2004
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A NEW FUZZY MORPHOLOGY APPROACH BASED ON THE FUZZYVALUED GENERALIZED DEMPSTERSHAFER THEORY
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In this paper, a new Fuzzy Morphology (FM) based on the GeneralizedDempsterShafer Theory (GDST) is proposed. At first, in order to clarify the similarity ofdefinitions between Mathematical Morphology (MM) and DempsterShafer 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 αcuts, making a nestedset of convex images, where each dilated image at a larger αcut is a subset of the dilatedimage at a smaller αcut. Dual statement applies to eroded images.
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SAFAR
HATAMI
SAFAR
HATAMI
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
Iran
s.hatami@ece.ut.ac.ir
BABAK N.
ARAABI
BABAK N.
ARAABI
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
Iran
araabi@ut.ac.ir
CARO
LUCAS
CARO
LUCAS
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
Iran
lucas@ipm.ir
Generalized DempsterShafer theory
Mathematical Morphology
Fuzzy Morphology
Generalized DempsterShafer Theory’s Fuzzy Morphology
[[1] B. N. Araabi, N. Kehtarnavaz and C. Lucas, Restrictions imposed by the fuzzy extension of relations##and functions, Journal of Intelligent and Fuzzy Systems, 11(1/2) (2001) 922.##[2] I. Bloch and H. Maitre, Mathematical morphology on fuzzy sets, Proc. Int. Workshop Mathematical##Morphology and its Applications to Signal Processing, Barcelona, Spain, (1993) 151156.##[3] I. Bloch and H. Maitre, Fuzzy mathematical morphologies: A comparative study, Pattern##Recognition, 28(9) (1995) 13411387.##[4] A. P. Dempster, Upper and lower probabilities induced by a multivalued mapping, Annals of##Mathematical Statistics, 38(2) (1967) 325339.##[5] C. R. Giardina and D. Sinha, Image processing using pointed fuzzy sets, Proc. VIII SPIE Conf.##Intelligent Robots and Computer Vision: Algorithms and Techniques, Philadelphia, USA, 1192##(1989) 659668.##[6] V.Goetcherian, From binary to gray tone image processing using fuzzy logic concepts, Pattern##Recognition, 12(1) (1980) 715.##[7] R. C. Gonzalez and R. E. Woods, Digital image processing, Prentice Hall, New York, USA, (2002). ##[8] M. Kauffman and M. M. Gupta, Fuzzy mathematical models in engineering and management##science, Elsevier, NorthHolland, New York, USA (1988).##[9] J. S. J. Lee, R. M. Haralick, and L. G. Shapiro, Morphologic edge detection, IEEE Transactions on##Robotics and Automation, 3(2) (1987) 142156.##[10] C. Lucas and B. N. Araabi, Generalization of the DempsterShafer theory: A fuzzyvalued measure,##IEEE Transactions on Fuzzy Systems, 7(3) (1999) 255270.##[11] P. Maragos and R. W. Schafer, Morphological filtersPart I: Their settheoretic analysis and##relations to linear shiftinvariant filters, IEEE Transactions on Acoustics, Speech, and Signal##Processing, 35(8) (1987) 11531169.##[12] P. Maragos and R. W. Schafer, Morphological filtersPart II: Their relations to median,##orderstatistics, and stack filters, IEEE Transactions on Acoustics, Speech, and Signal Processing,##35(8) (1987) 11701184.##[13] G. Matheron, Random sets and integral geometry, John Wiley, New York, USA, (1975).##[14] J. Serra, Image analysis and mathematical morphology, Academic press, London, UK, (1982).##[15] J. Serra, Introduction to mathematical morphology, Computer Vision, Graphics and Image##Processing, 35(3) (1986) 283305.##[16] G. Shafer, A mathematical theory of evidence, Princeton University Press, Princeton, USA, (1976).##[17] D. Sinha and E. R. Dougherty, A General axiomatic theory of intrinsically fuzzy mathematical##morphologies, IEEE Transactions on Fuzzy Systems, 3(4) (1995) 389403.##[18] D. Sinha and E. R. Dougherty, Fuzzy mathematical morphology, Visual Communication and Image##Representation, 3(3) (1992) 286302.##[19] D. Sinha, P. Sinha, E. R. Dougherty, and S. Batman, Design and analysis of fuzzy morphological##algorithms for image processing, IEEE Transactions on Fuzzy Systems, 5(4) (1997) 570584.##[20] R. L. Stevenson and G. R. Arce, Morphological filters: Statistics and further syntactic properties,##IEEE Transactions on Circuits and Systems, 34(11) (1987) 12921305.##[21] L. XiangJi and D. RunTao, Fuzzy morphological operators to edge enhancing of images, Proc. 4th##IEEE Int. Conf. Signal Processing, Beijing, China, 2 (1998) 10171020.##]
FUZZY GRADE OF I.P.S. HYPERGROUPS OF ORDER 7
FUZZY GRADE OF I.P.S. HYPERGROUPS OF ORDER 7
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i.p.s. hypergroups are canonical hypergroups such that$[forall(a,x),a+xni x]Longrightarrow[a+x=x].$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].
