ORIGINAL_ARTICLE
Cover vol.6, no.4, December 2009
http://ijfs.usb.ac.ir/article_2893_0fa650b3a78b4af038f002c7c971f878.pdf
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10.22111/ijfs.2009.2893
ORIGINAL_ARTICLE
PREFACE
http://ijfs.usb.ac.ir/article_510_246b0915a4bd4d8e824617b2d62f1222.pdf
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10.22111/ijfs.2009.510
ORIGINAL_ARTICLE
FUZZY HV -SUBSTRUCTURES IN A TWO DIMENSIONAL
EUCLIDEAN VECTOR SPACE
In this paper, we study fuzzy substructures in connection withHv-structures. The original idea comes from geometry, especially from thetwo dimensional Euclidean vector space. Using parameters, we obtain a largenumber of hyperstructures of the group-like or ring-like types. We connect,also, the mentioned hyperstructures with the theta-operations to obtain morestrict hyperstructures, as Hv-groups or Hv-rings (the dual ones).
http://ijfs.usb.ac.ir/article_512_94729afa39b1eadfc3e4cce33987760e.pdf
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10.22111/ijfs.2009.512
Hv-structures
Hv-group
Fuzzy sets
Fuzzy Hv-group
Achilles
Dramalidis
adramali@psed.duth.gr
true
1
School of Sciences of Education, Democritus University of
Thrace, 681 00 Alexandroupolis, Greece
School of Sciences of Education, Democritus University of
Thrace, 681 00 Alexandroupolis, Greece
School of Sciences of Education, Democritus University of
Thrace, 681 00 Alexandroupolis, Greece
AUTHOR
Thomas
Vougiouklis
tvougiou@eled.duth.gr
true
2
School of Sciences of Education, Democritus University of
Thrace, 681 00 Alexandroupolis, Greece
School of Sciences of Education, Democritus University of
Thrace, 681 00 Alexandroupolis, Greece
School of Sciences of Education, Democritus University of
Thrace, 681 00 Alexandroupolis, Greece
LEAD_AUTHOR
[1] N. Antampoufis, Hypergroups and Hb-groups in complex numbers, Proceedings of 9th AHA
1
Congress, Journal of Basic Science, Babolsar, Iran, 4(1) (2008), 17-25.
2
[2] P. Corsini and V. Leoreanu, Applications of hyperstructures theory, Kluwer Academic Publishers,
3
Boston/Dordrecht/London.
4
[3] B. Davvaz, Fuzzy Hv-groups, Fuzzy Sets and Systems, 101 (1999), 191-195.
5
[4] B. Davvaz, T-fuzzy Hv-subrings of an Hv-ring, J. Fuzzy Math., 11(1) (2003), 215-224.
6
[5] A. Dramalidis, Dual Hv-rings, Rivista di Mathematica Pura ed Applicata, 17 (1996), 55-62.
7
[6] A. Dramalidis, On some classes of Hv-structures, Italian Journal of Pure and Applied Mathematics,
8
17 (2005), 109-114.
9
[7] A. Dramalidis and T. Vougiouklis, Two fuzzy geometric-like hyperoperations defined on the
10
same set, 9th AHA, Iran, 2005.
11
[8] S. Hoskova, Binary hyperstructures determined by relational and transformation systems,
12
Habilitation thesis, Faculty of Science, University of Ostrava, (2008) 90.
13
[9] S. Hoskova and J. Chvalina, Abelizations of proximal Hv-rings using graphs of good homomorphisms
14
and diagonals of direct squares of hyperstructures, 8th AHA, Greece, (2003),
15
[10] S. Hoskova and J. Chvalina, Discrete transformation hypergroups and transformation hypergroups
16
with phase tolerance space, Discrete Mathematics, 308(18) (2008), 4133-4143.
17
[11] L. Konguetsof, Sur les hypermonoides, Bulletin de la Societe Mathematique de Belgique, t.
18
XXV, 1973.
19
[12] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
20
[13] T. Vougiouklis, The fundamental relation in hyperrings: the general hyperfield, Proc. 4th
21
AHA, World Scientific, (1991), 203-211.
22
[14] T. Vougiouklis, Hyperstructures and their representations, Monographs, Hadronic Press,
23
USA, 1994.
24
[15] T. Vougiouklis, A new class of hyperstructures, J. Comb. Inf. Syst. Sciences, 20 (1995),
25
[16] T. Vougiouklis, The @ hyperoperation, Proceedings: Structure Elements of Hyperstructures,
26
Alexandroupolis, Greece, (2005), 53-64.
