ORIGINAL_ARTICLE
Cover vol. 14, no. 6, December 2017
http://ijfs.usb.ac.ir/article_3504_e75c3dcf8c1fe24b35436246ee473aff.pdf
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10.22111/ijfs.2017.3504
ORIGINAL_ARTICLE
F-TRANSFORM FOR NUMERICAL SOLUTION OF TWO-POINT BOUNDARY VALUE PROBLEM
We propose a fuzzy-based approach aiming at finding numerical solutions to some classical problems. We use the technique of F-transform to solve a second-order ordinary differential equation with boundary conditions. We reduce the problem to a system of linear equations and make experiments that demonstrate applicability of the proposed method. We estimate the order of accuracy of the proposed method. We show that the F-transform-based approach does not only extend the set of its applications, but has a certain advantage in the solution of ill-posed problems.
http://ijfs.usb.ac.ir/article_3495_ccab4ef5ff4c62aba8a2fe33db1a5b8e.pdf
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13
10.22111/ijfs.2017.3495
F-transform
Differential equation
Boundary value problem
Second order differential equation
Irina
Perfilieva
irina.perfilieva@osu.cz
true
1
University of Ostrava, Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
University of Ostrava, Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
University of Ostrava, Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
LEAD_AUTHOR
Petra
Stevuliakova
true
2
University of Ostrava, Centre of Excellence IT4Innovations,
Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03
Ostrava 1, Czech Republic
University of Ostrava, Centre of Excellence IT4Innovations,
Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03
Ostrava 1, Czech Republic
University of Ostrava, Centre of Excellence IT4Innovations,
Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03
Ostrava 1, Czech Republic
AUTHOR
Radek
Valasek
true
3
University of Ostrava, Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1,
Czech Republic
University of Ostrava, Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1,
Czech Republic
University of Ostrava, Centre of Excellence IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, 30. dubna 22, 701 03 Ostrava 1,
Czech Republic
AUTHOR
[1] V. I. Arnold and R. Cook, Ordinary Differential Equations, Springer Textbook, Springer,
1
Berlin Heidelberg, 1992. ISBN 9783540548133.
2
[2] U. Ascher, Collocation for two-point boundary value problems revisited, SIAM J. Numer.
3
Anal. 23 (1986), 596{609.
4
[3] K. E. Atkinson, An Introduction to Numerical Analysis, 2nd ed., John Wiley, Iowa, USA,
5
[4] N. S. Bakhvalov, N. P. Zhidkov and G. M. Kobelkov, Numerical Methods, Nauka, Moskva,
6
(1987), 600 p.
7
[5] W. Chen and Y. Schen, Approximate solution for a class of second-order ordinary differenci-
8
tal equations by the fuzzy transform, Intelligent and Fuzzy Systems. 27 (2014), 73{82.
9
[6] H. Keller, Numerical Methods for Two-Point Boundary Value Problems, Ginn (Blaisdell),
10
Boston, 1968.
11
[7] A. Khastan, I. Perfilieva and Z. Alijani, A new fuzzy approximation method to Cauchy prob-
12
lems by fuzzy transform, Fuzzy Sets and Systems, 288 (2016), 75{95.
13
[8] A. Khastan, Z. Alijani and I. Perfilieva, Fuzzy transform to approximate solution of two-
14
point boundary value problems, Mathematical Methods in the Applied Sciences. (2016),
15
http://dx.doi.org/10.1002/mma.3832.
16
[9] I. Perfilieva, Fuzzy transforms: Theory and applications, Fuzzy Sets and Systems, 157 (2006),
17
[10] I. Perfilieva, Fuzzy approach to solution of differential equations with imprecise data: appli-
18
cation to reef growth problem, in: R.V. Demicco, G.J. Klir (Eds.), Fuzzy Logic in Geology,
19
Academic Press, Amsterdam, (2003), 275-300.
20
[11] I. Perfilieva, M. Holcapek and V. Kreinovich, A new reconstruction from the F-transform
21
components, Fuzzy Sets and Systems, 288 (2016), 3{25.
22
[12] A. Quarteroni, R. Sacco and F. Saleri, Numerical Mathematics, Springer, New York, 2007.
23
[13] P. Stevuliakova, I. Perfilieva and R. Valasek, R., A New Approach to Fuzzy Boundary Value
24
Problem, in: World Scientific Proceedings Series on Computer Engineering and Information
25
Science, 10 (2016), 276{281.
26
ORIGINAL_ARTICLE
DIAGNOSIS OF BREAST LESIONS USING THE LOCAL CHAN-VESE MODEL, HIERARCHICAL FUZZY PARTITIONING AND FUZZY DECISION TREE INDUCTION
Breast cancer is one of the leading causes of death among women. Mammography remains today the best technology to detect breast cancer, early and efficiently, to distinguish between benign and malignant diseases. Several techniques in image processing and analysis have been developed to address this problem. In this paper, we propose a new solution to the problem of computer aided detection and interpretation for breast cancer. In the proposed approach, a Local Chan-Vese (LCV) model is used for the mass lesion segmentation step to isolate a suspected abnormality in a mammogram. In the classification step, we propose a two-step process: firstly, we use the hierarchical fuzzy partitioning (HFP) to construct fuzzy partitions from data, instead of using the only human information, available from expert knowledge, which are not sufficiently accurate and confronted to errors or inconsistencies. Secondly,fuzzy decision tree induction are proposed to extract classification knowledge from a set of feature-based examples. Fuzzy decision trees are first used to determine the class of the abnormality detected (well-defined mass, ill-defined mass, architectural distortion, or speculated masses), then, to identify the Severity of the abnormality, which can be benign or malignant. The proposed system is tested by using the images from Mammographic Image Analysis Society[MIAS] database. Experimental results show the efficiency of the proposed approach, resulting in an accuracy rate of 87, a sensitivity of 82.14\%, and good specificity of 91.42
http://ijfs.usb.ac.ir/article_3496_9e3953081f1d3b480e734c66534326f0.pdf
2017-12-30T11:23:20
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10.22111/ijfs.2017.3496
Breast cancer
Mass segmentation
Local Chan-Vese model fuzzy decision tree
Fuzzy partitioning
Computer-aided detection
Fouzia
Boutaouche
boutaouche-f@netcourrier.com
true
1
laboraoire SIMPA, Departement d'informatique, Faculte des
mathematiques et d'informatique, Universite des sciences et de la technologie d'Oran "Mohamed BOUDIAF", USTO-MB; BP 1505 El M'naouer 31000, Oran, Algerie
laboraoire SIMPA, Departement d'informatique, Faculte des
mathematiques et d'informatique, Universite des sciences et de la technologie d'Oran "Mohamed BOUDIAF", USTO-MB; BP 1505 El M'naouer 31000, Oran, Algerie
laboraoire SIMPA, Departement d'informatique, Faculte des
mathematiques et d'informatique, Universite des sciences et de la technologie d'Oran "Mohamed BOUDIAF", USTO-MB; BP 1505 El M'naouer 31000, Oran, Algerie
LEAD_AUTHOR
Nacéra
Benamrane
true
2
laboratoire SIMPA, Departement d'informatique, Faculte des
mathematiques et d'informatique, Universite des sciences et de la technologie d'Oran "Mohamed BOUDIAF", USTO-MB; BP 1505 El M'naouer 31000, Oran, Algerie
laboratoire SIMPA, Departement d'informatique, Faculte des
mathematiques et d'informatique, Universite des sciences et de la technologie d'Oran "Mohamed BOUDIAF", USTO-MB; BP 1505 El M'naouer 31000, Oran, Algerie
laboratoire SIMPA, Departement d'informatique, Faculte des
mathematiques et d'informatique, Universite des sciences et de la technologie d'Oran "Mohamed BOUDIAF", USTO-MB; BP 1505 El M'naouer 31000, Oran, Algerie
AUTHOR
[1] S. N. Acho and W. I. D. Rae, Dependence of shape-based descriptors and mass segmentation
1
areas on initial contour placement using the chan-vese method on digital mammograms,
2
Computational and Mathematical Methods in Medicine, 2015 (2015), 1-16.
3
[2] American Cancer Society, Cancer facts and figures, Atlanta, Ga: American Cancer Society,
4
(2013), 1-60.
5
[3] R. Bellotti, A completely automated CAD system for mass detection in a large mammographic
6
database, Medical Physics, 33(8) (2006), 3066–3075.
7
[4] L. Breslo and D. Aha, Simplifying decision trees: a survey, The Knowledge Engineering
8
Review, 12(1) (1997), 1-40.
9
[5] L. F. A. Campos, A. C Silva and A. K. Barros, Diagnosis of breast cancer in digital mammograms
10
using independent component analysis and neural networks, X Iberoamerican, Conference
11
on Pattern Recognition, Havana, Lecture notes in computer science, 3773 (2005),
12
460–469.
13
[6] T. F. Chan and L. A. Vese, Active contours without edges, IEEE Trans. Image Process, 10(2)
14
(2001), 266-277.
