. L. Chen, Y.C. Liy,On solving the initial-value problems using the dier-
49
ential transformation method, Appl. Math. Comput., 115 (2000), 145- 160.
50
[27] L. J. Jowers, J. J. Buckley and K. D. Reilly, Simulating continuous fuzzy systems, Inform.
51
Sci., 177 (2007), 436-448.
52
[28] O. Kaleva, Fuzzy dierential equations, Fuzzy Set. Syst., 24 (1987), 301-317.
53
[29] O. Kaleva, The Cauchy problem for fuzzy dierential equations, Fuzzy Set. Syst., 35 (1990),
54
[30] O. Kaleva, A note on fuzzy dierential equations, Nonlinear Anal.,64 (2006) 895-900.
55
[31] R. R. Lopez, Comparison results for fuzzy dierential equations, Inform. Sci., 178 (2008),
56
1756-1779.
57
[32] M. Ma, M. Friedman and A. Kandel, Numerical solutions of fuzzy dierential equations,
58
Fuzzy Set. Syst., 105 (1999), 133-138.
59
[33] M. T. Mizukoshi, L. C. Barros, Y. Chalco-Cano, H. Romn-Flores and R. C. Bassanezi, Fuzzy
60
dierential equations and the extension principle, Inform. Sci., 177(2007) , 3627-3635.
61
[34] M. Oberguggenberger and S. Pittschmann,Dierential equations with fuzzy parameters,
62
Math. Mod. Syst., 5 (1999), 181-202.
63
[35] G. Papaschinopoulos, G. Stefanidou and P. Efraimidi, Existence uniqueness and asymptotic
64
behavior of the solutions of a fuzzy dierential equation with piecewise constant argument,
65
Inform. Sci., 177 (2007), 3855-3870.
66
[36] M. L. Puri and D. A. Ralescu, Dierentials of fuzzy functions, J. Math. Anal. Appl., 91
67
(1983), 552-558.
68
[37] M. L. Puri and D. Ralescu, Fuzzy random variables, J. Math. Anal. Appl., 114 (1986),
69
[38] H. J. Zimmermann, Fuzzy sets theory and its applications, Kluwer Academic Press, Dor-
70
drecht, 1991.
71
ORIGINAL_ARTICLE
A Quadratic Programming Method for Ranking Alternatives Based on Multiplicative and Fuzzy Preference Relations
This paper proposes a quadratic programming method (QPM) for ranking alternatives based on multiplicative preference relations (MPRs) and fuzzy preference relations (FPRs). The proposed QPM can be used for deriving a ranking from either a MPR or a FPR, or a group of MPRs, or a group of FPRs, or their mixtures. The proposed approach is tested and examined with two numerical examples, and comparative analyses with the existing methods are provided to show the effectiveness and advantages of the QPM.
http://ijfs.usb.ac.ir/article_2431_b2acd260e89417f6d83b41078b14e53e.pdf
2016-06-30T11:23:20
2017-09-20T11:23:20
83
94
10.22111/ijfs.2016.2431
Quadratic programming
Group decision making (GDM)
Multiplicative preference relation (MPR)
Fuzzy preference relation (FPR)
Ranking alternatives
Yejun
Xu
xuyejohn@163.com
true
1
State Key Laboratory of Hydrology-Water Resources and Hydraulic
Engineering, Hohai University, No.1 Xikang Road, Nanjing, 210098, Jiangsu,China and
Business School, Hohai University, Jiangning Campus, No.8 Focheng West Road, Jiangning, Nanjing, 211100, Jiangsu, China
State Key Laboratory of Hydrology-Water Resources and Hydraulic
Engineering, Hohai University, No.1 Xikang Road, Nanjing, 210098, Jiangsu,China and
Business School, Hohai University, Jiangning Campus, No.8 Focheng West Road, Jiangning, Nanjing, 211100, Jiangsu, China
State Key Laboratory of Hydrology-Water Resources and Hydraulic
Engineering, Hohai University, No.1 Xikang Road, Nanjing, 210098, Jiangsu,China and
Business School, Hohai University, Jiangning Campus, No.8 Focheng West Road, Jiangning, Nanjing, 211100, Jiangsu, China
LEAD_AUTHOR
Qianqian
Wang
true
2
State Key Laboratory of Hydrology-Water Resources and Hydraulic
Engineering, Hohai University, No.1 Xikang Road, Nanjing, 210098, Jiangsu, China and
Business School, Hohai University, Jiangning Campus, No.8 Focheng West Road, Jiangning, Nanjing, 211100, Jiangsu, China
State Key Laboratory of Hydrology-Water Resources and Hydraulic
Engineering, Hohai University, No.1 Xikang Road, Nanjing, 210098, Jiangsu, China and
Business School, Hohai University, Jiangning Campus, No.8 Focheng West Road, Jiangning, Nanjing, 211100, Jiangsu, China
State Key Laboratory of Hydrology-Water Resources and Hydraulic
Engineering, Hohai University, No.1 Xikang Road, Nanjing, 210098, Jiangsu, China and