27
[17] T. Vougiouklis, Hv-fields and Hv-vector spaces with @-operations, Proceedings of the 6th
28
Panhellenic Conference in Algebra and Number Theory, Thessaloniki, Greece, (2006), 95-
29
ORIGINAL_ARTICLE
FUZZY PSEUDOTOPOLOGICAL HYPERGROUPOIDS
On a hypergroupoid one can define a topology such that the hyperoperationis pseudocontinuous or continuous. In this paper we extend thisconcepts to the fuzzy case. We give a connection between the classical and thefuzzy (pseudo)continuous hyperoperations.
http://ijfs.usb.ac.ir/article_525_3002cda7ac4819fff3a72f0b67c2dfe7.pdf
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10.22111/ijfs.2009.525
Hypergroupoid
(Fuzzy) pseudocontinuous hyperoperation
(Fuzzy)
continuous hyperoperation
Fuzzy topological space
Irina
Cristea
irinacri@yahoo.co.uk
true
1
DIEA, University of Udine, Via delle Scienze 206, 33100 DIEA, University of Udine, Via delle Scienze 206, 33100 Udine, Italy, Italy
DIEA, University of Udine, Via delle Scienze 206, 33100 DIEA, University of Udine, Via delle Scienze 206, 33100 Udine, Italy, Italy
DIEA, University of Udine, Via delle Scienze 206, 33100 DIEA, University of Udine, Via delle Scienze 206, 33100 Udine, Italy, Italy
AUTHOR
Sarka
Hoskova
sarka.hoskova@seznam.cz
true
2
Department of Mathematics and Physics, University of Defence
Brno, Kounicova 65, 61200 Brno, Czech Republic
Department of Mathematics and Physics, University of Defence
Brno, Kounicova 65, 61200 Brno, Czech Republic
Department of Mathematics and Physics, University of Defence
Brno, Kounicova 65, 61200 Brno, Czech Republic
LEAD_AUTHOR
[1] R. Ameri, Topological (transposition) hypergroups, Ital. J. Pure Appl. Math., 13 (2003),
1
[2] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182-190.
2
[3] P. Corsini, Prolegomena of hypergroup theory, Aviani Editore, 1993.
3
[4] P. Corsini, Join spaces, power sets, fuzzy sets, Proc. Fifth International Congress on A.H.A.,
4
1993, Ia¸si, Romania, Hadronic Press, (1994), 45-52.
5
[5] P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Asian Bull.
6
Math., 27 (2003), 221-229.
7
[6] P. Corsini, Hyperstructures associated with fuzzy sets endowed with two membership functions,
8
J. Comb. Inform. Syst. Sci., 31 (2006), 247-254.
9
[7] P. Corsini and V. Leoreanu, Join spaces associated with fuzzy sets, J. Combin. Inform. Syst.
10
Sci., 20(1-4) (1995), 293-303
11
[8] P. Corsini and I. Tofan, On fuzzy hypergroups, Pure Math. Appl., 8 (1997), 29-37.
12
[9] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publishers,
13
Advances in Mathematics, 2003.
14
[10] I. Cristea, A property of the connection between fuzzy sets and hypergroupoids, Ital. J. Pure
15
Appl. Math., 21 (2007), 73-82.
16
[11] I. Cristea, Hyperstructures and fuzzy sets endowed with two membership functions, Fuzzy
17
Sets and Systems, 160 (2009), 1114-1124.
18
[12] I. Cristea, About the fuzzy grade of the direct product of two hypergroupoids, Iran. J. Fuzzy
19
Syst., to appear.
20
[13] B. Davvaz, Fuzzy Hv-groups, Fuzzy Sets and Systems, 101 (1999), 191-195.
21
[14] B. Davvaz, Fuzzy Hv-submodules, Fuzzy Sets and Systems, 117 (2001), 477-484.
22
[15] B. Davvaz and W. A. Dudek, Intuitionistic Hv-ideals, Int. J. Math. Math. Sci., Art. ID
23
65921, (2006), 11.
24
[16] B. Davvaz, W. A. Dudek and Y. B. Jun, Intuitionistic fuzzy Hv-submodules, Inform. Sci.,
25
176 (2006), 285-300.
26
[17] B. Davvaz, J. Zhan and K. P. Shum, Generalized fuzzy Hv-submodules endowed with interval
27
valued membership functions, Inform. Sci., 178 (2008), 3147-315.
28
[18] W. A. Dudek, J. Zhan and B. Davvaz, On intuitionistic (S, T)-fuzzy hypergroups, Soft Computing,
29
12 (2008), 1229-1238.
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32
[21] M. Ganster, D. N. Georgiou and S. Jafari, On fuzzy topological groups and fuzzy continuous
33
functions, Hacet. J. Math. Stat., 34S (2005), 45-51
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[22] S. Hoskova, Topological hypergroupoids, submitted.
35
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36
(1997), 97-19.
