ORIGINAL_ARTICLE
Cover Vol.1, No.2
http://ijfs.usb.ac.ir/article_3127_7558552a3bca8b71e43a23a9e773e760.pdf
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10.22111/ijfs.2004.3127
ORIGINAL_ARTICLE
A NEW FUZZY MORPHOLOGY APPROACH BASED ON THE FUZZY-VALUED GENERALIZED DEMPSTER-SHAFER THEORY
In this paper, a new Fuzzy Morphology (FM) based on the GeneralizedDempster-Shafer Theory (GDST) is proposed. At first, in order to clarify the similarity ofdefinitions between Mathematical Morphology (MM) and Dempster-Shafer Theory (DST),dilation and erosion morphological operations are studied from a different viewpoint. Then,based on this similarity, a FM based on the GDST is proposed. Unlike previous FM’s,proposed FM does not need any threshold to obtain final eroded or dilated set/image. Thedilation and erosion operations are carried out independently but complementarily. The GDSTbased FM results in various eroded and dilated images in consecutive α-cuts, making a nestedset of convex images, where each dilated image at a larger α-cut is a subset of the dilatedimage at a smaller α-cut. Dual statement applies to eroded images.
http://ijfs.usb.ac.ir/article_497_1bac70711c4eaabff92384bf9ad33486.pdf
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10.22111/ijfs.2004.497
Generalized Dempster-Shafer theory
Mathematical Morphology
Fuzzy Morphology
Generalized Dempster-Shafer Theory’s Fuzzy Morphology
SAFAR
HATAMI
s.hatami@ece.ut.ac.ir
true
1
RESEARCH ASSISTANT, CONTROL AND INTELLIGENT PROCESSING CENTER OF
EXCELLENCE, ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, UNIVERSITY OF TEHRAN,
P.O. BOX 14395/515, TEHRAN, IRAN.
RESEARCH ASSISTANT, CONTROL AND INTELLIGENT PROCESSING CENTER OF
EXCELLENCE, ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, UNIVERSITY OF TEHRAN,
P.O. BOX 14395/515, TEHRAN, IRAN.
RESEARCH ASSISTANT, CONTROL AND INTELLIGENT PROCESSING CENTER OF
EXCELLENCE, ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, UNIVERSITY OF TEHRAN,
P.O. BOX 14395/515, TEHRAN, IRAN.
AUTHOR
BABAK N.
ARAABI
araabi@ut.ac.ir
true
2
CONTROL AND INTELLIGENT PROCESSING CENTER OF
EXCELLENCE, ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, UNIVERSITY OF TEHRAN,
P.O. BOX 14395/515, TEHRAN, IRAN.
CONTROL AND INTELLIGENT PROCESSING CENTER OF
EXCELLENCE, ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, UNIVERSITY OF TEHRAN,
P.O. BOX 14395/515, TEHRAN, IRAN.
CONTROL AND INTELLIGENT PROCESSING CENTER OF
EXCELLENCE, ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT, UNIVERSITY OF TEHRAN,
P.O. BOX 14395/515, TEHRAN, IRAN.
LEAD_AUTHOR
CARO
LUCAS
lucas@ipm.ir
true
3
CONTROL AND INTELLIGENT PROCESSING CENTER OF EXCELLENCE, ELECTRICAL
AND COMPUTER ENGINEERING DEPARTMENT, UNIVERSITY OF TEHRAN, P.O. BOX 14395/515,
TEHRAN, IRAN.
CONTROL AND INTELLIGENT PROCESSING CENTER OF EXCELLENCE, ELECTRICAL
AND COMPUTER ENGINEERING DEPARTMENT, UNIVERSITY OF TEHRAN, P.O. BOX 14395/515,
TEHRAN, IRAN.
CONTROL AND INTELLIGENT PROCESSING CENTER OF EXCELLENCE, ELECTRICAL
AND COMPUTER ENGINEERING DEPARTMENT, UNIVERSITY OF TEHRAN, P.O. BOX 14395/515,
TEHRAN, IRAN.
AUTHOR
[1] B. N. Araabi, N. Kehtarnavaz and C. Lucas, Restrictions imposed by the fuzzy extension of relations
1
and functions, Journal of Intelligent and Fuzzy Systems, 11(1/2) (2001) 9-22.