Business School, Hohai University, Jiangning Campus, No.8 Focheng West Road, Jiangning, Nanjing, 211100, Jiangsu, China
AUTHOR
Huimin
Wang
hmwang@hhu.edu.cn
true
3
State Key Laboratory of Hydrology-Water Resources and Hydraulic
Engineering, Hohai University, No.1 Xikang Road, Nanjing, 210098, Jiangsu, China and
Business School, Hohai University, Jiangning Campus, No.8 Focheng West Road, Jiangning, Nanjing, 211100, Jiangsu, China
State Key Laboratory of Hydrology-Water Resources and Hydraulic
Engineering, Hohai University, No.1 Xikang Road, Nanjing, 210098, Jiangsu, China and
Business School, Hohai University, Jiangning Campus, No.8 Focheng West Road, Jiangning, Nanjing, 211100, Jiangsu, China
State Key Laboratory of Hydrology-Water Resources and Hydraulic
Engineering, Hohai University, No.1 Xikang Road, Nanjing, 210098, Jiangsu, China and
Business School, Hohai University, Jiangning Campus, No.8 Focheng West Road, Jiangning, Nanjing, 211100, Jiangsu, China
AUTHOR
[1] S. Alonso, F. Cabrerizo, F. Chiclana, F. Herrera and E. Herrera-Viedma, Group decision mak-
1
ing with incomplete fuzzy linguistic preference relations, International Journal of Intelligent
2
Systems, 24 (2009), 201{222.
3
[2] F. Chiclana, F. Herrera and E. Herrera-Viedma, Integrating multiplicative preference relations
4
in a multipurpose decision-making model based on fuzzy preference relations, Fuzzy Sets and
5
Systems, 122 (2001), 277{291.
6
[3] F. Chiclana, F. Herrera and E. Herrera-Viedma, Integrating three representation models in
7
fuzzy multipurpose decision making based on fuzzy preference relations, Fuzzy Sets and Sys-
8
tems, 97 (1998), 33{48.
9
[4] K. O. Cogger and P. L. Yu, Eigenweight vectors and least-distance approximation for revealed
10
preference in pairwise weight ratios, Journal of Optimization Theory and Applications, 46
11
(1985), 483{491.
12
[5] G. Crawford and C. Williams, A note on the analysis of subjective judgement matrices,
13
Journal of Mathematical Psychology, 29 (1985), 387{405.
14
[6] Z. P. Fan, J. Ma, Y. P. Jiang, Y. H. Sun and L. Ma, A goal programming approach to group
15
decision making based on multiplicative preference relations and fuzzy preference relations,
16
European Journal of Operational Research, 174 (2006), 311{321.
17
[7] Z. P. Fan, J. Ma and Q. Zhang, An approach to multiple attribute decision making based on
18
fuzzy preference information on alternatives, Fuzzy Sets and Systems, 131 (2002), 101{106.
19
[8] Z. P. Fan, S. H. Xiao and G. F. Hu, An optimization method for integrating two kinds of
20
preference information in group decision-making, Computers & Industrial Engineering, 46
21
(2004), 329{335.
22
[9] Z. P. Fan and Y. Zhang, A goal programming approach to group decision-making with three
23
formats of incomplete preference relations, Soft Computing, 14 (2010), 1083{1090.
24
[10] E. Fernandez and J. C. Leyva, A method based on multiobjective optimization for deriving
25
a ranking from a fuzzy preference relation, European Journal of Operational Research, 154
26
(2004), 110{124.
27
[11] P. T. Harker, Alternative modes of questioning in the analytic hierarchy process, Mathemat-
28
ical Modelling, 9 (1987), 353{360.
29
[12] F. Herrera, E. Herrera-Viedma and F. Chiclana, Multiperson decision-making based on multi-
30
plicative preference relations, European Journal of Operational Research,129(2001),372{385.
31
[13] R. E. Jensen, An alternative scaling method for priorities in hierarchy structures, Journal of
32
Mathematical Psychology, 28 (1984), 317{332.
33
[14] J. Kacprzyk, Group decision making with a fuzzy linguistic majority, Fuzzy Sets and Systems,
34
18 (1986), 105{118.
35
[15] J. Kacprzyk and M. Roubens, Non-Conventional Preference Relations in Decision-Making,
36
Springer, Berlin, 1988.
37
[16] S. Lipovetsky, The synthetic hierarchy method: An optimizing approach to obtaining priori-
38
ties in the AHP, European Journal of Operational Research, 93 (1996), 550{564.
39
[17] S. Lipovetsky and A. Tishler, Interval estimation of priorities in the AHP, European Journal
40
of Operational Research, 114 (1999), 153{164.
41
[18] H. Nurmi, Approaches to collective decision making with fuzzy preference relations, Fuzzy
42
Sets and Systems, 6 (1981), 249{259.