15
[7] R. Crandall, Image segmentation using Chan Vese algorithm, ECE532 Project fall, 2009.
16
[8] A. Keles and Y. Ugur,Expert system based on neuro-fuzzy rules for diagnosis breast cancer,
17
Expert Syst Appl., 38(5)(2011), 5719–5726.
18
[9] U. Khan, H. Shin, J. P. Choi and M. Kim, Weighted fuzzy decision trees for prognosis of
19
breast cancer survivability, Proc of the Australasian Data Mining Conferenre, Glenelg, South
20
Australia, 7(3) (2008), 141-152.
21
[10] Z. Lei and K. Ardrew Chan, An artificial intelligent algorithm for tumor detection in screening
22
mammogram, IEEE Trans. on Medical Imaging, 20(7) (2009), 559-567.
23
[11] M. Leonardo de Oliveira, G. Braz Junior, C. S. .Aristofanes, A. Cardoso de Paiva and M.
24
Gattass, Detection of masses in digital mammograms using K-means and support vector
25
machine, Electronic Letters on Computer Vision and Image Analysis, 8(2) (2009), 39-50.
26
[12] A. M.Maciej. Y.J.Lo, P.B.Harrawood and D. G Tourassc, Mutual information-based template
27
matching scheme for detection of breast masses: From mammography to digital breast
28
tomosynthesis, Journal of Biomedical Informatics 44(5) (2011), 815-823.
29
[13] C. Marsala, Apprentissage inductif en pr´esence de donn´ees impr´ecises : construction et
30
utilisation d’arbres de d´ecision flous, Th`ese de doctorat, Universit´e de Paris 6, (1988).
31
[14] C. Marsala, Fuzzy decision trees to help flexible querying, KYBERNETICA, 36 (2006), 689–
32
[15] L. Martins, A. Dos Santos, A. Silva and A. Paiva,Classification of normal, benign and malignant
33
tissues using co-occurrence matrix and bayesian neural network in mammographic
34
images, Proceedings of the Ninth Brazilian Symposium on Neural Networks, (2006), 479–486.
35
[16] A. Materka and M. Strzelecki, Texture analysis methods, A review, COST B11 Technical
36
Report, Lodz-Brussels: Technical University of Lodz, (1998), 9-11.
37
[17] G. H. B. Miranda and J. C Felipe,Computer-aided diagnosis system based on fuzzy logic for
38
breast cancer categorization, Computers in Biology and Medicine, 64(1) (2015), 334-34.
39
[18] J. I. Mohamed, M. Ahmadi and A. S. A. Maher, An efficient automatic mass classification
40
method in digitized mammograms using artificial neural network, International Journal of
41
Artificial Intelligence and Application (IJAIA), 1(3) (2010), 1-13.
42
[19] E. Molins, F. Macia and F. Ferrer, Association between radiologists’ experience and accuracy
43
in interpreting screening mammograms, BMC Health Serv Res., 8(91) (2008), 1-10.
44
[20] S. K. Murthy, Automatic construction of decision trees from data: a multi-disciplinary survey,
45
Data Min Knowl Disc, 2(4) (1998), 345-389.
46
[21] C. Olaru anf L. Wehenkel, A complete fuzzy decision tree technique, Fuzzy Sets and Systems,
47
138(2) (2003), 221-254.
48
[22] A. Oliver, J. Freixenet, R Mart´ı et al., A novel breast tissue density classification methodology,
49
IEEE Transactions on Information Technology in Biomedicine, 12(1) (2008), 55–65.
50
[23] S. Osher and N. Paragios, Geometric level set methods in imaging, vision and Graphics,
51
Springer-Verlag, 2003.
52
[24] G. Palma, G. Peters, S. Muller and I. Bloch, Masses classification using fuzzy active contours
53
and fuzzy decision tree, SPIE Symposium on Medical Imaging, San Diego, CA, USA,
54
6915(2008), 691509.1-691509.11.
55
[25] o. Pitchumani Angayarkanni and N. Banu Kamal, Association rule mining based decision tree
56
induction for efficient detection of cancerous masses in mammogram, International Journal
57
of Computer Applications, 31(6) (2011), 1-5.
58
[26] P. Rahmati, A. Adler and G. Hamarneh, Mammography segmentation with maximum likelihood
59
active contours, Medical Image Analysis, 16(6) (2012), 1167–1186.
60
[27] R. Ramani and N. Suthanthira Vanitha, Computer aided detection of tumours in mammograms,
61
international .Journal of Image, Graphics and Signal Processing, 6(4) (2014), 54-59.
62
[28] M. Ramdani, Syst`eme d’induction formelle `a base de connaissances impr´ecises, Th`ese de
63
doctorat, Paris 6, LIP6, 1994.
64
[29] R. S. Safavian and D. Landgrebe, A survey of decision tree classifier methodology, IEEE
65
Transactions on Systems, Man, and Cybernetics, 3(21) (1991), 660–674.
66
[30] G. Saborta, Probabilit´es, Analyse des donn´ees et Statistique, Ed. Technip, 1990.
67
[31] M. S. Salve and A. Chakkarwar, Classification of mammographic images using Gabor Wavelet
68
and discrete wavelet transform, International Journal of Advanced Research in Electronics
69
and Communication Engineering (IJARECE), 2(5) (2013).
70
[32] G. Serge and B. Charnomordic, Generating an interpretable family Of fuzzy partitions, IEEE
71
Transactions on Fuzzy Systems, 12(3) (2004), 324– 335.
72
[33] G. Serge, Induction de r`egles floues interpr´etables, Th`ese de Doctorat, INSA Toulouse,
73
France, 2001.
74
[34] S. Shanthi and M. BhaskaraR, Intuistionistic fuzzy C-means and decision tree approach for
75
breast cancer detection and classification, European Journal of Scientific research, 66(I3)
76
(2011), 345-351.
77
[35] J. Suckling, J. Parker, D. R. Dance et al., The mammographic image analysis society digital
78
mammogram database, Excerpta Medica International Congress Series, (1069) (1994), 375-
79
[36] T. Takagi and M. Sugeno, Fuzzy identification of systems and its applications to modeling
80
and control, IEEE Trans. Syst. Man Cybern, 15 (1985), 116–132.
81
[37] H. D. Thanh, Mesures de discrimination et leurs applications en apprentissage inductif,
82
Th`ese de doctorat, Universit´e de Paris 6, 2007.
83
[38] X. F. Wang, D. S. Huang and H. Xu, An efficient local Chan–vese model for image segmentation,
84
Pattern Recognition, 43(3) (2010), 603-618.
85
[39] Y. Wu, O. Alagoz, M. U. S. Ayvaci, A. Munoz del Rio, A. D. J. Vanness, R. Woods and E. S.
86
Burnsise, A comprehensive methodology for determining the most informative mammographic
87
features, Journal of digital imaging, 26(5) (2013), 941-947.
88
[40] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338-353.
89
ORIGINAL_ARTICLE
INFORMATION MEASURES BASED TOPSIS METHOD FOR MULTICRITERIA DECISION MAKING PROBLEM IN INTUITIONISTIC FUZZY ENVIRONMENT
In the fuzzy set theory, information measures play a paramount role in several areas such as decision making, pattern recognition etc. In this paper, similarity measure based on cosine function and entropy measures based on logarithmic function for IFSs are proposed. Comparisons of proposed similarity and entropy measures with the existing ones are listed. Numerical results limpidly betoken the efficiency of these measures over others. An intuitionistic fuzzy weighted measures (IFWM) with TOPSIS method for multi-criteria decision making (MCDM) quandary is introduced to grade the alternatives. This approach is predicated on entropy and weighted similarity measures for IFSs. An authentic case study is discussed to rank the four organizations. To compare the different rankings, a portfolio selection problem is considered. Various portfolios have been constructed and analysed for their risk and return. It has been examined that if the portfolios are developed using the ranking obtained with proposed method, the return is increased with slight increment in risk.
http://ijfs.usb.ac.ir/article_3497_b79c7d8a35da236ddbc695172d3305b4.pdf
2017-12-30T11:23:20
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63
10.22111/ijfs.2017.3497
Fuzzy set
Intuitionistic fuzzy set
Entropy
Similarity measure
TOPSIS
MCDM
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
Pratibha
Rani
pratibha138@gmail.com
true
2
Department of Mathematics, Jaypee University of Engineering and
Technology, Guna-473226, M. P., India
Department of Mathematics, Jaypee University of Engineering and
Technology, Guna-473226, M. P., India
Department of Mathematics, Jaypee University of Engineering and
Technology, Guna-473226, M. P., India
AUTHOR
[1] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.
1
[2] P. Burillo and H. Bustince, Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy
2
sets, Fuzzy Sets and Systems, 78 (1996), 305-316.
3
[3] C. T. Chen, Extensions of the TOPSIS for group decision-making under fuzzy environment,
4
Fuzzy Sets and Systems, 114 (2000), 01-09.