2
[2] I. Bloch and H. Maitre, Mathematical morphology on fuzzy sets, Proc. Int. Workshop Mathematical
3
Morphology and its Applications to Signal Processing, Barcelona, Spain, (1993) 151-156.
4
[3] I. Bloch and H. Maitre, Fuzzy mathematical morphologies: A comparative study, Pattern
5
Recognition, 28(9) (1995) 1341-1387.
6
[4] A. P. Dempster, Upper and lower probabilities induced by a multi-valued mapping, Annals of
7
Mathematical Statistics, 38(2) (1967) 325-339.
8
[5] C. R. Giardina and D. Sinha, Image processing using pointed fuzzy sets, Proc. VIII SPIE Conf.
9
Intelligent Robots and Computer Vision: Algorithms and Techniques, Philadelphia, USA, 1192
10
(1989) 659-668.
11
[6] V.Goetcherian, From binary to gray tone image processing using fuzzy logic concepts, Pattern
12
Recognition, 12(1) (1980) 7-15.
13
[7] R. C. Gonzalez and R. E. Woods, Digital image processing, Prentice Hall, New York, USA, (2002).
14
[8] M. Kauffman and M. M. Gupta, Fuzzy mathematical models in engineering and management
15
science, Elsevier, North-Holland, New York, USA (1988).
16
[9] J. S. J. Lee, R. M. Haralick, and L. G. Shapiro, Morphologic edge detection, IEEE Transactions on
17
Robotics and Automation, 3(2) (1987) 142-156.
18
[10] C. Lucas and B. N. Araabi, Generalization of the Dempster-Shafer theory: A fuzzy-valued measure,
19
IEEE Transactions on Fuzzy Systems, 7(3) (1999) 255-270.
20
[11] P. Maragos and R. W. Schafer, Morphological filters-Part I: Their set-theoretic analysis and
21
relations to linear shift-invariant filters, IEEE Transactions on Acoustics, Speech, and Signal
22
Processing, 35(8) (1987) 1153-1169.
23
[12] P. Maragos and R. W. Schafer, Morphological filters-Part II: Their relations to median,
24
order-statistics, and stack filters, IEEE Transactions on Acoustics, Speech, and Signal Processing,
25
35(8) (1987) 1170-1184.
26
[13] G. Matheron, Random sets and integral geometry, John Wiley, New York, USA, (1975).
27
[14] J. Serra, Image analysis and mathematical morphology, Academic press, London, UK, (1982).
28
[15] J. Serra, Introduction to mathematical morphology, Computer Vision, Graphics and Image
29
Processing, 35(3) (1986) 283-305.
30
[16] G. Shafer, A mathematical theory of evidence, Princeton University Press, Princeton, USA, (1976).
31
[17] D. Sinha and E. R. Dougherty, A General axiomatic theory of intrinsically fuzzy mathematical
32
morphologies, IEEE Transactions on Fuzzy Systems, 3(4) (1995) 389-403.
33
[18] D. Sinha and E. R. Dougherty, Fuzzy mathematical morphology, Visual Communication and Image
34
Representation, 3(3) (1992) 286-302.
35
[19] D. Sinha, P. Sinha, E. R. Dougherty, and S. Batman, Design and analysis of fuzzy morphological
36
algorithms for image processing, IEEE Transactions on Fuzzy Systems, 5(4) (1997) 570-584.
37
[20] R. L. Stevenson and G. R. Arce, Morphological filters: Statistics and further syntactic properties,
38
IEEE Transactions on Circuits and Systems, 34(11) (1987) 1292-1305.
39
[21] L. XiangJi and D. RunTao, Fuzzy morphological operators to edge enhancing of images, Proc. 4th
40
IEEE Int. Conf. Signal Processing, Beijing, China, 2 (1998) 1017-1020.