43
[19] S. A. Orlovsky, Decision-making with a fuzzy preference relation, Fuzzy Sets and Systems, 1
44
(1978), 155{167.
45
[20] T. L. Saaty, The Analytic Hierarchy Process, McGraw-Hill, New York, 1980.
46
[21] T. Tanino, Fuzzy preference orderings in group decision-making, Fuzzy Sets and Systems, 12
47
(1984), 117{131.
48
[22] T. Tanino, Fuzzy preference relation in group decision making, in: J. Kacprzyk, M. Roubens
49
(Eds.) Non-Conventional Preference Relation in Decision Making, Springer, Berlin, (1988),
50
[23] T. Tanino, On group decision making under fuzzy preferences, in: J. Kacprzyk, M. Fedrizzi
51
(Eds.) Multiperson Decision Making Using Fuzzy Sets and Possibility Theory, Kluwer,
52
Netherlands, 1990, 172{185.
53
[24] L. G. Vargas, An overview of the analytic process and its applications, European Journal of
54
Operational Research, 48 (1990), 2{8.
55
[25] L. F.Wang and S. B. Xu, The Introduction to the Analytic Hierarchy Process, Chinese People
56
University Press, Beijing, 1990.
57
[26] Y. M.Wang and Z. P. Fan, Fuzzy preference relations: Aggregation and weight determination,
58
Computers & Industrial Engineering, 53 (2007), 163{172.
59
[27] Y. M. Wang and Z. P. Fan, Group decision analysis based on fuzzy preference relations:
60
Logarithmic and geometric least squares methods, Applied Mathematics and Computation,
61
194 (2007), 108{119.
62
[28] Y. M. Wang, Z. P. Fan and Z. S. Hua, A chi-square method for obtaining a priority vector
63
from multiplicative and fuzzy preference relations, European Journal of Operational Research,
64
182 (2007), 356{366.
65
[29] Y. M. Wang and C. Parkan, Multiple attribute decision making based on fuzzy preference
66
information on alternatives: Ranking and weighting, Fuzzy Sets and Systems, 153 (2005),
67
[30] D. A. Wismer, Introduction to Nonlinear Optimization: A Problem Solving Approach, North-
68
Holland Company, New York, 1978.
69
[31] Y. J. Xu, L. Chen, K. W. Li and H. M. Wang, A chi-square method for priority derivation in
70
group decision making with incomplete reciprocal preference relations, Information Sciences,
71
36 (2015), 166{179.
72
[32] Y. J. Xu, L. Chen and H. M. Wang, A least deviation method for priority derivation in
73
group decision making with incomplete reciprocal preference relations, International Journal
74
of Approximate Reasoning, 66 (2015), 91{102.
75
[33] Y. J. Xu, Q. L. Da and L. H. Liu, Normalizing rank aggregation method for priority of a fuzzy
76
preference relation and its eectiveness, International Journal of Approximate Reasoning, 50
77
(2009), 1287{1297.
78
[34] Y. J. Xu, Q. L. Da and H. M. Wang, A note on group decision-making procedure based on
79
incomplete reciprocal relations, Soft Computing, 15 (2011), 1289{1300.
80
[35] Y. J. Xu, J. N. D. Gupta and H. M.Wang, The ordinal consistency of an incomplete reciprocal
81
preference relation, Fuzzy Sets and Systems, 246(2014), 62{77.
82
[36] Y.J. Xu, K.W. Li and H.M. Wang, Incomplete interval fuzzy preference relations and their
83
applications, Computers & Industrial Engineering, 67 (2014), 93{103.
84
[37] Y. J. Xu, F. Ma, F. F. Tao and H. M. Wang, Some methods to deal with unacceptable
85
incomplete 2-tuple fuzzy linguistic preference relations in group decision making, Knowledge-
86
Based Systems, 56 (2014), 179{190.
87
[38] Y.J. Xu, R. Patnayakuni and H. M. Wang, Logarithmic least squares method to priority
88
for group decision making with incomplete fuzzy preference relations, Applied Mathematical
89
Modelling, 37 (2013), 2139{2152.
90
[39] Y. J. Xu, R. Patnayakuni and H. M. Wang, A method based on mean deviation for weight
91
determination from fuzzy preference relations and multiplicative preference relations, Inter-
92
national Journal of Information Technology & Decision Making, 11 (2012), 627{641.
93
[40] Y. J. Xu, R. Patnayakuni and H. M. Wang, The ordinal consistency of a fuzzy preference
94
relation, Information Sciences, 224 (2013), 152{164.
95
[41] Y. J. Xu and H. M. Wang, Eigenvector method, consistency test and inconsistency repairing
96
for an incomplete fuzzy preference relation, Applied Mathematical Modelling, 37 (2013),
97
5171{5183.
98
[42] Z. S. Xu, Generalized chi square method for the estimation of weights, Journal of Optimiza-
99
tion Theory and Applications, 107 (2000), 183{192.