5
[4] A. De Luca and S. Termini, A denition of non-probabilistic entropy in the setting of fuzzy
6
set theory, Inform. and Control, 20 (1972), 301-312.
7
[5] S. Ebrahimnejad, H. Hashemi, S. M. Mousavi and B. Vahdani, A new interval-valued intu-
8
itionistic fuzzy model to group decision making for the selection of outsourcing providers,
9
Journal of Economic Computation and Economic Cybernetics Studies and Research, 49
10
(2015), 269-290.
11
[6] P. Grzegorzewski, On possible and necessary inclusion of intuitionistic fuzzy sets, Information
12
Sciences, 181 (2011), 342-350.
13
[7] D. S. Hooda and A. R. Mishra, On trigonometric fuzzy information measures, ARPN Journal
14
of Science and Technology, 05 (2015), 145-152.
15
[8] D. S. Hooda, A. R. Mishra and D. Jain, On generalized fuzzy mean code word lengths,
16
American Journal of Applied Mathematics, 02 (2014), 127-134.
17
[9] C. C. Hung and L. H. Chen, A fuzzy TOPSIS decision making model with entropy weight
18
under intuitionistic fuzzy environment, In: Proceedings of the international multi conference
19
of engineers and computer scientists (IME CS-2009), 01 (2009), 13-16.
20
[10] W. L. Hung and M. S. Yang, Fuzzy entropy on intuitionistic fuzzy sets, International Journal
21
of Intelligent Systems, 21 (2006), 443-451.
22
[11] W. L. Hung and M. S. Yang, On similarity measures between intuitionistic fuzzy sets, Inter-
23
national Journal of Intelligent Systems, 23 (2008), 364-383.
24
[12] W. L. Hung and M. S. Yang, Similarity measures of intuitionistic fuzzy sets based on Haus-
25
dor distance, Pattern Recognition Letters, 25 (2004), 1603-1611.
26
[13] C. L. Hwang and K. S. Yoon, Multiple attribute decision making: methods and applications,
27
Berlin: Springer-Verlag, 1981.
28
[14] D. Joshi and S. Kumar, Intuitionistic fuzzy entropy and distance measure based TOPSIS
29
method for multi-criteria decision making, Egyptian informatics journal, 15 (2014), 97-104.
30
[15] A. Jurio, D. Paternain, H. Bustince, C. Guerra and G. Beliakov, A construction method of
31
attanassov's intuitionistic fuzzy sets for image processing, In: Proceedings of the Fifth IEEE
32
Conference on Intelligent Systems, 01 (2010), 337-342.
33
[16] D. F. Li, Relative ratio method for multiple attribute decision making problems, International
34
Journal of Information Technology & Decision Making, 08 (2010), 289-311.
35
[17] D. Li and C. Cheng, New similarity measures of intuitionistic fuzzy sets and application to
36
pattern recognition, Pattern Recognition Letters, 23 (2003), 221-225.
37
[18] J. Li, G. Deng, H. Li and W. Zeng, The relationship between similarity measure and entropy
38
of intuitionistic fuzzy sets, Information Science, 188 (2012), 314-321.
39
[19] F. Li, Z. H. Lu and L. J. Cai, The entropy of vague sets based on fuzzy sets, J. Huazhong
40
Univ. Sci. Tech., 31 (2003), 24-25.
41
[20] Z. Z. Liang and P. F. Shi, Similarity measures on intuitionistic fuzzy sets, Pattern Recognition
42
Letters, 24 (2003), 2687-2693.
43
[21] L. Lin, X. H. Yuan and Z. Q. Xia, Multicriteria fuzzy decision-making methods based on
44
intuitionistic fuzzy sets, J. Comp. Syst. Sci., 73 (2007), 84-88.
45
[22] H. W. Liu and G. J. Wang, Multi-criteria decision-making methods based on intuitionistic
46
fuzzy sets, European Journal of Operational Research, 179 (2007), 220-233.
47
[23] H. M. Markowitz, Foundations of portfolio theory, J. Finance, 469 (1991), 469-471.
48
[24] H. M. Markowitz, Portfolio selection, J. Finance, 01 (1952), 77-91.
49
[25] A. R. Mishra, Intuitionistic fuzzy information measures with application in rating of township
50
development, Iranian Journal of Fuzzy Systems, 13(3) (2016), 49-70.
51
[26] A. R. Mishra, D. Jain and D. S. Hooda, Exponential intuitionistic fuzzy information measure
52
with assessment of service quality, International journal of fuzzy systems, 19(3) (2017), 788-
53
[27] A. R. Mishra, D. Jain and D. S. Hooda, Intuitionistic fuzzy similarity and information mea-
54
sures with physical education teaching quality assessment, Proceedings of the Second Inter-
55
national Conference on Computer and Communication Technologies, Advances in Intelligent
56
Systems and Computing, 379 (2016), 387-399.
57
[28] A. R. Mishra, D. Jain and D. S. Hooda, On fuzzy distance and induced fuzzy information
58
measures, Journal of Information and Optimization Sciences, 37 (2) (2016), 193-211.
59
[29] A. R. Mishra, D. Jain and D. S. Hooda, On logarithmic fuzzy measures of information and
60
discrimination, Journal of Information and Optimization Sciences, 37 (2) (2016), 213-231.
61
[30] A. R. Mishra, D. S. Hooda and D. Jain, On exponential fuzzy measures of i--07.
62
[31] A. R. Mishra, D. S. Hooda and D. Jain, Weighted trigonometric and hyperbolic fuzzy infor-
63
mation measures and their applications in optimization principles, International Journal Of
64
Computer And Mathematical Sciences, 03 (2014), 62-68.
65
[32] H. B. Mitchell, On the Dengfeng-Chuntian similarity measure and its application to pattern
66
recognition, Pattern Recognition Letters, 24 (2003), 3101-3104.
67
[33] S. M. Mousavi, H. Gitinavard and B. Vahdani, Evaluating construction projects by a new
68
group decision-making model based on intuitionistic fuzzy logic concepts, International Jour-
69
nal of Engineering, 28 (2015), 1313-1319.
70
[34] S. M. Mousavi and B. Vahdani, Cross-docking location selection in distribution systems: a
71
new intuitionistic fuzzy hierarchical deci--109.
72
[35] S. M. Mousavi, S. Mirdamadi, S. Siadat, J. Dantan and R. Tavakkoli-Moghaddam, An intu-
73
itionistic fuzzy grey model for selection problems with an application to the inspection plan-
74
ning in manufacturing rms, Engineering Applications of Articial Intelligence, 39 (2015),
75
[36] S. M. Mousavi, B. Vahdani and S. Sadigh Behzadi, Designing a model of intuitionistic fuzzy
76
VIKOR in multi-attribute group decision-making problems, Iranian Journal of Fuzzy Systems,
77
13(1) (2016), 4565.
78
[37] O. Parkash, P. K. Sharma and R. Mahajan, New measures of weighted fuzzy entropy and
79
their applications for the study of maximum weighted fuzzy entropy principle, Information
80
Sciences, 178 (2008), 23892395.
81
[38] B. Soylu, Integrating PROMETHEE II with tchebyche function for multi criteria decision
82
making, International Journal of Information Technology & Decision Making, 09 (2010),
83
[39] E. Szmidt and J. Kacprzyk, Entropy for Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems,
84
118 (2011), 467-477.
85
[40] B. Vahdani, M. Salimi and S. M. Mousavi, A new compromise decision making model based
86
on TOPSIS and VIKOR for solving multi-objective large-scale programming problems with a
87
block angular structure under uncertainty, International Journal of Engineering Transactions
88
B: Applications, 27 (2014), 16731680.
89
[41] I. K. Vlachos and G. D. Sergiagis, Intuitionistic fuzzy information { Application to pattern
90
recognition, Pattern Recognition Lett., 28 (2007), 197-206.
91
[42] X. Z. Wang, B. De Baets and E. Kerre, A comparative study of similarity measures, Fuzzy
92
Sets and Systems, 73 (1995), 259-268.
93
[43] P. Z. Wang, Fuzzy Sets and Its Applications, Shanghai Science and Technology Press, Shang-
94
hai, 1983.
95
[44] C. P. Wei and Y. Zhang, Entropy measures for interval-valued intuitionistic fuzzy sets and
96
their application in group decision making, Mathematical Problems in Engineering, Article
97
ID 563745, 2015 (2015), 0113.
98
[45] C. P. Wei, P. Wang and Y. Zhang, Entropy, similarity measure of interval-valued intuition-
99
istic fuzzy sets and their applications, Information Sciences, 181 (2011), 4273-4286.
100
[46] Z. B.Wu and Y. H. Chen, The maximizing deviation method for group multiple attribute deci-
101
sion making under linguistic environment, Fuzzy Sets and Systems, 158 (2007), 1608-1617.