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[24] A. Kehagias and K. Serafimidis, The L-fuzzy Nakano hypergroup, Inform. Sci., 169 (2005),
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39
Theory, World Scientific, 9 (1997).
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43
Stockholm, (1934), 45-49.
44
[29] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
45
[30] M. S¸tef˘anescu and I. Cristea, On the fuzzy grade of hypergroups, Fuzzy Sets and Systems,
46
159(9) (2008), 1097-1106.
47
[31] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
48
[32] J. Zhan, B. Davvaz and K. P. Shum, On fuzzy isomorphism theorems of hypermodules, Soft
49
Computing, 11 (2007), 1053-1057.
50
[33] J. Zhan, B. Davvaz and K. P. Shum, A new view of fuzzy hypermodules, Acta Math. Sin.
51
(Engl. Ser.), 23(8) (2007), 1345-1356.
52
[34] J. Zhan, B. Davvaz and K. P. Shum, Isomorphism theorems of hypermodules, Acta Math.
53
Sinica (Chin. Ser.), 50(4) (2007), 909-914.
54
[35] J. Zhan, B. Davvaz and K. P. Shum, A new view of fuzzy hypernear-rings, Inform. Sci.,
55
178(2) (2008), 425-438.
56
[36] J. Zhan and W. A. Dudek, Interval valued intuitionistic (S, T)-fuzzy Hv-submodules, Acta
57
Math. Sin. (Engl. Ser.), 22 (2006), 963-970.
58
[37] J. Zhan, B. Davvaz and K. P. Shum, A new view of fuzzy hyperquasigroups, J. Intell. Fuzzy
59
Systems, 20 (2009), 147-157.
60
ORIGINAL_ARTICLE
FUZZY HYPERIDEALS IN TERNARY SEMIHYPERRINGS
In a ternary semihyperring, addition is a hyperoperation and multiplicationis a ternary operation. Indeed, the notion of ternary semihyperringsis a generalization of semirings. Our main purpose of this paper is to introducethe notions of fuzzy hyperideal and fuzzy bi-hyperideal in ternary semihyperrings.We give some characterizations of fuzzy hyperideals and investigateseveral kinds of them.
http://ijfs.usb.ac.ir/article_531_0053c03c8b8bdfeb9038476ff6bc0a5a.pdf
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10.22111/ijfs.2009.531
Semiring
Semihyperring
Ternary semihyperring
Hyperideal
Subsemihyperring
Fuzzy set
Fuzzy hyperideal
Fuzzy bi-hyperideal
Bijan
Davvaz
davvaz@yazduni.ac.ir, bdavvaz@yahoo.com
true
1
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
AUTHOR
[1] R. Ameri and H. Hedayati, On k-hyperideals of semihyperrings, J. Discrete Math. Sci. Cryptogr.,
1
10 (2007), 41-54.
2
[2] S. M. Anvariyeh and B. Davvaz, Strongly transitive geometric spaces associated to hypermodules,
3
Journal of Algebra, 322 (2009), 1340-1359.
4
[3] S. M. Anvariyeh, S. Mirvakili and B. Davvaz, - Relation on hypermodules and fundamental
5
modules over commutative fundamental rings, Communications in Algebra, 36(2) (2008),
6
[4] S. K. Bhakat and P. Das, Fuzzy subrings and ideals redefined, Fuzzy Sets and Systems, 81
7
(1996), 383-393.
8
[5] A. Chronowski, On ternary semigroups of lattice homomorphisms, Quasigroups Related Systems,
9
3 (1996), 55-72.
10
[6] A. Chronowski, Congruences on ternary semigroups, Ukrainian Math. J., 56 (2004), 662-681.
11
[7] P. Corsini, Prolegomena of hypergroup theory, Second edition, Aviani editor, 1993.
12
[8] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Advances in Mathematics,
13
Kluwer Academic Publishers, Dordrecht, 2003.
14
[9] G. Crombez, On (n,m)-rings, Abh. Math. Semin. Univ. Hamburg, 37 (1972), 180-199.
15
[10] G. Crombez and J. Timm, On (n,m)-quotient rings, Abh. Math. Semin. Univ. Hamburg, 37
16
(1972), 200-203.
17
[11] B. Davvaz, Fuzzy Hv-groups, Fuzzy Sets and Systems, 101 (1999), 191-195.
18
[12] B. Davvaz, Fuzzy Hv-submodules, Fuzzy Sets and Systems, 117 (2001), 477-484.
19
[13] B. Davvaz, Hyperideals in ternary semihyperrings, submitted.
20
[14] B. Davvaz, P. Corsini and V. Leoreanu-Fotea, Fuzzy n-ary subpolygroups, Computers &
21
Mathematics with Applications, 57 (2009), 141-152.