100
[43] Z. S. Xu, Goal programming models for obtaining the priority vector of incomplete fuzzy
101
preference relation, International Journal of Approximate Reasoning, 36 (2004), 261{270.
102
[44] Z. S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Transations on Fuzzy Systems, 15
103
(2007), 1179{1187.
104
[45] Z. S. Xu and Q. L. Da, A least deviation method to obtain a priority vector of a fuzzy
105
preference relation, European Journal of Operational Research, 164 (2005), 206{216.
106
ORIGINAL_ARTICLE
Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces
We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furthermore, we define and study uniform local $mbbe$-connectedness, generalizing a classical definition from the theory of uniform convergence spaces to the lattice-valued case. In particular it is shown that if the underlying lattice is completely distributive, the quotient space of a uniformly locally $mbbe$-connected space and products of locally uniformly $mbbe$-connected spaces are locally uniformly $mbbe$-connected.
http://ijfs.usb.ac.ir/article_2432_940f5735f6a8674b2e5e69ca8fbb8ebb.pdf
2016-06-30T11:23:20
2017-09-20T11:23:20
95
111
10.22111/ijfs.2016.2432
$L$-topology
$L$-uniform convergence space
Uniform connectedness
Local connectedness
Gunther
Jager
g.jager@ru.ac.za, gunther.jaeger@fh-stralsund.de
true
1
School of Mechanical Engineering, University of Applied Sciences
Stralsund, 18435 Stralsund, Germany
School of Mechanical Engineering, University of Applied Sciences
Stralsund, 18435 Stralsund, Germany
School of Mechanical Engineering, University of Applied Sciences
Stralsund, 18435 Stralsund, Germany
LEAD_AUTHOR
[1] J. Adamek, H. Herrlich, and G.E. Strecker, Abstract and Concrete Categories, Wiley, New
1
York, 1989.
2
[2] G. Cantor, Uber unendliche lineare Punktmannichfaltigkeiten, Math. Ann., 21 (1883), 545{
3
[3] A. Craig and G. Jager, A common framework for lattice-valued uniform spaces and probabilistic
4
uniform limit spaces, Fuzzy Sets and Systems, 160 (2009), 1177 { 1203.
5
[4] J. Fang, Lattice-valued semiuniform convergence spaces, Fuzzy Sets and Systems, 195 (2012),
6
[5] W. Gahler, Grundstrukturen der Analysis I, Birkhauser Verlag, Basel and Stuttgart, 1977.
7
[6] J. Gutierrez Garca, A unied approach to the concept of fuzzy L-uniform space, Thesis,
8
Universidad del Pais Vasco, Bilbao, Spain, 2000.
9
[7] J. Gutierrez Garca, M.A. de Prada Vicente and A. P. Sostak, A unied approach to the
10
concept of fuzzy L-uniform space, In: S. E. Rodabaugh, E. P. Klement (Eds.), Topological
11
and algebraic structures in fuzzy sets, Kluwer, Dordrecht, (2003), 81{114.
12
[8] F. Hausdor, Grundzuge der Mengenlehre, Leipzig, 1914.
13
[9] U. Hohle and A. P. Sostak, Axiomatic foundations of xed-basis fuzzy topology, In: U. Hohle,
14
S.E. Rodabauch (Eds.), Mathematics of Fuzzy Sets. Logic, Topology and Measure Theory,
15
Kluwer, Boston/Dordrecht/London (1999), 123{272.
16
[10] G. Jager, A category of L-fuzzy convergence spaces, Quaestiones Math., 24 (2001), 501{517.
17
[11] G. Jager, Subcategories of lattice-valued convergence spaces, Fuzzy Sets and Systems, 156
18
(2005), 1{24.
19
[12] G. Jager and M. H. Burton, Stratied L-uniform convergence spaces, Quaest. Math., 28
20
(2005), 11 { 36.
21
[13] G. Jager, Lattice-valued convergence spaces and regularity, Fuzzy Sets and Systems, 159
22
(2008), 2488{2502.
23
[14] G. Jager, Level spaces for lattice-valued uniform convergence spaces, Quaest. Math., 31
24
(2008), 255{277.
25
[15] G. Jager, Compactness in lattice-valued function spaces, Fuzzy Sets and Systems, 161 (2010),
26
2962{2974.
27
[16] G. Jager, Lattice-valued Cauchy spaces and completion, Quaest. Math., 33 (2010), 53{74.
28
[17] G. Jager, Connectedness and local connectedness for lattice-valued convergence spaces, Fuzzy
29
Sets and Systems, to appear, doi:10.1016/j.fss.2015.11.013.
30
[18] G. Kneis, Contributions to the theory of pseudo-uniform spaces, Math. Nachrichten, 89
31
(1979), 149{163.
32
[19] S. G. Mrowka and W. J. Pervin, On uniform connectedness, Proc. Amer. Math. Soc., 15
33
(1964), 446{449.
34
[20] G. Preu, E-Zusammenhangende Raume, Manuscripta Mathematica, 3 (1970), 331{342.