102
[47] M. M. Xia and Z. S. Xu, Entropy/cross entropy-based group decision making under intu-
103
itionistic fuzzy environment, Information Fusion, 13 (2012), 31-47.
104
[48] Z. H. Xu, Intuitionistic preference relations and their application in group decision making,
105
Information Sciences, 177 (2007), 2363-2379.
106
[49] Z. H. Xu, J. Chen and J. J.Wu, Clustering algorithm for intuitionistic fuzzy sets, Information
107
Sciences, 178 (2008), 37753790.
108
[50] Z. S. Xu and Q. L. Da, The ordered weighted geometric averaging operators, International
109
Journal of Intelligent Systems, 17 (2002), 709716.
110
[51] Z. S. Xu and X. Q. Cai, Non linear optimization models for multiple attribute group decision
111
making with intuitionistic fuzzy information, International Journal of Intelligent Systems, 25
112
(2010), 489513.
113
[52] R. R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision
114
making, IEEE Transactions on Systems, Man, and Cybernetics, 18 (1988), 183190.
115
[53] J. Ye, Two eective measures of intuitionistic fuzzy entropy, Computing, 87 (2010), 5562.
116
[54] J. Ye, Fuzzy decision-making method based on the weighted correlation coecient under
117
intuitionistic fuzzy environment, European Journal of Operational Research, 205 (2010),
118
[55] Z. Yue, Extension of TOPSIS to determine weight of decision maker for group decision
119
making problems with uncertain information, Exp. Syst. Appl., 39 (2012), 63436350.
120
[56] L. A. Zadeh, Fuzzy sets, Information and Control, 08 (1965), 338353.
121
[57] L. A. Zadeh, Is there a need for fuzzy logic?, Information Sciences, 178 (2008), 27512779.
122
ORIGINAL_ARTICLE
MULTIPERIOD CREDIBILITIC MEAN SEMI-ABSOLUTE DEVIATION PORTFOLIO SELECTION
In this paper, we discuss a multiperiod portfolio selection problem with fuzzy returns. We present a new credibilitic multiperiod mean semi- absolute deviation portfolio selection with some real factors including transaction costs, borrowing constraints, entropy constraints, threshold constraints and risk control. In the proposed model, we quantify the investment return and risk associated with the return rate on a risky asset by its credibilitic expected value and semi- absolute deviation. Since the proposed model is a nonlinear dynamic optimization problem with path dependence, we design a novel forward dynamic programming method to solve it. Finally, we provide a numerical example to demonstrate the performance of the designed algorithm and the application of the proposed model.
http://ijfs.usb.ac.ir/article_3498_174cd4e7a275172b16ebbf632749d7bd.pdf
2017-12-30T11:23:20
2018-05-22T11:23:20
65
86
10.22111/ijfs.2017.3498
Finance
Multiperiod portfolio selection
Mean semi-absolute deviation
Entropy constraints
The forward dynamic programming method
Peng
Zhang
zhangpeng300478@aliyun.com
true
1
School of Economics and Management, South China Normal University,
Guangzhou 510006, P. R. China
School of Economics and Management, South China Normal University,
Guangzhou 510006, P. R. China
School of Economics and Management, South China Normal University,
Guangzhou 510006, P. R. China
LEAD_AUTHOR
[1] T. Bodnar, N. Parolya and W. Schmid, A closed-form solution of the multi-period portfo-
1
lio choice problem for a quadratic utility function, Annals of Operations Research, 229(1)
2
(2015), 121{158.
3
[2] K. C. Butler and D. C. Joaquin, Are the gains from international portfolio diversification
4
exaggerated? The in
5
fluence of downside risk in bear markets, Journal of International Money
6
and Finance, 21(7) (2002), 981{1011.
7
[3] G. C. Calaore, Multi-period portfolio optimization with linear control policies, Automatica,
8
44(10) (2008), 2463{2473.
9
[4] U. C elikyurt and S. Oekici, Multiperiod portfolio optimization models in stochastic mar-
10
kets using the meanCvariance approach, European Journal of Operational Research, 179(1)
11
(2007), 186{202.
12
[5] J. Estrada, The cost of equity in Internet stocks: a downside risk approach, European J.
13
Finance, 10(4) (2004), 239{254.
14
[6] Y. Fang, K. K. Lai and S. Y. Wang, Portfolio rebalancing model with transaction costs based
15
on fuzzy decision theory, European Journal of Operational Research, 175(2) (2006), 879{893.
16
[7] N. Gulpnar and B. Rustem, Worst-case robust decisions for multi-period meanCvariance
17
portfolio optimization, European Journal of Operational Research, 183(3) (2007), 981{1000.
18
[8] X. Huang, Mean-semivariance models for fuzzy portfolio selection, Journal of Computational
19
and Applied Mathematics, 217(1) (2008), 1-8.
20
[9] X. Huang and L. Qiao, A risk index model for multi-period uncertain portfolio selection,
21
Information Sciences, 217(24) (2012), 108{116.
22
[10] J. E. Ingersoll, Theory of Financial Decision Making, Rowman & Littleeld, Savage, (1987),
23
[11] P. Jana, T. K. Roy and S. K. Mazumder, Multi-objective possibilistic model for portfolio
24
selection with transaction cost, Journal of Computational and Applied Mathematics, 228(1)
25
(2009), 188{196.
26
[12] J. N. Kapur, Maximum Entropy Models in Science and Engineering, Wiley Eastern Limited,
27
New Delhi, (1990), 428{436.
28
[13] M. Koksalan and C. T. Sakar, An interactive approach to stochastic programming-based
29
portfolio optimization, To appear in Annals of Operations Research, 245(1{2) (2016), 47{
30
[14] H. Konno and H. Yamazaki, Mean absolute portfolio optimisation model and its application
31
to Tokyo stock market, Management Science ,37(5) (1991), 519{531.
32
[15] C. J. Li and Z. F. Li, Multi-period portfolio optimization for assetCliability management with
33
bankrupt control, Applied Mathematics and Computation, 218(22) (2012), 11196{11208.
34
[16] D. Li and W. L. Ng, Optimal dynamic portfolio selection: multiperiod meanCvariance for-
35
mulation, Mathematical Finance, 10(3) (2000), 387{406.
36
[17] X. Li, Z. Qin and S. Kar, Mean-variance-skewness model for portfolio selection with fuzzy
37
returns, European Journal of operational Research, 202(1)(2010), 239{247.
38
[18] D. Lien and Y. K. Tse, Hedging downside risk: futures vs options, Internat. Rev. Econom.
39
Finance, 10(2) (2001), 159{169.
40
[19] B. Liu, Inequalities and convergence concepts of fuzzy and rough variables, Fuzzy Optimization
41
and Decision Making, 2 (2) (2003), 87{100.
42
[20] B. Liu and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE
43
Transactions on Fuzzy Systems, 10(4) (2002), 445{450.
44
[21] Y. J. Liu and W. G. Zhang, A multi-period fuzzy portfolio optimization model with minimum
45
transaction lots, European Journal of Operational Research, 242 (3) (2015), 933{941 .
46
[22] Y.J. Liu, W. G. Zhang and Q. Zhang, Credibilistic multi-period portfolio optimization model
47
with bankruptcy control and affine recourse, Applied Soft Computing, 38(3) (2016), 890{906.
48
[23] R. Mansini, W. Ogryczak and M. G. Speranza, Conditional value at risk and related lin-
49
ear programming models for portfolio optimization, Annals of Operations Research ,152(1)
50
(2007), 227{256.
51
[24] H. M. Markowitz, Portfolio selection, Journal of Finance, 7(1) (1952),77{91.
52
[25] Y. Simaan, Estimation risk in portfolio selection: The mean variance model and the mean-
53
absolute deviation model, Management Science, 43(10) (1997), 1437{1446.
54
[26] M.G. Speranza, Linear programming model for portfolio optimization, Finance, 14(1) (1993),
55
[27] S. Stevenson, Emerging markets, downside risk and the asset allocation decision, Emerging
56
Markets Rev., 2(1) (2001), 50{66.
57
[28] A. B. Terol, B. P. Gladish, M. A. Parra and M. V. R. Ura, Fuzzy compromise programming
58
for portfolio selection, Applied Mathematics and Computation, 173(1) (2006), 251{264
59
[29] J. H. Van Binsbergen and M. Brandt, Solving dynamic portfolio choice problems by recursing
60
on optimized portfolio weights or on the value function?, Computational Economics ,29(3-4)
61
(2007), 355{367.
62
[30] E. Vercher, J. Bermudez and J. Segura, Fuzzy portfolio optimization under downside risk
63
measures, Fuzzy Sets and Systems, 158(7) (2007), 769{782.
64
[31] S.Y. Wang and S.S. Zhu, On fuzzy portfolio selection problem, Fuzzy Optimization and
65
Decision Making, 1(14) (2002),361{377
66
[32] H. L. Wu and Z. F. Li, Multi-period meanCvariance portfolio selection with regime switching
67
and a stochastic cash
68
ow, Insurance: Mathematics and Economics, 50(3) (2012), 371{384.