41
ORIGINAL_ARTICLE
FUZZY GRADE OF I.P.S. HYPERGROUPS OF ORDER 7
i.p.s. hypergroups are canonical hypergroups such that$[\forall(a,x),a+x\ni x]\Longrightarrow[a+x=x].$i.p.s. hypergroups were investigated in [1], [2], [3], [4] and it was proved thatif the order is less than 9, they are strongly canonical (see [13]). In this paperwe obtain the sequences of fuzzy sets and of join spaces determined (see [8])by all i.p.s. hypergroups of order seven. For the meaning of the hypergroupsiH and the notations, see [7], [8].
http://ijfs.usb.ac.ir/article_499_f14b97072c6b8a952f174eaabb80457c.pdf
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10.22111/ijfs.2004.499
Fuzzy grade
Strong fuzzy grade
i.p.s. hypergroups
Join spaces
Whypergroups
Piergiulio
Corsini
corsini@dimi.uniud.it; corsini2002@yahoo.com
true
1
Dipartimento di Matematica e Informatica, Via delle Scienze 206,
33100 Udine, Italy, fax: 0039-0432-558499
Dipartimento di Matematica e Informatica, Via delle Scienze 206,
33100 Udine, Italy, fax: 0039-0432-558499
Dipartimento di Matematica e Informatica, Via delle Scienze 206,
33100 Udine, Italy, fax: 0039-0432-558499
AUTHOR
Irina
Cristea
irinacri@yahoo.co.uk
true
2
Faculty of Mathematics, Al.I. Cuza University, 6600 Ias¸i, Romania,
fax: 0040-232-201160
Faculty of Mathematics, Al.I. Cuza University, 6600 Ias¸i, Romania,
fax: 0040-232-201160
Faculty of Mathematics, Al.I. Cuza University, 6600 Ias¸i, Romania,
fax: 0040-232-201160
LEAD_AUTHOR
[1] P. Corsini, Sugli ipergruppi canonici finiti con identit`a parziali scalari, Rend. Circolo Mat.
1
di Palermo, Serie II, Tomo XXXVI (1987).
2
[2] P. Corsini, (i.p.s.) Ipergruppi di ordine 6, Ann. Sc. de l’Univ. Blaise Pascal, Clermont–Ferrand
3
II (1987).
4
[3] P. Corsini, (i.p.s.) Ipergruppi di ordine 7, Atti Sem. Mat. Fis. Univ. Modena, XXXIV
5
(1985–1986).
6
[4] P. Corsini, (i.p.s.) Hypergroups of order 8, Aviani Editore (1989) 1–106.
7
[5] P. Corsini, Prolegomena of hypergroups, Aviani Editore (1993).
8
[6] P. Corsini, On W–hypergroups, Proceedings of I.R.B. InternationalWorkshops, New Frontiers
9
in Multivalued Hyperstructures, Monteroduni (1995).
10
[7] P. Corsini, Join spaces, power sets, fuzzy sets, Proceedings of the Fifth International Congress
11
on Algebraic Hyperstructures and Applications, 1993, Ia¸si, Hadronic Press (1994).
12
[8] P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Asian Bull. of
13
Math. SEAMS, 27 (2003).
14
[9] P. Corsini and I. Cristea, Fuzzy grade of i.p.s. hypergroups of order less or equal to 6, accepted
15
by PU.M.A., Budapest (2004).
16
[10] P. Corsini and V. Leoreanu, Join spaces associated with fuzzy sets, J. of Combinatorics,
17
Information and System Sciences, 20 (1) (1995).
18
[11] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Advances in Math.,
19
Kluwer Academic Publishers (2003).
20
[12] J. Mittas, Hypergroupes canoniques, Math. Balkanica, 2 (1972).
21
[13] J. Mittas, Hypergroupes canoniques, values et hypervalues. hypergroupes fortement et
22
sup´erieurement canoniques, Math. Balk., 8 (1978).
23
[14] W. Prenowitz and J. Jantosciak, Geometries and join spaces, J. reine und angewandte Math.,
24
257 (1972) 100–128.
25
[15] L. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338–353.