22
[15] B. Davvaz, P. Corsini and V. Leoreanu-Fotea, Atanassov’s intuitionistic (S, T)-fuzzy n-ary
23
subhypergroups and their properties, Information Sciences, 179 (2009), 654-666.
24
[16] B. Davvaz and V. Leoreanu, Applications of interval valued fuzzy n-ary polygroups with
25
respect to t-norms (t-conorms), Computers & Mathematics with Applications, 57 (2009),
26
1413-1424.
27
[17] B. Davvaz, J. Zhan and K. P. Shum, Generalized fuzzy Hv-ideals of Hv-rings, Int. J. General
28
Systems, 37(3) (2008), 329-346.
29
[18] B. Davvaz, J. Zhan and K. P. Shum, Generalized fuzzy Hv-submodules endowed with interval
30
valued membership functions, Information Sciences, 178(15) (2008), 3147-3159.
31
[19] B. Davvaz, Approximations in n-ary algebraic systems, Soft Computing, 12 (2008), 409-418.
32
[20] B. Davvaz, Rings derived from semihyper-rings, Algebras Groups Geom., 20 (2003), 245-252.
33
[21] B. Davvaz, Some results on congruences in semihypergroups, Bull. Malays. Math. Soc., 23(2)
34
(2000), 53-58.
35
[22] B. Davvaz and V. Leoreanu-Fotea, Hyperring theory and applications, International Academic
36
Press, USA, 2007.
37
[23] B. Davvaz and V. Leoreanu-Fotea, Binary relations on ternary semihypergroups, Communications
38
in Algebra, to appear.
39
[24] B. Davvaz and A. Salasi, A realization of hyperrings, Communications in Algebra, 34(12)
40
(2006), 4389-4400.
41
[25] B. Davvaz and T. Vougiouklis, Commutative rings obtained from hyperrings (Hv-rings) with
42
-relations, Communications in Algebra, 35(11) (2007), 3307-3320.
43
[26] B. Davvaz and T. Vougiouklis, n-Ary hypergroups, Iranian Journal of Science and Technology,
44
Transaction A, 30(A2) (2006), 165-174.
45
[27] B. Davvaz, W. A. Dudek and S. Mirvakili, Neutral elements, fundamental relations and n-ary
46
hypersemigroups, International Journal of Algebra and Computation, 19(4) (2009), 567-583.
47
[28] B. Davvaz, W. A. Dudek and T. Vougiouklis, A generalization of n-ary algebraic systems,
48
Communications in Algebra, 37 (2009), 1248-1263.
49
[29] V. N. Dixit and S. Dewan, A note on quasi and bi-ideals in ternary semigroups, Internat. J.
50
Math. & Math. Sci., 18 (1995), 501-508.
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[30] W. D¨ornte, Untersuchungen ¨uber einen verallgemeinerten Gruppenbegriff, Math. Z., 29
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(1928), 1-19.
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[31] W. A. Dudek, Idempotents in n-ary semigroups, Southeast Asian Bull. Math., 25 (2001),
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[32] W. A. Dudek On the divisibility theory in (m, n)-rings, Demonstratio Math., 14 (1981),
55
[33] T. K. Dutta and S. Kar, On regular ternary semirings, Advances in Algebra, Proceedings of
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the ICM Satellite Conference in Algebra and Related Topics, World Scientific, New Jersey,
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(2003), 343-355.
58
[34] K. Is´eki, Ideals in semirings, Proc. Japan Acad., 34 (1958), 29-31.
59
[35] E. Kasner, An extension of the group concept, Bull. Amer. Math. Soc., 10 (1904), 290-291.
60
[36] O. Kazancı, S. Yamak and B. Davvaz, The lower and upper approximations in a quotient
61
hypermodule with respect to fuzzy sets, Information Sciences, 178(10) (2008), 2349-2359.
62
[37] D. H. Lehmer, A ternary analogue of abelian groups, American J. Math., 59 (1932), 329-338.
63
[38] D. H. Lehmer, A ternary analogue of abelian groups, Amer. J. Math., 59 (1932), 329-338.
64
[39] V. Leoreanu-Fotea and B. Davvaz, Roughness in n-ary hypergroups, Information Sciences,
65
178 (2008), 4114-4124.
66
[40] V. Leoreanu-Fotea and B. Davvaz, n-hypergroups and binary relations, European Journal of
67
Combinatorics, 29 (2008), 1027-1218.
68
[41] W. G. Lister, Ternary rings, Trans. Amer. Math. Soc., 154 (1971), 37-55.
69
[42] W. J. Liu, Fuzzy Invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982),
70
[43] F. Marty, Sur une generalization de la notion de group, 8th Congress Math. Scandenaves,
71
Stockholm, (1934), 45-49.