69
[33] W. Yan and S. R. Li, A class of multi-period semi-variance portfolio selection with a four-
70
factor futures price model, Journal of Applied Mathematics and Computing, 29(1-2) (2009),
71
[34] W. Yan, R. Miao and S.R. Li, Multi-period semi-variance portfolio selection: Model and
72
numerical solution, Applied Mathematics and Computation, 194(1)(2007), 128{134
73
[35] M. Yu, S. Takahashi, H. Inoue and S. Y. Wang, Dynamic portfolio optimization with risk
74
control for absolute deviation model, European Journal of Operational Research, 201(2)
75
(2010), 349{364.
76
[36] M. Yu and S. Y. Wang, Dynamic optimal portfolio with maximum absolute deviation model,
77
Journal of Global Optimization, 53(2) (2012), 363{380.
78
[37] L. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1(3-28)
79
(1978), 61{72.
80
[38] L. Zadeh, A theory of approximate reasoning, in: J. Hayes, D. Michie, R.M. Thrall (Eds.),
81
Mathematical Frontiers of the Social and Policy Sciences, Westview Press, Boulder, Colorado,
82
(1979), 69{129.
83
[39] W. G. Zhang, Y. J. Liu and W. J. Xu, A new fuzzy programming approach for multi-period
84
portfolio Optimization with return demand and risk control, Fuzzy Sets and Systems, 246(4)
85
(2014), 107{126.
86
[40] W. G. Zhang and Y. J. Liu, Credibilitic mean-variance model for multi-period portfolio se-
87
lection problem with risk control, OR Spectrum, 36(1) (2014), 113{132.
88
[41] W.G. Zhang, Y. J. Liu and W. J. Xu, A possibilistic mean-semivariance-entropy model
89
for multi-period portfolio selection with transaction costs, European Journal of Operational
90
Research, 222(2) (2012), 341{349.
91
[42] W. G. Zhang, Y. L. Wang, Z. P. Chen and Z. K. Nie, Possibilistic meanCvariance models
92
and ecient frontiers for portfolio selection problem, Information Sciences, 177(13) (2007),
93
2787{2801.
94
[43] P. Zhang and W. G. Zhang, Multiperiod mean absolute deviation fuzzy portfolio selection
95
model with risk control and cardinality constraints, Fuzzy Sets and Systems, 255(2) (2014),
96
[44] W. G. Zhang, X. L. Zhang and W. L. Xiao, Portfolio selection under possibilistic meanC-
97
variance utility and a SMO algorithm, European Journal of Operational Research, 197(2)
98
(2009), 693{700.
99
[45] S. S. Zhu, D. Li and S. Y. Wang, Risk control over bankruptcy in dynamic portfolio selection:
100
a generalized meanCvariance formulation, IEEE Transactions on Automatic Control, 49(3)
101
(2004), 447{457.
102
ORIGINAL_ARTICLE
ON CONVERGENCE THEOREMS FOR FUZZY HENSTOCK INTEGRALS
The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by Wu and Gong \cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which the point-wise limit of a sequence of fuzzy Henstock integrable functions is fuzzy Henstock integrable has been established.
http://ijfs.usb.ac.ir/article_3499_6f4cc2d0c57b2e8308bf4c95c9724bbb.pdf
2017-12-30T11:23:20
2018-05-22T11:23:20
87
102
10.22111/ijfs.2017.3499
Fuzzy number
Fuzzy number function
Fuzzy Henstock integral
Fuzzy monotone sequence
B. M.
Uzzal Afsan
true
1
Department of Mathematics, Sripat Singh College, Jiaganj-742123, Murshidabad, West Bengal, India
Department of Mathematics, Sripat Singh College, Jiaganj-742123, Murshidabad, West Bengal, India
Department of Mathematics, Sripat Singh College, Jiaganj-742123, Murshidabad, West Bengal, India
LEAD_AUTHOR
[1] R. G. Bartle, A convergence theorem for generalized Riemann integrals, Real Anal. Exchange,
1
20(2) (1994-95), 119{124.
2
[2] B. Bongiorno, L. Di Piazza and K. Musia l, A decomposition theorem for the fuzzy Henstock
3
integral (I), Fuzzy Sets and Systems, 200 (2012), 36{47.
4
[3] R. Goetschel and W. Voxman, Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1986),
5
[4] Z. Gong, On the problem of characterizing derivatives for the fuzzy-valued functions (II):
6
almost everywhere differentiability and strong Henstock integral, Fuzzy Sets and Systems,
7
145 (2004), 381{393.
8
[5] Z. Gong and Y. Shao, The controlled convergence theorems for the strong Henstock integrals
9
of fuzzy-number-valued functions, Fuzzy Sets and Systems, 160 (2009), 1528{1546.
10
[6] Z. Gong and L. Wang, The Henstock-Stieltjes integral for fuzzy-number-valued functions,
11
Inform. Sci., 188 (2012), 276{297.
12
[7] Z. Guang-Quan, Fuzzy continuous function and its properties, Fuzzy Sets and Systems, 43
13
(1991), 159{171.
14
[8] R. Henstock, Theory of Integration, Butterworths, London, 1963.
15
[9] J. Kurzweil, Generalized ordinary dierential equations and continuous dependence on a
16
parameter, Czechoslovak Math. J., 7(82) (1957), 418{446.
17
[10] Ma Ming, On embedding problem of fuzzy number space: Part 4, Fuzzy Sets and Systems,
18
58 (1993), 185{193.
19
[11] K. Musia l, A decomposition theorem for Banach space valued fuzzy Henstock integral, Fuzzy
20
Sets and Systems, 259 (2015), 21{28.
21
[12] C. Wu and Z. Gong, On Henstock integral of fuzzy-number-valued functions, Fuzzy Sets and
22
Systems, 120 (2001), 523{532.
23
[13] C. Wu and Ma Ming, On embedding problem of fuzzy number space: Part 1, Fuzzy Sets and
24
Systems, 44 (1991), 33{38.
25
ORIGINAL_ARTICLE
CREDIBILITY THEORY ORIENTED PREFERENCE INDEX FOR RANKING FUZZY NUMBERS
This paper suggests a novel approach for ranking the most applicable fuzzy numbers, i.e. $LR$-fuzzy numbers. Applying the $\alpha$-optimistic values of a fuzzy number, a preference criterion is proposed for ranking fuzzy numbers using the Credibility index. The main properties of the proposed preference criterion are also studied. Moreover, the proposed method is applied for ranking fuzzy numbers using target-rank-based methods. Some numerical examples are used to illustrate the proposed ranking procedure. The proposed preference criterion is also examined in order to compare with some common methods and the feasibility and effectiveness of the proposed ranking method is cleared via some numerical comparisons.
http://ijfs.usb.ac.ir/article_3500_c8f1b5309e61cf8692e840b8009dfcf8.pdf
2017-12-30T11:23:20
2018-05-22T11:23:20
103
117
10.22111/ijfs.2017.3500
Credibility index
$alpha$-optimistic values
Robustness
Reciprocity
Fuzzy target
Gholamreza
Hesamian
ghesamian@math.iut.ac.ir
true
1
Department of Statistics, Payame Noor University,, Tehran
19395-3697, Iran
Department of Statistics, Payame Noor University,, Tehran
19395-3697, Iran
Department of Statistics, Payame Noor University,, Tehran
19395-3697, Iran
LEAD_AUTHOR
Farid
Bahrami
f.ahmadi@math.iut.ac.ir
true
2
Department of Mathematical Sciences,, Isfahan University of Technology,, Isfahan 84156-83111, Iran
Department of Mathematical Sciences,, Isfahan University of Technology,, Isfahan 84156-83111, Iran
Department of Mathematical Sciences,, Isfahan University of Technology,, Isfahan 84156-83111, Iran
AUTHOR
[1] S. Abbasbandy and B. Asady, Ranking of fuzzy numbers by sign distance, Information Sciences,
1
176 (2006), 2405-24016.
2
[2] B. Asady and A. Zendehnam, Ranking fuzzy numbers by distance minimization, Applied
3
Mathematical Modelling, 31(2007), 2589-2598.
4
[3] R. G. Bartle, The Elements of Integration and Lebesgue Measure, Wiley Interscience, 1995.
5
[4] G. Bortolan and R. A. Degani, Review of some methods for ranking fuzzy subsets, Fuzzy Sets
6
and Systems, 15 (1985), 1-19.
7
[5] S. Chanas, M. Delgado, J. L. Verdegay and M. A. Vila, Ranking fuzzy interval numbers in
8
the setting of random sets, Information Sciences, 69 (1993), 201-217.
9
[6] S. Chanas and P. Zielinski, Ranking fuzzy interval numbers in the setting of random sets-
10
further results, Information Sciences, 117 (1999), 191-200.