35
[21] G. Preu, Trennung und Zusammenhang, Monatshefte fur Mathematik, 74(1970), 70{87.
36
[22] W. W. Taylor, Fixed-point theorems for nonexpansive mappings in linear topological spaces,
37
J. Math. Anal. Appl., 40 (1972), 164{173.
38
[23] R. Vainio, A note on products of connected convergence spaces, Acta Acad. Aboensis, Ser.
39
B, 36(2) (1976), 1{4.
40
[24] R. Vainio, The locally connected and the uniformly locally connected core
41
ector in general
42
convergence theory, Acta Acad. Aboensis, Ser. B, 39(1) (1979), 1{13.
43
[25] R. Vainio, On connectedness in limit space theory, in: Convergence structures and applications
44
II, Abhandlungen der Akad. d. Wissenschaften der DDR, Berlin (1984), 227{232.
45
ORIGINAL_ARTICLE
Optimal coincidence best approximation solution in non-Archimedean Fuzzy Metric Spaces
In this paper, we introduce the concept of best proximal contraction theorems in non-Archimedean fuzzy metric space for two mappings and prove some proximal theorems. As a consequence, it provides the existence of an optimal approximate solution to some equations which contains no solution. The obtained results extend further the recently development proximal contractions in non-Archimedean fuzzy metric spaces and famous Banach contraction principle.
http://ijfs.usb.ac.ir/article_2433_a6abe3e087f96471b03c9cbff8f841d2.pdf
2016-06-30T11:23:20
2017-09-20T11:23:20
113
124
10.22111/ijfs.2016.2433
Fuzzy metric space
Optimal approximate solution
Fuzzy proximal contraction
Fuzzy expansive
Fuzzy isometry
s-increasing sequence
t-norm
Naeem
Saleem
naeem.saleem2@gmail.com
true
1
Department of Mathematics, National University of Computer and
Emerging Sciences, Lahore - Pakistan
Department of Mathematics, National University of Computer and
Emerging Sciences, Lahore - Pakistan
Department of Mathematics, National University of Computer and
Emerging Sciences, Lahore - Pakistan
LEAD_AUTHOR
Mujahid
Abbas
abbas.mujahid@gmail.com
true
2
Department of Mathematics and Applied Mathematics, University of
Pretoria, Lynnwood road, Pretoria 0002, South Africa and Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Department of Mathematics and Applied Mathematics, University of
Pretoria, Lynnwood road, Pretoria 0002, South Africa and Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Department of Mathematics and Applied Mathematics, University of
Pretoria, Lynnwood road, Pretoria 0002, South Africa and Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
AUTHOR
Zahid
Raza
zahid.raza@nu.edu.pk
true
3
Department of Mathematics, National University of Computer and
Emerging Sciences, Lahore - Pakistan
Department of Mathematics, National University of Computer and
Emerging Sciences, Lahore - Pakistan
Department of Mathematics, National University of Computer and
Emerging Sciences, Lahore - Pakistan
AUTHOR
[1] S. Chauhan, W. Shatanawi, S. Kumar and S. Radenovic, Existence and uniqueness of xed
1
points in modied intuitionistic fuzzy metric spaces, Journal of Nonlinear Sciences and Ap-
2
plications, 7(1) (2014), 28{41.
3
[2] K. Fan, Extensions of two xed point theorems of F. E. Browder, Mathematische Zeitschrift,
4
112(3) (1969), 234{240.
5
[3] J. G. Garcia and S. Romaguera, Examples of non-strong fuzzy metrics, Fuzzy sets and sys-
6
tems, 162(1) (2011), 91{93.
7
[4] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,
8
64(3) (1994), 395{399.
9
[5] A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets
10
and Systems, 90(3) (1997), 365{368.
11
[6] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27(3) (1983),
12
[7] V. Gregori and A. Sapena, On xed-point theorems in fuzzy metric spaces, Fuzzy Sets and
13
Systems, 125(2) (2002), 245{252.
14
[8] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11(5)
15
(1975), 336{344.
16
[9] C. Mongkolkeha, Y. J. Cho and P. Kumam, Best proximity points for generalized proxi-
17
mal contraction mappings in metric spaces with partial orders, Journal of Inequalities and
18
Applications, 94(1) (2013), 94{105.
19
[10] S. Sadiq Basha, Best proximity points, optimal solutions, Journal of Optimal Theory and
20
Applications, 151(1) (2011), 210{216.
21
[11] S. Sadiq Basha, Common best proximity points: Global minimization of multi-objective func-
22
tions, Journal of Global Optimization, 54(2) (2012), 367{373.
23
[12] N. Saleem, B. Ali, M. Abbas and Z. Raza, Fixed points of Suzuki type generalized multivalued
24
mappings in fuzzy metric spaces with applications, Fixed Point Theory and Applications,
25
(36)(1) (2015).