72
[44] V. Maslov, New superposition principle for optimization problems, Sem. sur les Equations
73
avec D´eriv´ees Partielles 1985/6, Centre Math´ematique de l’Ecole Polytechnique Palaiseau,
74
esp. 24, 1986.
75
[45] S. Mirvakili and B. Davvaz, Relations on Krasner (m, n)-hyperrings, European Journal of
76
Combinatorics, to appear.
77
[46] S. Mirvakili, S. M. Anvariyeh and B. Davvaz, On -relation and transitivity conditions of ,
78
Communications in Algebra, 36 (2008), 1695-1703.
79
[47] D. Monk and F. M. Sioson, m-semigroups, semigroups, function representations, Fund.
80
Math., 59 (1966), 233-241.
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[48] A. Nakassis, Expository and survey article recent results in hyperring and hyperfield theory,
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Internat. J. Math. Math. Sci., 11 (1988), 209-220.
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[49] P. M. Pu and Y. M. Liu, Fuzzy topology I, neighborhood structure of a fuzzy point and
84
Moors-Smith convergence, J. Math. Anal., 76 (1980), 571-599.
85
[50] E. L. Post, Polyadic groups, Trans. Amer. Math. Soc., 48 (1940), 208-350.
86
[51] F. Poyatos, The Jordan-H¨older theorem for A-semimodules (Spanish), Rev. Mat. Hisp.-
87
Amer., 32(4) (1972), 251-260; ibid. 33(4) (1973) 36-48; ibid. 33(4) (1973), 122-132.
88
[52] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
89
[53] S. A. Rusakov, Some applications of n-ary group theory, Belaruskaya Navuka, Minsk, 1998.
90
[54] M. K. Sen and M. R. Adhikari, On k-ideals of semirings, Internat. J. Math. & Math. Sci.,
91
15 (1992), 347-350.
92
[55] F. M. Sioson, Ideal theory in ternary semigroups, Math. Jpn., 10 (1965), 63-84.
93
[56] T. Vougiouklis, Hyperstructures and their representations, Hadronic Press, USA, 1994.
94
[57] T. Vougiouklis, On some representations of hypergroups, Ann. Sci. Univ. Clermont-Ferrand
95
II Math., 26 (1990), 21-29.
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[58] T. Vougiouklis, The fundamental relation in hyperrings, the general hyperfield, Proc. Fourth
97
Int. Congress on Algebraic Hyperstructures and Applications (AHA 1990), World Scientific,
98
(1991), 203-211.
99
[59] X. H. Yuan, C. Zhang and Y. H. Ren, Generalized fuzzy groups and many valued applications,
100
Fuzzy Sets and Systems, 138 (2003), 205-211.
101
[60] M. M. Zahedi, M. Bolurian and A. Hasankhani, On polygroups and fuzzy subpolygroups, J.
102
Fuzzy Math., 3 (1995), 1-15.
103
ORIGINAL_ARTICLE
T-FUZZY CONGRUENCES AND T-FUZZY FILTERS OF A
BL-ALGEBRA
In this note, we introduce the concept of a fuzzy filter of a BLalgebra,with respect to a t-norm briefly, T-fuzzy filters, and give some relatedresults. In particular, we prove Representation Theorem in BL-algebras. Thenwe generalize the notion of a fuzzy congruence (in a BL-algebra) was definedby Lianzhen et al. to a new fuzzy congruence, specially with respect to a tnorm.We prove that there is a correspondence bijection between the set of allT-fuzzy filters of a BL-algebra and the set of all T-fuzzy congruences in thatBL-algebra. Next, we show how T-fuzzy filters induce T-fuzzy congruences,and construct a new BL-algebras, called quotient BL-algebras, and give somehomomorphism theorems.
http://ijfs.usb.ac.ir/article_533_ef8cf353ee369065e65b7a1205e85bf2.pdf
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10.22111/ijfs.2009.533
T-fuzzy filter
T-fuzzy congruence
Rajab Ali
Borzooei
borzooei@sbu.ac.ir
true
1
Department of Mathematics, Shahid Beheshti University, Tehran,
Iran
Department of Mathematics, Shahid Beheshti University, Tehran,
Iran
Department of Mathematics, Shahid Beheshti University, Tehran,
Iran
LEAD_AUTHOR
Mahmood
Bakhshi
bakhshi@ub.ac.ir, bakhshimahmood@yahoo.com
true
2
Department of Mathematics, Bojnord University, Bojnord, Iran
Department of Mathematics, Bojnord University, Bojnord, Iran
Department of Mathematics, Bojnord University, Bojnord, Iran
AUTHOR
[1] M. Bakhshi and R. A. Borzooei, Lattice structure of fuzzy congruence relations on a hypergroupoid,
1
Inform. Sci., 177(16) (2007), 3305-3316.