11
[7] P. T. Chang and E. S. Lee, Ranking of fuzzy sets based on the concept of existence, Computers
12
and Mathematics with Applications, 27 (1994), 1-21.
13
[8] S. H. Chen, Ranking fuzzy numbers with maximizing set and minimizing set, Fuzzy Sets and
14
Systems, 17 (1985), 113-129.
15
[9] S. J. Chen and S. M. Chen, Fuzzy risk analysis based on the ranking of generalized trapezoidal
16
fuzzy numbers, Applied Intelligence, 26 (2007), 1-11.
17
[10] L. H. Chen and H. W. Lu, An approximate approach for ranking fuzzy numbers based on left
18
and right dominance, Computers and Mathematics with Applications, 41 (2001), 1589-1602.
19
[11] T. C. Chu and C. T. Tsao, Ranking fuzzy numbers with an area between the centroid point
20
and original point, Computers and Mathematics with Applications, 43 (2002), 111-117.
21
[12] L. Decampos and G. A. Mu~noz, A subjective approach for ranking fuzzy numbers, Fuzzy Sets
22
and Systems, 29 (1989), 145-153.
23
[13] M. Delgado, J. L. Verdegay and M. A. Vila, A procedure for ranking fuzzy numbers using
24
fuzzy relations, Fuzzy Sets and Systems, 26 (1988), 49-62.
25
[14] Y. Deng, Z. Zhenfu and L. Qi, Ranking fuzzy numbers with an area method using radius of
26
gyration, Computers and Mathematics with Applications, 51 (2006), 1127-1136.
27
[15] P. Diamond, and P. Kloeden, Metric Spaces of Fuzzy Sets, World Scientic, Singapore 1994.
28
[16] D. Dubois and H. Prade, Ranking fuzzy numbers in the setting of possibility theory, Information
29
Sciences, 30 (1983), 183-224.
30
[17] D. Dubois and H. Prade, Possibility theory: an approach to computerized processing of
31
uncertainty, Plenum Press, New York, 1998.
32
[18] P. Y. Ekel, I. V. Kokshenev, R. O. Parreiras, G. B. Alves and P. M. N. Souza, Fuzzy set
33
based models and methods of decision making and power engineering problems, Engineering,
34
5 (2013), 41-51.
35
[19] R. Ezzati, T. Allahviranloo, S. Khezerloo and M. Khezerloo, An approach for ranking of
36
fuzzy numbers, Expert Systems with Applications, 39 (2012), 690-695.
37
[20] G. Hesamian and M. Shams, Parametric testing statistical hypotheses for fuzzy random vari-
38
ables, Soft Computing, 20 (2015), 1537-1548.
39
[21] V. H. Huynh, Y. Nakamori and J. Lawry, A probability-based approach to comparison of fuzzy
40
numbers and applications to target-oriented decision making, IEEE Transactions on Fuzzy
41
Systems, 16 (2008), 371-387.
42
[22] R. Jain, Decision making in the presence of fuzzy variables, IEEE Transactions on Systems,
43
Man, and Cybernetics , 6 (1976), 698-703.
44
[23] K. Kim and K. S. Park, Ranking fuzzy numbers with index of optimism, Fuzzy Sets and
45
Systems, 35 (1990), 143-150.
46
[24] A. Kumar, P. Singh, P. Kaur and A. Kaur, A new approach for ranking of LR type generalized
47
fuzzy numbers, Expert Systems with Applications, 38 (2011), 10906{10910.
48
[25] H. L. Kwang and J. H. Lee, A method for ranking fuzzy numbers and its application to
49
decision-making, IEEE T. Fuzzy Syst., 7 (1999), 677-685.
50
[26] K. H. Lee, First Course on Fuzzy Theory and Applications, Springer-Verlag, Berlin, 2005.
51
[27] E. S. Lee and R. J. Li, Comparison of fuzzy numbers based on the probability measure of
52
fuzzy events, Computers and Mathematics with Applications, 15(1988), 887-896.
53
[28] D. F. Li, A ratio ranking method of triangular intuitionistic fuzzy numbers and its application
54
to MADM problems, Computers and Mathematics with Applications, 60 (2010), 1557-1570.
55
[29] T. S. Liou and M. J. Wang, Ranking fuzzy numbers with integral value, Fuzzy Sets and
56
Systems, 50 (1992), 247-255.
57
[30] B. Liu, Uncertainty Theory, Springer-Verlag, Berlin, 2004.
58
[31] X. W. Liu and S. L. Han, Ranking fuzzy numbers with preference weighting function expec-
59
tations, Computers and Mathematics with Applications, 49 (2005), 1731-1753.
60
[32] M. Modarres and S. S. Nezhad, Ranking fuzzy numbers by preference ratio, Fuzzy Sets and
61
Systems, 118 (2001), 429-436.
62
[33] J. Peng, H. Liu and G. Shang, Ranking fuzzy variables in terms of credibility measure,
63
Proceedings of the 3th international conference on Fuzzy Systems and Knowledge Discovery,
64
Xi'an, China, (2006), 24-28.
65
[34] S. Rezvani, Ranking generalized exponential trapezoidal fuzzy numbers based on variance,
66
Applied Mathematics and Computation, 262 (2015), 191{198.
67
[35] J. Saade and H. Schwarzlander, Ordering fuzzy sets over the real line: an approach based on
68
decision making under uncertainty, Fuzzy Sets and Systems, 50 (1992), 237-246.
69
[36] H. Sun and J. Wu, A new approach for ranking fuzzy numbers based on fuzzy simulation
70
analysis method, Applied Mathematics and Computation, 174 (2006), 755-767.
71
[37] L. Tran and L. Duckstein, Comparison of fuzzy numbers using a fuzzy distance measure,
72
Fuzzy Sets and Systems, 130 (2002), 331-341.
73
[38] E. Valvis, A new linear ordering of fuzzy numbers on subsets of F(R), Fuzzy Optimazation
74
and Decision Making, 8 (2009), 141-163.
75
[39] Y. M. Wang, Centroid defuzzication and the maximizing set and minimizing set ranking
76
based on alpha level sets, Computers and Industrial Engineering, 57 (2009), 228-236.
77
[40] X. Wang and E. E. Kerre, Reasonable properties for the ordering of fuzzy quantities (I),
78
Fuzzy Sets and Systems, 118 (2001), 375-385.
79
[41] X. Wang and E. E. Kerre, Reasonable properties for the ordering of fuzzy quantities (II),
80
Fuzzy Sets and Systems, 118 (2001), 387-405.
81
[42] Y. J. Wang and H. S. Lee, The revised method of ranking fuzzy numbers with an area between
82
the centroid and original points, Computers and Mathematics with Applications, 55 (2008),
83
2033-2042.
84
[43] Z. X. Wang, Y. J. Liu, Z. P. Fan and B. Feng, Ranking LR-fuzzy number based on deviation
85
degree, Information Science, 179 (2009), 2070-2077.
86
[44] Y.M. Wang and Y. Luo, Area ranking of fuzzy numbers based on positive and negative ideal
87
points, Computers and Mathematics with Applications, 58 (2009), 1769-1779.
88
[45] Z. X. Wang and Y. N. Mo, Ranking fuzzy numbers based on ideal solution, Fuzzy Information
89
and Engineering, 2 (2010), 27-36.
90
[46] P. Xu, X. Su, J. Wu, X. Sun, Y. Zhang and Y. Deng, A note on ranking generalized fuzzy
91
numbers, Expert Systems with Applications, 39 (2012), 6454-6457.
92
[47] Y. Yuan, Criteria for evaluating fuzzy ranking methods, Fuzzy Sets and Systems, 43 (1991),
93
ORIGINAL_ARTICLE
SOME PROBABILISTIC INEQUALITIES FOR FUZZY RANDOM VARIABLES
In this paper, the concepts of positive dependence and linearlypositive quadrant dependence are introduced for fuzzy random variables. Also,an inequality is obtained for partial sums of linearly positive quadrant depen-dent fuzzy random variables. Moreover, a weak law of large numbers is estab-lished for linearly positive quadrant dependent fuzzy random variables. Weextend some well known inequalities to independent fuzzy random variables.Furthermore, a weak law of large numbers for independent fuzzy random vari-ables is stated and proved.
http://ijfs.usb.ac.ir/article_3501_4354e3e5670f8d20ba3ab0bb1f95685b.pdf
2017-12-30T11:23:20
2018-05-22T11:23:20
119
134
10.22111/ijfs.2017.3501
Fuzzy random variable
Linearly Positive Quadrant Dependence
Independence
Law of Large Numbers
Hamed
Ahmadzade
ahmadzadeh.h.63@gmail.com
true
1
Department of Statistics, University of Sistan and Baluchestan,
Zahedan, Iran
Department of Statistics, University of Sistan and Baluchestan,
Zahedan, Iran
Department of Statistics, University of Sistan and Baluchestan,
Zahedan, Iran
AUTHOR
Mohammad
Amini
mamini48@yahoo.com
true
2
Department of Statistics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad 91775, Iran
Department of Statistics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad 91775, Iran
Department of Statistics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad 91775, Iran
LEAD_AUTHOR
Seyed Mahmoud
Taheri
sm_taheri@yahoo.com
true
3
Faculty of Engineering Science, College of Engineering,
University of Tehran, Tehran, Iran
Faculty of Engineering Science, College of Engineering,
University of Tehran, Tehran, Iran
Faculty of Engineering Science, College of Engineering,
University of Tehran, Tehran, Iran
AUTHOR
Abolghasem
Bozorgnia
a.bozorgnia@khayyam.ac.ir
true
4
Department of Statistics, Khayyam University, Mashhad,
Iran
Department of Statistics, Khayyam University, Mashhad,
Iran
Department of Statistics, Khayyam University, Mashhad,
Iran
AUTHOR
[1] H. Agahi and E. Eslami, A general inequality of Chebyshev type for semi(co)normed fuzzy
1
integrals, Soft Computing, 15 (2011), 771{780.