26
[13] M. Sangurlu and D. Turkoglu, Fixed point theorems for ( o') contractions in a fuzzy metric
27
spaces, Journal of Nonlinear Sciences and Applications. 8(5) (2015), 687{694.
28
[14] B. Schweizer and A. Sklar, Statistical metric spaces, Pacic Journal of Mathematics, 10(1)
29
(1960), 313{334.
30
[15] C. Vetro and P. Salimi, Best proximity point results in non-Archimedean fuzzy metric spaces,
31
Fuzzy Information and Engineering, 5(4) (2013), 417{429.
32
[16] L. A. Zadeh, Fuzzy Sets, Informations and Control, 8(3) (1965), 338{353.
33
ORIGINAL_ARTICLE
On $L$-double fuzzy rough sets
ur aim of this paper is to introduce the concept of $L$-double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$-double fuzzy lower (resp. upper) approximation operators is defined and the basic properties of them are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L$-double fuzzy upper (resp. lower) approximation of $L$-double fuzzy rough sets. Finally, from $L$-double fuzzy approximation operators, we generated Alexandrov $L$-double fuzzy topology.
http://ijfs.usb.ac.ir/article_2434_831f05c10319bc6599ac74ffc8002dd2.pdf
2016-06-30T11:23:20
2017-09-20T11:23:20
125
142
10.22111/ijfs.2016.2434
$L$-fuzzy sets
$L$-double fuzzy relations
$L$-double fuzzy rough sets
$L$-double fuzzy approximation operators
$L$-double fuzzy topology
A. A.
Abd El-latif
true
1
Department of Mathematics, Faculty of Science and Arts at
Belqarn, P. O. Box 60, Sabt Al-Alaya 61985, Bisha University, Saudi Arabia
Department of Mathematics, Faculty of Science and Arts at
Belqarn, P. O. Box 60, Sabt Al-Alaya 61985, Bisha University, Saudi Arabia
Department of Mathematics, Faculty of Science and Arts at
Belqarn, P. O. Box 60, Sabt Al-Alaya 61985, Bisha University, Saudi Arabia
LEAD_AUTHOR
A. A.
Ramadan
true
2
Department of Mathematics, Beni-suef University, Beni-suef, Egypt
Department of Mathematics, Beni-suef University, Beni-suef, Egypt
Department of Mathematics, Beni-suef University, Beni-suef, Egypt
AUTHOR
[1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96.
1
[2] K. Atanassov, Intuitionistic fuzzy sets: theory and applications, Physica-Verlag, Heidelberg,
2
[3] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182-190.
3
[4] J. K. Chen and J. J. Li, An application of rough sets to graph theory, Information Sciences,
4
201 (2012), 114-127.
5
[5] D. C oker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems,
6
88 (1997), 81-89.
7
[6] D. C oker and M. Demirci, An introduction to intuitionistic fuzzy topological spaces in Sostak's
8
sense, Busefal, 67 (1996), 67-76.
9
[7] D. C oker, Fuzzy rough sets are intuitionistic L-fuzzy sets, Fuzzy Sets and Systems, 96(3)
10
(1998), 381-383.
11
[8] D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of
12
General System, 17 (1990), 191-208.
13
[9] A. A. Estaji, M. R. Hooshmandasl and B. Davvaz, Rough set theory applied to lattice theory,
14
Information Sciences, 200 (2012), 108-122.
15
[10] J. G. Garcia and S. E. Rodabaugh, Order-theoretic, topological, categorical redundancides
16
of intervalvalued sets, grey sets, vague sets, interval-valued intuitionistic sets, intuitionistic
17
fuzzy sets and topologies, Fuzzy Sets and Systems, 156 (2005), 445-484.
18
[11] J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl., 18 (1967), 145-174.
19
[12] J. A. Goguen, The fuzzy tychono theorem, J. Math. Anal. Appl., 34 (1973), 734-742.
20
[13] J. Hao and Q. Li, The relationship between L-fuzzy rough set and L-topology, Fuzzy Sets and
21
Systmes, 178 (2011), 74-83.
22
[14] U. Hohle and A. P. Sostak, A general theory of fuzzy topological spaces, Fuzzy Sets and
23
Systmes, 73(1) (1995), 131-149.
24
[15] S. P. Jena and S. K. Ghosh, Intuitionistic fuzzy rough sets, Notes on Intuitionistic Fuzzy
25
Sets, 8 (2002), 1-18.
26
[16] Y. B. Jun, Roughness of ideals in BCK-algebras, Scientiae Mathematicae Japonicae, 75(1)
27
(2003), 165-169.
28
[17] M. Kryszkiewicz, Rough set approach to incomplete information systems, Information Sciences,
29
112 (1998), 39-49.
30
[18] T. Kubiak, On fuzzy topologies, Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, (1985).
31
[19] L. Lin, X. H. Yuan and Z. Q. Xia, Multicriteria fuzzy decision-making methods based on
32
intuitionistic fuzzy sets, Journal of Computer and System Sciences, 73(1) (2007), 84-88.