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i.p.s. hypergroups are canonical hypergroups such that$[forall(a,x),a+xni x]Longrightarrow[a+x=x].$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].
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Piergiulio
Corsini
Piergiulio
Corsini
Dipartimento di Matematica e Informatica, Via delle Scienze 206,
33100 Udine, Italy, fax: 00390432558499
Dipartimento di Matematica e Informatica,
Italy
corsini@dimi.uniud.it; corsini2002@yahoo.com
Irina
Cristea
Irina
Cristea
Faculty of Mathematics, Al.I. Cuza University, 6600 Ias¸i, Romania,
fax: 0040232201160
Faculty of Mathematics, Al.I. Cuza University,
Italy
irinacri@yahoo.co.uk
Fuzzy grade
Strong fuzzy grade
i.p.s. hypergroups
Join spaces
Whypergroups
[[1] P. Corsini, Sugli ipergruppi canonici finiti con identit`a parziali scalari, Rend. Circolo Mat.##di Palermo, Serie II, Tomo XXXVI (1987).##[2] P. Corsini, (i.p.s.) Ipergruppi di ordine 6, Ann. Sc. de l’Univ. Blaise Pascal, Clermont–Ferrand##II (1987).##[3] P. Corsini, (i.p.s.) Ipergruppi di ordine 7, Atti Sem. Mat. Fis. Univ. Modena, XXXIV##(1985–1986).##[4] P. Corsini, (i.p.s.) Hypergroups of order 8, Aviani Editore (1989) 1–106. ##[5] P. Corsini, Prolegomena of hypergroups, Aviani Editore (1993).##[6] P. Corsini, On W–hypergroups, Proceedings of I.R.B. InternationalWorkshops, New Frontiers##in Multivalued Hyperstructures, Monteroduni (1995).##[7] P. Corsini, Join spaces, power sets, fuzzy sets, Proceedings of the Fifth International Congress##on Algebraic Hyperstructures and Applications, 1993, Ia¸si, Hadronic Press (1994).##[8] P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Asian Bull. of##Math. SEAMS, 27 (2003).##[9] P. Corsini and I. Cristea, Fuzzy grade of i.p.s. hypergroups of order less or equal to 6, accepted##by PU.M.A., Budapest (2004).##[10] P. Corsini and V. Leoreanu, Join spaces associated with fuzzy sets, J. of Combinatorics,##Information and System Sciences, 20 (1) (1995).##[11] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Advances in Math.,##Kluwer Academic Publishers (2003).##[12] J. Mittas, Hypergroupes canoniques, Math. Balkanica, 2 (1972).##[13] J. Mittas, Hypergroupes canoniques, values et hypervalues. hypergroupes fortement et##sup´erieurement canoniques, Math. Balk., 8 (1978).##[14] W. Prenowitz and J. Jantosciak, Geometries and join spaces, J. reine und angewandte Math.,##257 (1972) 100–128.##[15] L. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338–353.##]
SOME QUOTIENTS ON A BCKALGEBRA GENERATED BY A
FUZZY SET
SOME QUOTIENTS ON A BCKALGEBRA GENERATED BY A
FUZZY SET
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First we show that the cosets of a fuzzy ideal μ in a BCKalgebraX form another BCKalgebra X/μ (called the fuzzy quotient BCKalgebra 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 BCKalgebra iscompatible, then P is a fuzzy quotient BCKalgebra. Finally we define thenotion of a coset of a fuzzy ideal and an element of a BCKalgebra and proverelated theorems.
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First we show that the cosets of a fuzzy ideal μ in a BCKalgebraX form another BCKalgebra X/μ (called the fuzzy quotient BCKalgebra 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 BCKalgebra iscompatible, then P is a fuzzy quotient BCKalgebra. Finally we define thenotion of a coset of a fuzzy ideal and an element of a BCKalgebra and proverelated theorems.