2
[2] H. Agahi, A. F. Franulic and S. M. Vaezpour, Fatou's lemma for Sugeno integral, Applied
3
Mathematics and Computation, 217(13) (2011), 6092{6096.
4
[3] H. Ahmadzade, M. Amini, S. M. Taheri and A. Bozorgnia, Some limit theorems for indepen-
5
dent fuzzy random variables, Thai Journal of Mathematics, 12 (2014), 537{548.
6
[4] H. Ahmadzade, M. Amini, S. M. Taheri and A. Bozorgnia, Some moment inequalities for
7
fuzzy martingales and their applications, Journal Uncertainty Analysis and Applications, 2
8
(2014), 1{14.
9
[5] H. Ahmadzade, M. Amini, S. M. Taheri and A. Bozorgnia, Maximal inequalities and some
10
convergence theorems for fuzzy random variables, Kybernetika, 52(2) (2016), 307{328.
11
[6] H. Ahmadzade, M. Amini, S. M. Taheri and A. Bozorgnia, Negative Dependence for Fuzzy
12
Random Variables: Basic Denitions and Some Limit Theorems, Filomat, 30(9) (2016),
13
2535{2549.
14
[7] T. Birkel, A functional central limit theorem for positively dependent random variables, Jour-
15
nal of Multivariate Analysis, 44 (1993), 314{320.
16
[8] P. Diamond and P. Kloeden, Metric space of fuzzy sets, Fuzzy Sets and Systems, 35 (1990),
17
[9] Y. Feng, An approach to generalize laws of large numbers for fuzzy random variables, Fuzzy
18
Sets and Systems, 128 (2002), 237{245.
19
[10] Y. Feng, L. Hu and H. Shu, The variance and covariance of fuzzy random variables and their
20
applications, Fuzzy Sets and Systems, 120 (2001), 487{497.
21
[11] K. Fu and L. X. Zhang, Strong limit theorems for random sets and fuzzy random sets with
22
slowly varying weights, Information Sciences, 178 (2008), 2648{2660.
23
[12] A. Gut, Probability: A Graduate Course, Springer, New York, 2005.
24
[13] L. Hongxing, Probability representations of fuzzy systems, Science China Information Sci-
25
ences, 49 (2006), 339{363.
26
[14] S. Y. Joo, Strong law of large numbers for tight fuzzy random variables, Journal of the Korean
27
Statistical Society, 31 (2002), 129{140.
28
[15] S. Y. Joo, Y. K. Kim and J. S. Kwon, On Chung's type law of large numbers for fuzzy random
29
variables, Statistics and Probability Letteres, 74 (2005), 67{75.
30
[16] S. Y. Joo, S. S. Lee and Y. H. Yoo, A strong law of large numbers for stationary fuzzy random
31
variables, Journal of the Korean Statistical Society, 30 (2001), 153-161.
32
[17] E. P. Klement, M. L. Puri and D. A. Ralescu, Limit theorems for fuzzy random variables,
33
Proceedings of the Royal Society of London A, 407 (1986), 171-182.
34
[18] G. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic-Theory and Applications, Prentice-Hall,
35
Upper Saddle River, NJ, 1995.
36
[19] R. Korner, On the variance of fuzzy random variables, Fuzzy Sets and Systems 92 (1997),
37
[20] V. Kratschmer, Probability theory in fuzzy sample spaces, Metrika, 60 (2004), 167{180.
38
[21] R. Kruse and K. D. Meyer, Statistics with vague data, Reidel Publishing Company, Dordrecht,
39
[22] H. Kwakernaak, Fuzzy random variables I. Information Sciences, 15 (1978), 1{29.
40
[23] Z. Lin and Z. Bai, Probability inequalities, Springer, New York, 2010.
41
[24] Y. K. Liu and B. Liu, Fuzzy Random Variables: A Scalar Expected Value Operator, Fuzzy
42
Optimization and Decision Making, 2 (2003), 143{160.
43
[25] S. Louhichi, Rosenthal's inequality for LPQD sequences, Statistics and Probability Letters,
44
42 (1992), 139-144.
45
[26] M. Miyakoshi and M. Shimbo, A strong law of large numbers for fuzzy random variables.
46
Fuzzy Sets and Systems 12 (1984), 133-142.
47
[27] R. E. Moore, R. B. Kearfott and M. J. Cloud, Introduction to Interval Analysis, Siam,
48
Philadelphia, 2009.
49
[28] C. M. Newman, Asymptotic independence and limit theorems for positively and negatively
50
dependent random variables, Statistics and Probability, 5 (1984), 127{140.
51
[29] H. T. Nguyen, T. Wang and B. Wu, On probabilistic methods in fuzzy theory, International
52
Journal of Intelligent Systems, 19 (2004), 99-109.
53
[30] M. L. Puri and D. A. Ralescu, Fuzzy random variables. Journal of Mathematical Analysis
54
and Applications, 114 (1986), 402{422.
55
[31] M. Rong, N. K. Mahapatra and M. Maiti, A multi-objective wholesaler-retailers inventory-
56
distribution model with controllable lead-time based on probabilistic fuzzy set and triangular
57
fuzzy number, Applied Mathematical Modelling, 32 (2008), 2670{2685.
58
[32] B. Sadeghpour Gildeh and S. Rahimpour, A Fuzzy Bootstrap Test for the Mean with Dp;q-
59
distance, Fuzzy Information and Engineering, 4 (2011), 351{358.
60
[33] Q. M. Shao, H. Yu, Weak convergence for weighted empirical processes of dependent se-
61
quences, Annals of Probability, 24 (1996), 2052{2078.
62
[34] R. L. Taylor, L. Seymour and Y. Chen, Weak laws of large numbers for fuzzy random sets,
63
Nonlinear Analysis, 47 (2001), 1245{125.
64
[35] R. Viertl. Statistical Methods for Fuzzy Data, John Wiley and Sons, Chichester, 2011.
65
[36] H. C. Wu, The central limit theorems for fuzzy random variables, Information Sciences. 120,
66
(1999), 239-256.
67
[37] H. C. Wu, The laws of large numbers for fuzzy random variables, Fuzzy Sets and Systems.
68
116 (2000), 245-262.
69
[38] H. C. Wu, Fuzzy Bayesian system reliability assessment based on exponential distribution,
70
Applied Mathematical Modelling, 30 (2006), 509{530.
71
[39] L. A. Zadeh, Fuzzy sets, Information and Control, 8, (1965), 338{353.
72
ORIGINAL_ARTICLE
ROBUSTNESS OF THE TRIPLE IMPLICATION INFERENCE METHOD BASED ON THE WEIGHTED LOGIC METRIC
This paper focuses on the robustness problem of full implication triple implication inference method for fuzzy reasoning. First of all, based on strong regular implication, the weighted logic metric for measuring distance between two fuzzy sets is proposed. Besides, under this metric, some robustness results of the triple implication method are obtained, which demonstrates that the triple implication method possesses a good behavior of robustness.
http://ijfs.usb.ac.ir/article_3502_3af181b32a04b615e978e930b50b64b4.pdf
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10.22111/ijfs.2017.3502
Robustness
Triple implication method
Weighted logic metric
Weighted logic similarity degree
Fuzzy reasoning
Jun
Li
lijun@lut.cn
true
1
School of Science, Lanzhou University of Technology, Lanzhou 730050,
Gansu, China
School of Science, Lanzhou University of Technology, Lanzhou 730050,
Gansu, China
School of Science, Lanzhou University of Technology, Lanzhou 730050,
Gansu, China
LEAD_AUTHOR
Chao
Fu
fuchao45612@sina.com
true
2
School of Science, Lanzhou University of Technology, Lanzhou 730050,
Gansu, China
School of Science, Lanzhou University of Technology, Lanzhou 730050,
Gansu, China
School of Science, Lanzhou University of Technology, Lanzhou 730050,
Gansu, China
AUTHOR
[1] R. Belohlavek, Fuzzy Relational Systems, Foundations and Principles, Kluwer Academic
1
Publishers, Dordrecht, (2002), 40-116.