26
ORIGINAL_ARTICLE
SOME QUOTIENTS ON A BCK-ALGEBRA GENERATED BY A
FUZZY SET
First we show that the cosets of a fuzzy ideal μ in a BCK-algebraX form another BCK-algebra X/μ (called the fuzzy quotient BCK-algebra of X by μ). Also we show thatX/μ is a fuzzy partition of X and we prove several some isomorphism theorems. Moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition P of a commutative BCK-algebra iscompatible, then P is a fuzzy quotient BCK-algebra. Finally we define thenotion of a coset of a fuzzy ideal and an element of a BCK-algebra and proverelated theorems.
http://ijfs.usb.ac.ir/article_503_c99fc7423f434249f96ead64e115875f.pdf
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10.22111/ijfs.2004.503
Fuzzy similarity relations
Fuzzy partitions
Fuzzy quotient
Fuzzy
ideal
Cosets
Quotient algebra
Abbas
Hasankhani
abhasan@mail.uk.ac.ir
true
1
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
LEAD_AUTHOR
Hamid
Saadat
saadat@iauk.ac.ir
true
2
Islamic Azad University Science and Research Campus, Kerman, Iran
Islamic Azad University Science and Research Campus, Kerman, Iran
Islamic Azad University Science and Research Campus, Kerman, Iran
AUTHOR
[1] A. Hasankhani, F-Spectrum of a BCK-algebra, J. Fuzzy Math. Vol. 8, No. 1 (2000), 1-11.
1
[2] V. Hohle, Quotients with respect to similarity relations, Fuzzy sets and systems 27 (1988),
2
[3] C. S. Hoo, Fuzzy ideal of BCI and MV-algebra, Fuzzy sets and Systems 62 (1994), 111-114.
3
[4] Y. Imai and K. Iseki, On axiom systems of propositional calculi, XIV. Proc. Jopan Academy,
4
42 (1966), 19-22.
5
[5] K. Iseki, On ideals in BCK-algebra, Math. Seminar Notes, 3 (1975), Kobe University.
6
[6] K. Iseki, Some properties of BCK-algebra, 2 (1975), xxxv, these notes.
7
[7] K. Iseki and S. Tanaka, Ideal theory of BCK-algebra, Math. Japonica, 21 (1976), 351-366.
8
[8] K. Iseki and S. Tanaka, An introduction to the theory of BCK-algrba, Math. Japonica, 23
9
(1978), 1-26.
10
[9] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and Systems 8 (1982),
11
[10] S. Ovchinnikov, Similarity relations, fuzzy partitions, and fuzzy ordering, Fuzzy sets and
12
system, 40 (1991), 107-126.
13
[11] O. Xi, Fuzzy BCK-algebra, Math. Japonica, 36 (1991), 935-942.
14
[12] L. A. Zadeh, Similarity relations and fuzzy ordering, Inform. Sci. 3 (1971), 177-200.
15
[13] L. A. Zadeh, Fuzzy sets, Information and control, 8 (1965), 338-353.
16
ORIGINAL_ARTICLE
PEDOMODELS FITTING WITH FUZZY LEAST
SQUARES REGRESSION
Pedomodels have become a popular topic in soil science and environmentalresearch. They are predictive functions of certain soil properties based on other easily orcheaply measured properties. The common method for fitting pedomodels is to use classicalregression analysis, based on the assumptions of data crispness and deterministic relationsamong variables. In modeling natural systems such as soil system, in which the aboveassumptions are not held true, prediction is influential and we must therefore attempt toanalyze the behavior and structure of such systems more realistically. In this paper weconsider fuzzy least squares regression as a means of fitting pedomodels. The theoretical andpractical considerations are illustrated by developing some examples of real pedomodels.
http://ijfs.usb.ac.ir/article_505_dcb76238bd5f980beec986293a3c294e.pdf
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10.22111/ijfs.2004.505
Pedomodels
Pedotransfer Functions
Fuzzy Least Squares
Fuzzy regression
JAHANGARD
MOHAMMADI
j_mohammadi@sku.ac.ir
true
1
SOIL SCIENCE DEPARTMENT, COLLEGE OF AGRICULTURE,
SHAHREKORD UNIVERSITY, SHAHREKORD, IRAN.
SOIL SCIENCE DEPARTMENT, COLLEGE OF AGRICULTURE,
SHAHREKORD UNIVERSITY, SHAHREKORD, IRAN.
SOIL SCIENCE DEPARTMENT, COLLEGE OF AGRICULTURE,
SHAHREKORD UNIVERSITY, SHAHREKORD, IRAN.