2
[2] M. Bakhshi, M. Mashinchi and R. A. Borzooei, Representation of fuzzy structures, International
3
Review of Fuzzy Mathematics, 1(1) (2006), 73-87.
4
[3] C. C. Chang, Algebraic analysis of many valued logics, Trans. Amer. Math. Soc., 88 (1958),
5
[4] P. H´ajek, Metamathematics of fuzzy logic, Klower Academic Publishers, Dordrecht, 1998.
6
[5] E. P. Klement and R. Mesiar, Logical, algebraic, analytic and probabilistic aspects of triangular
7
norms, Elsevier, Netherlands, 2005.
8
[6] L. Liu and K. Li, Fuzzy filters of BL-algebras, Inform. Sci., 173 (2005), 141-154.
9
[7] L. Liu and K. Li, Fuzzy Boolean and positive implicative filters of BL-algebras, Fuzzy Sets
10
and Systems, 152 (2005), 333-348.
11
[8] V. Murali, Fuzzy congruence relations, Fuzzy Sets and Systems., 29 (1984), 391-394.
12
[9] E. Turunen, BL-algebras and basic fuzzy logic, Mathware and Soft Computing, 6 (1999),
13
[10] E. Turunen, Boolean deductive systems of BL-algebras, Arch. Math. Logic, 40 (2001), 467-
14
ORIGINAL_ARTICLE
ON SOME STRUCTURES OF FUZZY NUMBERS
The operations in the set of fuzzy numbers are usually obtained bythe Zadeh extension principle. But these definitions can have some disadvantagesfor the applications both by an algebraic point of view and by practicalaspects. In fact the Zadeh multiplication is not distributive with respect tothe addition, the shape of fuzzy numbers is not preserved by multiplication,the indeterminateness of the sum is too increasing. Then, for the applicationsin the Natural and Social Sciences it is important to individuate some suitablevariants of the classical addition and multiplication of fuzzy numbers that havenot the previous disadvantage. Here, some possible alternatives to the Zadehoperations are studied.
http://ijfs.usb.ac.ir/article_535_cf13b5071b8e0aecbbadec9a55cf16e2.pdf
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10.22111/ijfs.2009.535
Fuzzy numbers
Fuzzy algebraic structures
Alternative fuzzy operations
Fuzzy hyperoperations
Antonio
Maturo
amasturo@unich.it
true
1
Department of Social Sciences, University of Chieti-Pescara, via
dei Vestini, 66013, Chieti, Italia
Department of Social Sciences, University of Chieti-Pescara, via
dei Vestini, 66013, Chieti, Italia
Department of Social Sciences, University of Chieti-Pescara, via
dei Vestini, 66013, Chieti, Italia
AUTHOR
[1] B. Bede and J. Fodor, Product type operations between fuzzy numbers and their applications
1
in Geology, Acta Polytechnica Hungarica, 3(1) (2006), 123-139.
2
[2] P. Corsini, Prolegomena of hypergroup theory, Aviani Editore, Tricesimo, 1993.
3
[3] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publishers,
4
Dordrecht, Hardbound, 2003.
5
[4] B. De Finetti, Theory of probability, J. Wiley, New York, 1-2 (1974).
6
[5] D. Dubois and H. Prade, Fuzzy numbers: an overview, in J. C. Bedzek and Ed. Analysis of
7
Fuzzy Information , CRC-Press, Boca Raton, 2 (1988), 3-39.
8
[6] S. Hoskova, Binary hyperstructures determined by relational and transformation systems,
9
Habilitation Thesis, Faculty of Science, University of Ostrava, (2008), 90.
10
[7] S. Hoskova and J. Chvalina, Discrete transformation hypergroups and transformation hypergroups
11
with phase tolerance space, Discrete Mathematics, 308(18) (2008), 4133-4143.
12
[8] G. Klir and B. Yuan, Fuzzy sets and fuzzy logic: theory and applications, Prentice Hall, New
13
Jersey, 1995.
14
[9] M. Mares, Weak arithmetic on fuzzy numbers, Fuzzy Sets and Systems, 91(2) (1997), 143-
15
[10] A. Maturo, Grandezze aleatorie fuzzy e loro previsioni per le decisioni in condizione di informazione
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parziale, Current Topics in Computer Sciences, Cortellini and Luchian Ed., Panfilus,
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Iasi, (2004), 15-24.
18
[11] A. Maturo, Fuzzy conditional probabilities by the subjective point of view, Advances in Mathematics
19
of Uncertainty, Tofan Ed., Performantica, Iasi, (2006), 99-108.
20
[12] A. Maturo, Fuzzy events and their probability assessments, Journal of Discrete Mathematical
21
Sciences and Cryptography, 3(1-3) (2000), 83-94.