2
[2] K. Y. Cai, -equalities of fuzzy sets, Fuzzy Sets and Systems, 76(1) (1995), 97-112.
3
[3] K. Y. Cai, Robustness of fuzzy reasoning and -equalities of fuzzy sets, IEEE Transactions
4
on Fuzzy Systems, 9(5) (2001), 738-750.
5
[4] G. S. Cheng and Y. X. Fu, Error estimation of perturbations under CRI, IEEE Transactions
6
on Fuzzy Systems, 14(6) (2006), 709-715.
7
[5] S. S. Dai, D. W. Pei and S. M. Wang, Perturbation of fuzzy sets and fuzzy reasoning based
8
on normalized Minkowski distances, Fuzzy Sets and Systems, 189 (2012), 63-73.
9
[6] S. S. Dai, D. W. Pei and D. H. Guo, Robustness analysis of full implication inference method,
10
International Journal of Approximate Reasoning, 54(5) (2013), 653-666.
11
[7] D. Dubois, J. Lang and H. Prade, Fuzzy sets in approximate reasoning, parts 1 and 2, Fuzzy
12
Sets and Systems, 40(1) (1991), 143-244.
13
[8] P. Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, (1998),
14
[9] D. H. Hong and S. Y. Hwang, A note on the value similarity of fuzzy systems variables,
15
Fuzzy Sets and Systems, 66(3) (1994), 383-386.
16
[10] E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Kluwer Academic Publishers,
17
Dordrecht, (2000), 4-6.
18
[11] J. Li and J. T. Yao, Theory of integral truth degrees of formula in SMTL propositional logic,
19
Acta Electronica Sinica, 41(5) (2013), 878-883.
20
[12] Y. M. Li, D. C. Li, W. Pedrycz and J. J. Wu, An approach to measure the robustness of fuzzy
21
reasoning, International Journal of Intelligent Systems, 20(4) (2005), 393-413.
22
[13] H. W. Liu and G. J. Wang, Continuity of triple I methods based on several implications,
23
Computers and Mathematics with Applications, 56(8) (2008), 2079-2087.
24
[14] H. W. Liu and G. J. Wang, A note on the unied forms of triple I method, Computers and
25
Mathematics with Applications, 52(10) (2006), 1609-1613.
26
[15] H. W. Liu and G. J. Wang, Unied forms of fully implicational restriction methods for fuzzy
27
reasoning, Information Sciences, 177(3) (2007), 956-966.
28
[16] H. W. Liu and G. J. Wang, Triple I method based on pointwise sustaining degrees, Computers
29
and Mathematics with Applications, 55(11) (2008), 2680-2688.
30
[17] M. X. Luo and N. Yao, Triple I algorithms based on Schweizer- Sklar operators in fuzzy
31
reasoning, International Journal of Approximate Reasoning, 54(5) (2013), 640-652.
32
[18] C. P. Pappis, Value approximation of fuzzy systems variables, Fuzzy Sets and Systems, 39(1)
33
(1991), 111-115.
34
[19] D. W. Pei, Unied full implication algorithms of fuzzy reasoning, Information Sciences,
35
178(2) (2008), 520-530.
36
[20] G. J. Wang, Non-classical Mathematical Logic and Approximate Reasoning, second ed., Sci-
37
ence Press, Beijing, China, (2008), 155-165.
38
[21] G. J.Wang, Introduction to Mathematical Logic and Resolution Principle, second ed., Science
39
Press, Beijing, China, (2006), 160-162.
40
[22] G. J. Wang and H. Wang, Non-fuzzy versions of fuzzy reasoning in classical logics, Informa-
41
tion Sciences, 138 (2001), 211-236.
42
[23] G. J. Wang and J. Y. Duan, On robustness of the full implication triple I inference method
43
with respect to ner measurements, International Journal of Approximate Reasoning, 55(3)
44
(2014),787-796.
45
[24] S. W. Wang and W. X. Zheng, Real Variable Function and Functional Analysis, Higher
46
Education Press, Beijing, China, (2005), 4-5.
47
[25] G. J. Wang, The full implication triple I method of fuzzy reasoning, SCIENCE CHINA Ser.
48
E 29 (1999), 43-53.
49
[26] G. J. Wang and J. Y. Duan, Two types of fuzzy metric spaces suitable for fuzzy reasoning,
50
Science China Information Sciences, 44(5) (2014), 623-632.
51
[27] G. J. Wang and L. Fu, Unied forms of triple I method, Computers and Mathematics with
52
Applications, 49(5) (2005), 923-932.
53
[28] G. J. Wang, Formalized theory of general fuzzy reasoning, Information Sciences, 160(1)
54
(2004), 251-266.
55
[29] R. R. Yager, On some new classes of implication operators and their role in approximate
56
reasoning, Information Sciences, 167(1-4) (2004), 193-216.
57
[30] M. S. Ying, Perturbation of fuzzy reasoning, IEEE Transactions on Fuzzy Systems, 7(5)
58
(1999), 625-629.
59
[31] L. A. Zadeh, Outline of a new approach to the analysis of complex systems and decision
60
processes, IEEE Transactions on Systems Man and Cybernetics, 3(1) (1973), 28-33.
61
ORIGINAL_ARTICLE
ON STRATIFIED LATTICE-VALUED CONVERGENCE SPACES
In this paper we provide a common framework for different stratified $LM$-convergence spaces introduced recently. To this end, we slightly alter the definition of a stratified $LMN$-convergence tower space. We briefly discuss the categorical properties and show that the category of these spaces is a Cartesian closed and extensional topological category. We also study the relationship of our category to the categories of stratified $L$-topological spaces and of enriched $LM$-fuzzy topological spaces.
http://ijfs.usb.ac.ir/article_3503_08f77d70db13a2b7b2554e34ebcef52f.pdf
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10.22111/ijfs.2017.3503
Lattice-valued convergence
$LM$-convergence space
Stratified $LMN$-convergence tower space
Stratified $LM$-filter
Stratified $L$-topological space
Enriched $LM$-fuzzy topological space
Gunther
Jager
g.jager@ru.ac.za, gunther.jaeger@fh-stralsund.de
true
1
School of Mechanical Engineering, University of Applied Sciences
Stralsund, D-18435 Stralsund, Germany
School of Mechanical Engineering, University of Applied Sciences
Stralsund, D-18435 Stralsund, Germany
School of Mechanical Engineering, University of Applied Sciences
Stralsund, D-18435 Stralsund, Germany
LEAD_AUTHOR
[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Wiley, 1989.
1
[2] J. M. Fang, Categories isomorphic to L-FTOP, Fuzzy Sets and Systems, 157 (2006), 820 {
2
[3] P. V. Flores, R. N. Mohapatra and G. Richardson, Lattice-valued spaces: fuzzy convergence,
3
Fuzzy Sets and Systems, 157 (2006), 2706 { 2714.
4
[4] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott, A Compendium
5
of Continuous Lattices, Springer-Verlag Berlin Heidelberg, 1980.
6
[5] U. Hohle and A. P. Sostak, Axiomatic foundations of xed-basis fuzzy topology, In: U. Hohle,
7
S.E. Rodabauch (Eds.), Mathematics of Fuzzy Sets. Logic, Topology and Measure Theory,
8
Kluwer, Boston/Dordrecht/London 1999, 123 { 272.
9
[6] G. Jager, A category of L-fuzzy convergence spaces, Quaest. Math., 24 (2001), 501 { 518.
10
[7] G. Jager, A note on stratied LM-lters, Iranian Journal of Fuzzy Systems, 10(4) (2013),
11
135 { 142.
12
[8] G. Jager, Stratied LMN-convergence tower spaces, Fuzzy Sets and Systems, 282 (2016), 62
13
[9] K. Keimel and J. Lawson, Continuous and Completely Distributive Lattices, in: Lattice
14
Theory: Special Topics and Applications Vol. 1 (G. Gratzer, F. Wehring (Eds.)), Birkhauser
15
Basel 2014, 5-53.
16
[10] B. Pang, Enriched (L,M)-fuzzy convergence spaces, Journal of Intelligent & Fuzzy Systems,
17
27 (2014), 93 { 103.
18
[11] B. Pang and Y. Zhao, Stratied (L,M)-fuzzy Q-convergence spaces, Iranian Journal Fuzzy
19
Systems, 13(4) (2016), 95 { 111.
20
[12] B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland, New York, 1983.
21
[13] W. Yao, Moore-Smith convergence in (L, M)-fuzzy topology, Fuzzy Sets and Systems, 190
22
(2012), 47 { 62.
23
ORIGINAL_ARTICLE
Persian-translation Vol.14, No.6
http://ijfs.usb.ac.ir/article_3505_70f72100261fda6aa83bea4e659894cb.pdf
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10.22111/ijfs.2017.3505