33
[20] G. Liu, Generalized rough sets over fuzzy lattices, Information Sciences, 178 (2008), 1651-
34
[21] Z. Pawlak, Information system theoretical foundations, Information Sciences, 6(1981), 205-
35
[22] Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11
36
(1982), 341-356.
37
[23] Z. Pawlak, Rough sets: theoretical aspects of reasoning about data, Kluwer Academic Publishers,
38
Boston, 1991.
39
[24] Z. Pawlak and A. Skowron, Rudiments of rough sets, Information Sciences, 177 (2007), 3-27.
40
[25] Z. Pawlak and A. Skowron, Rough sets: some extensions, information sciences, Information
41
Sciences, 177 (2007), 28-40.
42
[26] W. Pedrycz, Granular computing: aanalysis and design of intelligent systems, CRC Press,
43
Boca Raton, 2013.
44
[27] K. Qin and Z. Pei, On the topological properties of fuzzy rough sets, Fuzzy Sets and Systmes,
45
151 (2005), 601-613.
46
[28] M. Quafafou, -RST: a generalization of rough set theory, Information Sciences, 124 (2000),
47
[29] A. M. Radzikowska, Rough approximation operations based on IF sets, Lecture Notes in
48
Computer Science , 4029 (2006), 528-537.
49
[30] A. M. Radzikowska and E. E. Kerre, Fuzzy rough sets based on residuated lattices, Transac-
50
tions on Rough Sets, Lecture Notes in Computer Sciences, 3135 (2004), 278-296.
51
[31] A. A. Ramadan, Smooth topological spaces, Fuzzy Sets and Systmes, 48 (1992), 371-375.
52
[32] A. A. Ramadanm and A. A. Abd El-latif, Supra fuzzy convergence of fuzzy lter, Bull. Korean
53
Math. Soc., 45(2) (2008), 207-220.
54
[33] A. A. Ramadanm and A. A. Abd El-latif, Images and preimages of L-fuzzy ideal bases, J.
55
Fuzzy Math., 17(3) (2009), 611-632.
56
[34] S. K. Samanta and T. K. Mondal, On intuitionistic gradation of openness, Fuzzy Sets and
57
Systmes, 131 (2002), 323-336.
58
[35] S. K. Samanta and T. K. Mondal, Intuitionistic fuzzy rough sets and rough intuitionistic
59
fuzzy sets, Journal of Fuzzy Mathematics, 9 (2001), 561-582.
60
[36] M. H. Shahzamanian, M. Shirmohammadi and B. Davvaz, Roughness in Cayley graphs,
61
Information Sciences, 180 (2010), 3362-3372.
62
[37] A. P. Sostak, On a fuzzy topological structure, Rend. Circ. Mat. Palermo 2 Suppl., 11 (1985),
63
[38] S. P. Tiwari and A. K. Srivastava, Fuzzy rough sets, fuzzy preorders and fuzzy topologies,
64
Fuzzy Sets and Systmes, 210 (2013), 63-68.
65
[39] L. K. Vlachos and G. D. Sergiadis, Intuitionistic fuzzy information applications to pattern
66
recognition, Pattern Recognition Letters, 177(11) (2007), 197-206.
67
[40] U. Wybraniec-Skardowska, On a generalization of approximation space, Bulletin of the Polish
68
Academy of Sciences: Mathematics, 37 (1989), 51-61.
69
[41] Z. S. Xu, Intuitionistic preference relations and their application in group decision making,
70
Information Sciences, 177 (11) (2007), 2363-2379.
71
[42] Y. Y. Yao, Relational interpretations of neighborhood operators and rough set approximation
72
operators, Information Sciences, 111 (1998), 239-259.
73
[43] D. S. Yeung, D. Chen, E. C. C. Tsang, J. W. T. Lee and X. Z. Wang, On the generalization
74
of fuzzy rough sets, IEEE Trans. Fuzzy Syst., 13 (2005), 343-361.
75
[44] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
76
[45] Z. Zhang, Generalized intuitionistic fuzzy rough sets based on intuitionistic fuzzy coverings,
77
Information Sciences, 198 (2012), 186-206.
78
[46] X. Zhang, B. Zhou and P. Li, A general frame for intuitionistic fuzzy rough sets, Information
79
Sciences, 216 (2012), 34-49.
80
[47] L. Zhou, W. Z. Wu and W. X. Zhang, On intuitionistic fuzzy rough sets and their topological
81
structures, International Journal of General Systems, 38 (2009), 589-616.
82
[48] W. Ziarko, Variable precision rough set model, Journal of Computer and System Sciences,
83
46 (1993), 39-59.