22
[13] A. Maturo, Alternative fuzzy operations and applications to social sciences, International
23
Journal of Intelligent Systems, to appear, printed on line by Wiley, 2009.
24
[14] A. Maturo and A. Ventre, On some extensions of the de Finetti coherent prevision in a fuzzy
25
ambit, Journal of Basic Science, 4(1) (2008), 95-103.
26
[15] M. Squillante and A. G. S. Ventre, Consistency for uncertainty measure, International Journal
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of Intelligent Systems, 13 (1998), 419-430.
28
[16] M. Sugeno, Theory of fuzzy integral and its applications, Ph. D. Thesis, Tokyo, 1974.
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[17] S. Weber, Decomposable measures and integrals for archimedean t-conorms, J. Math. Anal.
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Appl., 101(1) (1984), 114-138.
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[18] R. Yager, A characterization of the extension principle, Fuzzy Sets and Systems, 18(3)
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(1986), 205-217.
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[19] L. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338-353.
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[20] L. Zadeh, Probability measures of fuzzy events, J. Math. Anal. Appl., 23 (1968), 421-427.
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[21] L. Zadeh, The concept of a linguistic variable and its application to approximate reasoning
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I, II, III, Information Sciences, 8 (1975), 199-249 and 301-357, 9 (1975), 43-80.
37
ORIGINAL_ARTICLE
SPECTRUM OF PRIME FUZZY HYPERIDEALS
Let R be a commutative hyperring with identity. We introduceand study prime fuzzy hyperideals of R. We investigate the Zariski topologyon FHspec(R), the spectrum of prime fuzzy hyperideals of R.
http://ijfs.usb.ac.ir/article_537_ef95ff018ae298cc675cf347e2e9e311.pdf
2009-12-22T11:23:20
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10.22111/ijfs.2009.537
Commutative hyperring
Prime fuzzy hyperideals
Zariski topology
[1] R. Ameri and R. Mahjoob, Prime spectrum of L-submodules, Fuzzy Sets and Systems, 159(9)
1
(2008), 1107-1115.
2
[2] R. Ameri and R. Mahjoob, Zariski topology on the spectrum of prime L-submodules, Soft
3
Computing, 12(9) (2008), 901-908.
4
[3] R. Ameri and N. Shafiiyan, Fuzzy prime and primary ideals of hyperrings, to appear.
5
[4] S. K. Bhambri, R. Kumar and P. Kumar, Fuzzy prime submodules and radical of a fuzzy
6
submodules, Bull. Cal. Math. Soc., 87 (1993), 163-168.
7
[5] P. Corsini, Prolegomena of hypergroup theory , Second Edition Aviani Editer, 1993.
8
[6] V. N. Dixit, R. Kummar and N. Ajmal, Fuzzy ideals and fuzzy prime ideals of a ring, Fuzzy
9
Sets and Systems, 44 (1991), 127-138.
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[7] J. A. Goguen, L-fuzzy sets, Journal Math. Appl., 18 (1967), 145-174.
11
[8] H. Hadji-Abadi and M. M. Zahedi, Some results on fuzzy prime spectrum of a ring, Fuzzy
12
Sets and Systems, 77 (1996), 235-240.
13
[9] R. Kumar, Fuzzy prime spectrum of a ring, Fuzzy Sets and Systems, 46 (1992), 147-154.
14
[10] R. Kumar and J. K. Kohli, Fuzzy prime spectrum of a ring II, Fuzzy Sets and Systems, 59
15
(1993), 223-230.
16
[11] H. V. Kumbhojkar, Some comments on spectrum of prime fuzzy ideals of a ring, Fuzzy Sets
17
and Systems, 85 (1997), 109-114.
18
[12] H. V. Kumbhojkar, Spectrum of prime fuzzy ideals, Fuzzy Sets and Systems, 62 (1994),
19
[13] C . P. Lu, Prime submodules of modules, Comm. Math. Univ., 33 (1987), 61-69.
20
[14] C. P. Lu, The Zariski topology on the spectrum of a modules, Houston Journal of Mathematics,
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25(3) (1999), 417-432.
22
[15] C. P. Lu, Spectra of modules, Comm. in Algebra, 23(10) (1995), 3741-3752.
23
[16] F. Marty, Su rune generalization de la notion de groupe, 8th Congress Math. Scandinaves,
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Stokholm, (1934), 45-49.
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[17] C. G. Massouros, Free and cyclic hypermodules, Annali di Matematica Pura ed Applicata, 4
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(1988), 153-166.
27
[18] R. L. McCasland, M. E. Moore and P. F. Smith, On the spectrum of modules over a commutative
28
ring, Communications in Algebra, 25(1) (1997), 79-103.