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Abbas
Hasankhani
Abbas
Hasankhani
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar
Iran
abhasan@mail.uk.ac.ir
Hamid
Saadat
Hamid
Saadat
Islamic Azad University Science and Research Campus, Kerman, Iran
Islamic Azad University Science and Research
Iran
saadat@iauk.ac.ir
Fuzzy similarity relations
Fuzzy partitions
Fuzzy quotient
Fuzzy ideal
Cosets
Quotient algebra
[[1] A. Hasankhani, FSpectrum of a BCKalgebra, J. Fuzzy Math. Vol. 8, No. 1 (2000), 111.##[2] V. Hohle, Quotients with respect to similarity relations, Fuzzy sets and systems 27 (1988),##[3] C. S. Hoo, Fuzzy ideal of BCI and MValgebra, Fuzzy sets and Systems 62 (1994), 111114.##[4] Y. Imai and K. Iseki, On axiom systems of propositional calculi, XIV. Proc. Jopan Academy,##42 (1966), 1922.##[5] K. Iseki, On ideals in BCKalgebra, Math. Seminar Notes, 3 (1975), Kobe University.##[6] K. Iseki, Some properties of BCKalgebra, 2 (1975), xxxv, these notes.##[7] K. Iseki and S. Tanaka, Ideal theory of BCKalgebra, Math. Japonica, 21 (1976), 351366. ##[8] K. Iseki and S. Tanaka, An introduction to the theory of BCKalgrba, Math. Japonica, 23##(1978), 126.##[9] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and Systems 8 (1982),##[10] S. Ovchinnikov, Similarity relations, fuzzy partitions, and fuzzy ordering, Fuzzy sets and##system, 40 (1991), 107126.##[11] O. Xi, Fuzzy BCKalgebra, Math. Japonica, 36 (1991), 935942.##[12] L. A. Zadeh, Similarity relations and fuzzy ordering, Inform. Sci. 3 (1971), 177200.##[13] L. A. Zadeh, Fuzzy sets, Information and control, 8 (1965), 338353.##]
PEDOMODELS FITTING WITH FUZZY LEAST
SQUARES REGRESSION
PEDOMODELS FITTING WITH FUZZY LEAST
SQUARES REGRESSION
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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.
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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.
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JAHANGARD
MOHAMMADI
JAHANGARD
MOHAMMADI
SOIL SCIENCE DEPARTMENT, COLLEGE OF AGRICULTURE,
SHAHREKORD UNIVERSITY, SHAHREKORD, IRAN.
SOIL SCIENCE DEPARTMENT, COLLEGE OF AGRICULTURE,
S
Iran
j_mohammadi@sku.ac.ir
SYED MAHMOUD
TAHERI
SYED MAHMOUD
TAHERI
SCHOOL OF MATHEMATICAL SCIENCES, ISFAHAN, UNIVERSITY OF
TECHNOLOGY, ISFAHAN 84156, IRAN.
SCHOOL OF MATHEMATICAL SCIENCES, ISFAHAN,
Iran
sm_taheri@yahoo.com
Pedomodels
Pedotransfer Functions
Fuzzy Least Squares
Fuzzy regression
[[1] J. Bouma, Using soil survey data for qualitative land evaluation. In B.A. Stewart (Editor), Advances##in Soil Sciences, Vol. 9. SpringerVerlag, New York, (1989) 177213.##[2] R. L. Donahue, R. W. Miller, and J. C. Shickluna, Soils, an introduction to soils and plant growth.##PrenticeHall, (1983).##[3] K. J. Kim, H. Moskowitz, and M. Koksalan, Fuzzy versus statistical linear regression, Euro. J. Oper.##Res., 92 (1996) 417434.##[4] B. Minasny, and A. B. McBratney, The neurom method for fitting neural network parametric##pedotransfer functions, Soil Sci. Soc. Am. J., 66 (2002) 352361.##[5] A. L. Page, R. H. Miller, and D. R. Keeney, Methods of soil analysis, Part 2, Soil Science Society##of Ameriac, Madison, Wisconsin, (1982).##[6] B. Sadeghpour, and D. Gien, A goodness of fit index to reliability analysis in fuzzy model. In A.##Grmela (Editor), Advances in Intelligent Systems, Fuzzy Systems, Evolutionary Computation,##WSEAS Press, Greece, (2002).##[7] E. Salchow, R. Lal, N. R. Fausey, and A. Ward, Pedotransfer functions for variable alluvial soils in##southern Ohio, Geoderma, 73 (1996) 165181.##[8] S. M. Taheri, Trends in fuzzy statistics, Austrian J. Stat., 32 (2003) 239257.##[9] P. Wang, Fuzzy sets and its applications, Publishing House of Shanghai Science and Technology,##Shanghai, (1983).##[10] R. Xu, A linear regression model in fuzzy environment, Adv. Modelling Simulation, 27 (1991) 31##[11] R. Xu, and C. Li , Multidimensional leastsquares fitting with fuzzy model, Fuzzy Sets and Systems,##119 (2001) 215223.##[12] H. J. Zimmermann, Fuzzy set theory and its applications, Kluwer Academic, Boston, (1991).##]
FUZZY (POSITIVE, WEAK) IMPLICATIVE HYPER
BCKIDEALS
FUZZY (POSITIVE, WEAK) IMPLICATIVE HYPER
BCKIDEALS
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In this note first we define the notions of fuzzy positive implicativehyper BCKideals 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) hyperBCKideals and fuzzy positive implicative hyper BCKideals 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 BCKalgebras we give some theorems which show that how theprojections of a fuzzy (positive implicative, implicative) hyper BCKideal isagain a fuzzy (positive implicative, implicative) hyper BCKideal.