84
ORIGINAL_ARTICLE
On The Bicompletion of Intuitionistic Fuzzy Quasi-Metric Spaces
Based on previous results that study the completion of fuzzy metric spaces, we show that every intuitionistic fuzzy quasi-metric space, using the notion of fuzzy metric space in the sense of Kramosil and Michalek to obtain a generalization to the quasi-metric setting, has a bicompletion which is unique up to isometry.
http://ijfs.usb.ac.ir/article_2435_c6eb4675a88b0a2003c412c51c8822a3.pdf
2016-06-30T11:23:20
2017-09-20T11:23:20
143
151
10.22111/ijfs.2016.2435
Intuitionistic fuzzy quasi-metric
Bicomplete
Isometry
Bicompletion
Francisco
Castro-Company
fracasco@mat.upv.es
true
1
Gilmation S.L., Calle 232, 66 La Ca~nada, Paterna,
46182, Spain
Gilmation S.L., Calle 232, 66 La Ca~nada, Paterna,
46182, Spain
Gilmation S.L., Calle 232, 66 La Ca~nada, Paterna,
46182, Spain
LEAD_AUTHOR
Pedro
Tirado
pedtipe@mat.upv.es
true
2
Instituto Universitario de Matematica Pura y Aplicada, Universidad
Politecnica de Valencia, 46022, Valencia, Spain
Instituto Universitario de Matematica Pura y Aplicada, Universidad
Politecnica de Valencia, 46022, Valencia, Spain
Instituto Universitario de Matematica Pura y Aplicada, Universidad
Politecnica de Valencia, 46022, Valencia, Spain
AUTHOR
[1] C. Alaca, D. Turkoglu and C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos,
1
Solitons & Fractals, 29 (2006), 1073{1078.
2
[2] F. Castro-Company and P. Tirado, The bicompletion of intuitionistic fuzzy quasi-metric
3
spaces, 10th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM),
4
(2016), 844{847.
5
[3] F. Castro-Company, S. Romaguera and P. Tirado, The bicompletion of fuzzy quasi-metric
6
spaces, Fuzzy Sets and Systems, 166 (2011), 56{64.
7
[4] Y. J. Cho, M. Grabiec and V. Radu, On non symmetric topological and probabilistic struc-
8
tures, Nova Sci. Publ. Inc., New York, 2006.
9
[5] D. Dubois and P. Prade, Fundamentals of fuzzy sets, the handbooks of fuzzy sets series,
10
FSHS, 7, Kluwer Academic, 2000.
11
[6] P. Fletcher and W. F. Lindgren, Quasi-uniform spaces, Marcel Dekker, New York, 1982.
12
[7] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,
13
64 (1994), 395{399.
14
[8] V. Gregori and S. Romaguera, Fuzzy quasi-metric spaces, Appl. Gen. Topology, 5 (2004),
15
[9] V. Gregori, S. Romaguera and A. Sapena, A characterization of bicompletable fuzzy quasi-
16
metric spaces, Fuzzy Sets and Systems, 152 (2005), 395{402.
17
[10] V. Gregori, S. Romaguera and P. Veeramani, A note on intuitionistic fuzzy metric spaces,
18
Chaos, Solitons & Fractals, 28 (2006), 902{905.
19
[11] I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11
20
(1975), 326{334.
21
[12] H. P. A. Kunzi, Nonsymmetric topology, In: Proceedings of the Colloquium on Topology,
22
Szekszard, Colloq. Math. Soc. Janos Bolyai Math. Studies, Hungary, 4 (1995), 303{338.
23
[13] K. Menger, Statistical metrics, In: Proceedings of the National Academy of Sciences of the
24
United States of America, 28 (1942), 535{537.
25
[14] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22 (2004), 1039{
26
[15] S. Romaguera, A. Sapena and P. Tirado. The Banach xed point theorem in fuzzy quasi-
27
metric spaces with application to the domain of words, Topology Appl., 154 (2007), 2196{
28
[16] S. Romaguera and P. Tirado, Contraction maps on ifqm-spaces with application to recurrence
29
equations of Quicksort, Electronic Notes in Theoret. Comput. Sci., 225 (2009), 269{279.
30
[17] R. Saadati, S. M. Vaezpour and Y. J. Cho, Quicksort algorithm: Application of a xed point
31
theorem in intuitionistic fuzzy quasi-metric spaces at a domain of words, J. Comput. Appl.
32
Math., 228 (2009), 219{225.
33
[18] B. Schweizer and A. Sklar, Statistical metric spaces, Pacic J. Math., 10 (1960), 314{334.
34
[19] H. Sherwood, On the completion of probabilistic metric spaces, Z. Wahrsch. verw. Geb., 6
35
(1966), 62{64.
36
[20] R. Vasuki and P. Veeramani, Fixed point theorems and Cauchy sequences in fuzzy metric
37
spaces, Fuzzy Sets and Systems, 135 (2003), 415{417.
38
ORIGINAL_ARTICLE
Persian Translation of Abstracts
http://ijfs.usb.ac.ir/article_2628_bfb3bb2f69becd50c1f16db357730f57.pdf
2016-06-30T11:23:20
2017-09-20T11:23:20
154
164
10.22111/ijfs.2016.2628