AUTHOR
SYED MAHMOUD
TAHERI
sm_taheri@yahoo.com
true
2
SCHOOL OF MATHEMATICAL SCIENCES, ISFAHAN, UNIVERSITY OF
TECHNOLOGY, ISFAHAN 84156, IRAN.
SCHOOL OF MATHEMATICAL SCIENCES, ISFAHAN, UNIVERSITY OF
TECHNOLOGY, ISFAHAN 84156, IRAN.
SCHOOL OF MATHEMATICAL SCIENCES, ISFAHAN, UNIVERSITY OF
TECHNOLOGY, ISFAHAN 84156, IRAN.
LEAD_AUTHOR
[1] J. Bouma, Using soil survey data for qualitative land evaluation. In B.A. Stewart (Editor), Advances
1
in Soil Sciences, Vol. 9. Springer-Verlag, New York, (1989) 177-213.
2
[2] R. L. Donahue, R. W. Miller, and J. C. Shickluna, Soils, an introduction to soils and plant growth.
3
Prentice-Hall, (1983).
4
[3] K. J. Kim, H. Moskowitz, and M. Koksalan, Fuzzy versus statistical linear regression, Euro. J. Oper.
5
Res., 92 (1996) 417-434.
6
[4] B. Minasny, and A. B. McBratney, The neuro-m method for fitting neural network parametric
7
pedotransfer functions, Soil Sci. Soc. Am. J., 66 (2002) 352-361.
8
[5] A. L. Page, R. H. Miller, and D. R. Keeney, Methods of soil analysis, Part 2, Soil Science Society
9
of Ameriac, Madison, Wisconsin, (1982).
10
[6] B. Sadeghpour, and D. Gien, A goodness of fit index to reliability analysis in fuzzy model. In A.
11
Grmela (Editor), Advances in Intelligent Systems, Fuzzy Systems, Evolutionary Computation,
12
WSEAS Press, Greece, (2002).
13
[7] E. Salchow, R. Lal, N. R. Fausey, and A. Ward, Pedotransfer functions for variable alluvial soils in
14
southern Ohio, Geoderma, 73 (1996) 165-181.
15
[8] S. M. Taheri, Trends in fuzzy statistics, Austrian J. Stat., 32 (2003) 239-257.
16
[9] P. Wang, Fuzzy sets and its applications, Publishing House of Shanghai Science and Technology,
17
Shanghai, (1983).
18
[10] R. Xu, A linear regression model in fuzzy environment, Adv. Modelling Simulation, 27 (1991) 31-
19
[11] R. Xu, and C. Li , Multidimensional least-squares fitting with fuzzy model, Fuzzy Sets and Systems,
20
119 (2001) 215-223.
21
[12] H. J. Zimmermann, Fuzzy set theory and its applications, Kluwer Academic, Boston, (1991).
22
ORIGINAL_ARTICLE
FUZZY (POSITIVE, WEAK) IMPLICATIVE HYPER
BCK-IDEALS
In this note first we define the notions of fuzzy positive implicativehyper BCK-ideals of types 1,2,3 and 4. Then we prove some theorems whichcharacterize the above notions according to the level subsets. Also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperBCK-ideals and fuzzy positive implicative hyper BCK-ideals of types 5,6,7and 8. Then, we define the notions of fuzzy (weak) implicative hyper BCKidealsand we obtain some related results. Finally, by considering the productof two hyper BCK-algebras we give some theorems which show that how theprojections of a fuzzy (positive implicative, implicative) hyper BCK-ideal isagain a fuzzy (positive implicative, implicative) hyper BCK-ideal.