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In this note first we define the notions of fuzzy positive implicativehyper BCKideals 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) hyperBCKideals and fuzzy positive implicative hyper BCKideals 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 BCKalgebras we give some theorems which show that how theprojections of a fuzzy (positive implicative, implicative) hyper BCKideal isagain a fuzzy (positive implicative, implicative) hyper BCKideal.
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Mahmood
Bakhshi
Mahmood
Bakhshi
Department of Mathematics, Sistan and
Baluchestan University, Zahedan, Iran
Department of Mathematics, Sistan and
Baluchestan
Iran
mbakhshi@hamoon.usb.ac.ir
Rajab Ali
Borzooei
Rajab Ali
Borzooei
Department of Mathematics, Sistan and
Baluchestan University, Zahedan, Iran
Department of Mathematics, Sistan and
Baluchestan
Iran
Mohammad Mehdi
Zahedi
Mohammad Mehdi
Zahedi
Department of Mathematics, Shahid Bahonar University
of Kerman, Kerman, Iran
Department of Mathematics, Shahid Bahonar
Iran
zahedi−mm@mail.uk.ac.ir
Hyper BCKalgebra
Fuzzy (strong
weak
reflexive) hyper BCKideal
Fuzzy (positive
weak) implicative hyper BCKideals
[[1] R. A. Borzooei, M. Bakhshi, On positive implicative hyper BCKideals, Scientiae Mathematicae##Japonicae, Vol. 9(2003), 303314.##[2] R.A. Borzooei, M. Bakhshi, Some Results on Hyper BCKalgebras, Quasigroups and Related##Systems, Vol.11 (2004), 924.##[3] R. A. Borzooei, M. Bakhshi, (Weak) Implicative Hyper BCKideals, Quasigroups and Related##Systems, Vol.12, to appear##[4] R. A. Borzooei, A. Hasankhani, M. M. Zahedi, Y. B. Jun, On hyper Kalgebras, Math. Japon.,##Vol. 52, No.1(2000), 13121.##[5] R. A. Borzooei, M. M. Zahedi, Fuzzy structures on hyper Kalgebras, International Journal of##Uncertainty, Fuzziness and KnowledgeBased Systems, Vol. 10, No. 1(2002) 7793.##[6] Y. Imai, K. Is´eki, On axiom systems of propositional calculi XIV, Proc. Japan Academy, 42##(1966) 1922.##[7] Y. B. Jun, W. H. Shim, Fuzzy implicative hyper BCKideals of hyper BCKalgebras, Internat.##J. Math. Sci., 29 (2002), No. 2, 6370.##[8] Y. B. Jun, W. H. Shim, Fuzzy structures of PI(,,)BCKideals in hyper BCKalgebras,##Internat. J. Math. Sci. (2003), No. 9, 549556.##[9] Y. B. Jun, M. M. Zahedi, X. L. Xin, R. A. Borzooei, On hyper BCKalgebras, Italian Journal##of Pure and Applied Mathematics, No. 10 (2000), 127136.##[10] Y. B. Jun, X. L. Xin, E. H. Roh, M. M. Zahedi, Strong hyper BCKideals of hyper BCKalgebras,##Mathematicae Japonicae, Vol.51, 3 (2000), 493498.##[11] Y. B. Jun, X. L. Xin, Implicative hyper BCKideals of hyper BCKalgebras, Mathematicae##Japonicae, Vol. 52, No. 3, (2000), 435443.##[12] Y. B. Jun, X. L. Xin, Fuzzy hyper BCKideals of hyper BCKalgebras, Scientiae Mathematicae##Japonicae, 53, No. 2(2001), 353360.##[13] F. Marty, Sur une generalization de la notion de groups, 8th congress Math. Scandinaves,##Stockholm (1934) 4549.##[14] M. M. Zahedi, M. Bakhshi, R. A. Borzooei, Fuzzy positive implicative hyper BCKideals of##types 5,6,7 and 8, Journal of Basic Science, University of Mazandaran, Vol. 2, No. 2, (2003),##[15] M. M. Zahedi, R. A. Borzooei, H. Rezaei, Fuzzy positive implicative hyper Kideals of type##1,2,3 and 4, 9th IFSA World Congress and 20th NAFIPS 2001, July 2528 (2001), Vancover##(Canada), 12101215.##]
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