29
[19] J. N. Mordeson and D. S. Malik, Fuzzy commutative algebra, World Scientific Publishing Co.
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Pet. Ltd, 1998.
31
[20] T. K. Mukherjee and M. K. Sen, On fuzzy ideals of a ring I, Fuzzy Sets and Systems, 21
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(1987), 99-104.
33
[21] C. V. Negoita and D. A. Ralescu, Application of fuzzy systems analysis, Birkhauser, Basel,
34
[22] R. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
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[23] F. I. Sidky, On radical of fuzzy submodules and primary fuzzy submodules, Fuzzy Sets and
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Systems, 119 (2001), 419-425.
37
[24] L. A. Zadeh, Fuzzy sets, Inform and Control, 8 (1965), 338-353.
38
[25] F. Z. Pan, Fuzzy finitely generated modules, Fuzzy Sets and Systems, 21 (1987), 105-113.
39
ORIGINAL_ARTICLE
SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS
In this paper, we deal with Molaei’s generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of all T-fuzzy generalized subgroups of ageneralized group G, and the set of all T-fuzzy generalized subgroups of thecorresponding quotient generalized group. Subsequently, we study the quotientstructure of T-fuzzy generalized subgroups: we define the notion of aT-fuzzy normal generalized subgroup, give some related properties, constructthe quotient generalized group, state and prove the homomorphism theorem.Finally, we study the lattice of T-fuzzy generalized subgroups and prove thatTF(G) is a Heyting algebra.
http://ijfs.usb.ac.ir/article_542_29a3205d0a54855da6b624d09f45be58.pdf
2009-12-22T11:23:20
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10.22111/ijfs.2009.542
Generalized groups
Fuzzy generalized subgroups
t-norm
Heyting
algebra
Mahmood
Bakhshi
bakhshi@ub.ac.ir, bakhshimahmood@yahoo.com
true
1
Department of Mathematics, University of Bojnord, Bojnord,
Iran
Department of Mathematics, University of Bojnord, Bojnord,
Iran
Department of Mathematics, University of Bojnord, Bojnord,
Iran
AUTHOR
Rajab Ali
Borzooei
borzooei@sbu.ac.ir
true
2
Department of Mathematics, Shahid Beheshti University, Tehran,
Iran
Department of Mathematics, Shahid Beheshti University, Tehran,
Iran
Department of Mathematics, Shahid Beheshti University, Tehran,
Iran
LEAD_AUTHOR
[1] R. Ameri, M. Bakhshi, S. A. Nematollahzadeh and R. A. Borzooei, Fuzzy (strong) congruence
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relations on a hypergroupoid and hyper BCK-algebra, Quasigroups and Related Systems, 15
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(2007), 11-24.
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[2] J. M. Anthony and H. Sherwood, A characterization of fuzzy subgroups, Fuzzy Sets and
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Systems, 7 (1982), 297-305.
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[3] M. Bakhshi and R. A. Borzooei, Lattice structure on fuzzy congruence relations of a hypergroupoid,
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Inform. Sci., 177(16) (2007), 3305-3313.
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[4] G. Birkhoff, Lattice theory, Amer. Math. Soc., Providence, R. I., 1967.
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[5] R. A. Borzooei, M. Bakhshi and M. Mashinchi, Lattice structure on some fuzzy algebraic
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systems, Soft Computing, 12(8) (2008), 739-749.
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[6] R. A. Borzooei, G. R. Rezaei, M. R. Molaei and M. M. Zahedi, Characterization of generalized
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groups of orders 2 and 3, Pure Math. Appl., 11(4) (2000), 1-74.
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[7] E. P. Klement and R. Mesiar, Logical, algebraic, analytic and probabilistic aspects of triangular
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norms, Elsevier, Netherlands, 2005.
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[8] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Sysems, 8 (1982),
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[9] M. Mehrabi, M. R. Molaei and A. Oloomi, Generalized subgroups and homomorphisms, Arab
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(1999), 21-24.
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[11] J. N. Mordeson, K. R. Bhutani and A. Rosenfeld, Fuzzy group theory, Springer-Verlag Berlin
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Heidelberg, Netherlands, 2005.
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34 (1984), 225-239.
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USA, Florida, 2006.
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[15] E. H. Roh, B. Davvaz and K. H. Kim, T-fuzzy subhypernear-rings of hypernear-rings, Sci.
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Math. Jpn., 61(3) (2005), 535-545.
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[16] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
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[17] S. Sessa, On fuzzy subgroups and fuzzy ideals under triangular norms: short communiction,
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Fuzzy Sets and Systems, 13 (1984), 95-100.
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[18] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
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[19] J. Zhang, On properties of fuzzy hyperideals in hypernear-rings with t-norms, J. Appl. Math.
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Comput., 20 (2006), 255-277.
34