http://ijfs.usb.ac.ir/article_506_1cd574ace5a8a66b1d6f21e939dc2ec1.pdf
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10.22111/ijfs.2004.506
Hyper BCK-algebra
Fuzzy (strong
weak
reflexive) hyper BCKideal
Fuzzy (positive
weak) implicative hyper BCK-ideals
Mahmood
Bakhshi
mbakhshi@hamoon.usb.ac.ir
true
1
Department of Mathematics, Sistan and
Baluchestan University, Zahedan, Iran
Department of Mathematics, Sistan and
Baluchestan University, Zahedan, Iran
Department of Mathematics, Sistan and
Baluchestan University, Zahedan, Iran
LEAD_AUTHOR
Rajab Ali
Borzooei
true
2
Department of Mathematics, Sistan and
Baluchestan University, Zahedan, Iran
Department of Mathematics, Sistan and
Baluchestan University, Zahedan, Iran
Department of Mathematics, Sistan and
Baluchestan University, Zahedan, Iran
AUTHOR
Mohammad Mehdi
Zahedi
zahedi−mm@mail.uk.ac.ir
true
3
Department of Mathematics, Shahid Bahonar University
of Kerman, Kerman, Iran
Department of Mathematics, Shahid Bahonar University
of Kerman, Kerman, Iran
Department of Mathematics, Shahid Bahonar University
of Kerman, Kerman, Iran
AUTHOR
[1] R. A. Borzooei, M. Bakhshi, On positive implicative hyper BCK-ideals, Scientiae Mathematicae
1
Japonicae, Vol. 9(2003), 303-314.
2
[2] R.A. Borzooei, M. Bakhshi, Some Results on Hyper BCK-algebras, Quasigroups and Related
3
Systems, Vol.11 (2004), 9-24.
4
[3] R. A. Borzooei, M. Bakhshi, (Weak) Implicative Hyper BCK-ideals, Quasigroups and Related
5
Systems, Vol.12, to appear
6
[4] R. A. Borzooei, A. Hasankhani, M. M. Zahedi, Y. B. Jun, On hyper K-algebras, Math. Japon.,
7
Vol. 52, No.1(2000), 13-121.
8
[5] R. A. Borzooei, M. M. Zahedi, Fuzzy structures on hyper K-algebras, International Journal of
9
Uncertainty, Fuzziness and Knowledge-Based Systems, Vol. 10, No. 1(2002) 77-93.
10
[6] Y. Imai, K. Is´eki, On axiom systems of propositional calculi XIV, Proc. Japan Academy, 42
11
(1966) 19-22.
12
[7] Y. B. Jun, W. H. Shim, Fuzzy implicative hyper BCK-ideals of hyper BCK-algebras, Internat.
13
J. Math. Sci., 29 (2002), No. 2, 63-70.
14
[8] Y. B. Jun, W. H. Shim, Fuzzy structures of PI(,,)BCK-ideals in hyper BCK-algebras,
15
Internat. J. Math. Sci. (2003), No. 9, 549-556.
16
[9] Y. B. Jun, M. M. Zahedi, X. L. Xin, R. A. Borzooei, On hyper BCK-algebras, Italian Journal
17
of Pure and Applied Mathematics, No. 10 (2000), 127-136.
18
[10] Y. B. Jun, X. L. Xin, E. H. Roh, M. M. Zahedi, Strong hyper BCK-ideals of hyper BCKalgebras,
19
Mathematicae Japonicae, Vol.51, 3 (2000), 493-498.
20
[11] Y. B. Jun, X. L. Xin, Implicative hyper BCK-ideals of hyper BCK-algebras, Mathematicae
21
Japonicae, Vol. 52, No. 3, (2000), 435-443.
22
[12] Y. B. Jun, X. L. Xin, Fuzzy hyper BCK-ideals of hyper BCK-algebras, Scientiae Mathematicae
23
Japonicae, 53, No. 2(2001), 353-360.
24
[13] F. Marty, Sur une generalization de la notion de groups, 8th congress Math. Scandinaves,
25
Stockholm (1934) 45-49.
26
[14] M. M. Zahedi, M. Bakhshi, R. A. Borzooei, Fuzzy positive implicative hyper BCK-ideals of
27
types 5,6,7 and 8, Journal of Basic Science, University of Mazandaran, Vol. 2, No. 2, (2003),
28
[15] M. M. Zahedi, R. A. Borzooei, H. Rezaei, Fuzzy positive implicative hyper K-ideals of type
29
1,2,3 and 4, 9th IFSA World Congress and 20th NAFIPS 2001, July 25-28 (2001), Vancover
30
(Canada), 1210-1215.
31
ORIGINAL_ARTICLE
Persian-translation vol.1, no.2
http://ijfs.usb.ac.ir/article_3128_57612763133852cb23303b08bb744903.pdf
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10.22111/ijfs.2004.3128