University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
6
4
2009
12
30
Cover vol.6, no.4, December 2009
0
EN
10.22111/ijfs.2009.2893
http://ijfs.usb.ac.ir/article_2893.html
http://ijfs.usb.ac.ir/article_2893_0fa650b3a78b4af038f002c7c971f878.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
6
4
2009
12
22
PREFACE
1
1
EN
10.22111/ijfs.2009.510
http://ijfs.usb.ac.ir/article_510.html
http://ijfs.usb.ac.ir/article_510_246b0915a4bd4d8e824617b2d62f1222.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
6
4
2009
12
22
FUZZY HV -SUBSTRUCTURES IN A TWO DIMENSIONAL
EUCLIDEAN VECTOR SPACE
1
9
EN
Achilles
Dramalidis
School of Sciences of Education, Democritus University of
Thrace, 681 00 Alexandroupolis, Greece
adramali@psed.duth.gr
Thomas
Vougiouklis
School of Sciences of Education, Democritus University of
Thrace, 681 00 Alexandroupolis, Greece
tvougiou@eled.duth.gr
10.22111/ijfs.2009.512
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).
Hv-structures,Hv-group,Fuzzy sets,Fuzzy Hv-group
http://ijfs.usb.ac.ir/article_512.html
http://ijfs.usb.ac.ir/article_512_94729afa39b1eadfc3e4cce33987760e.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
6
4
2009
12
22
FUZZY PSEUDOTOPOLOGICAL HYPERGROUPOIDS
11
19
EN
Irina
Cristea
DIEA, University of Udine, Via delle Scienze 206, 33100 DIEA, University of Udine, Via delle Scienze 206, 33100 Udine, Italy, Italy
irinacri@yahoo.co.uk
Sarka
Hoskova
Department of Mathematics and Physics, University of Defence
Brno, Kounicova 65, 61200 Brno, Czech Republic
sarka.hoskova@seznam.cz
10.22111/ijfs.2009.525
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.
Hypergroupoid,(Fuzzy) pseudocontinuous hyperoperation,(Fuzzy)
continuous hyperoperation,Fuzzy topological space
http://ijfs.usb.ac.ir/article_525.html
http://ijfs.usb.ac.ir/article_525_3002cda7ac4819fff3a72f0b67c2dfe7.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
6
4
2009
12
22
FUZZY HYPERIDEALS IN TERNARY SEMIHYPERRINGS
21
36
EN
Bijan
Davvaz
Department of Mathematics, Yazd University, Yazd, Iran
davvaz@yazduni.ac.ir, bdavvaz@yahoo.com
10.22111/ijfs.2009.531
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.
Semiring,Semihyperring,Ternary semihyperring,Hyperideal,Subsemihyperring,Fuzzy set,Fuzzy hyperideal,Fuzzy bi-hyperideal
http://ijfs.usb.ac.ir/article_531.html
http://ijfs.usb.ac.ir/article_531_0053c03c8b8bdfeb9038476ff6bc0a5a.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
6
4
2009
12
22
T-FUZZY CONGRUENCES AND T-FUZZY FILTERS OF A
BL-ALGEBRA
37
47
EN
Rajab Ali
Borzooei
Department of Mathematics, Shahid Beheshti University, Tehran,
Iran
borzooei@sbu.ac.ir
Mahmood
Bakhshi
Department of Mathematics, Bojnord University, Bojnord, Iran
bakhshi@ub.ac.ir, bakhshimahmood@yahoo.com
10.22111/ijfs.2009.533
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.
T-fuzzy filter,T-fuzzy congruence
http://ijfs.usb.ac.ir/article_533.html
http://ijfs.usb.ac.ir/article_533_ef8cf353ee369065e65b7a1205e85bf2.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
6
4
2009
12
22
ON SOME STRUCTURES OF FUZZY NUMBERS
49
59
EN
Antonio
Maturo
Department of Social Sciences, University of Chieti-Pescara, via
dei Vestini, 66013, Chieti, Italia
amasturo@unich.it
10.22111/ijfs.2009.535
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.
Fuzzy numbers,Fuzzy algebraic structures,Alternative fuzzy operations,Fuzzy hyperoperations
http://ijfs.usb.ac.ir/article_535.html
http://ijfs.usb.ac.ir/article_535_cf13b5071b8e0aecbbadec9a55cf16e2.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
6
4
2009
12
22
SPECTRUM OF PRIME FUZZY HYPERIDEALS
61
72
EN
10.22111/ijfs.2009.537
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.
Commutative hyperring,Prime fuzzy hyperideals,Zariski topology
http://ijfs.usb.ac.ir/article_537.html
http://ijfs.usb.ac.ir/article_537_ef95ff018ae298cc675cf347e2e9e311.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
6
4
2009
12
22
SOME PROPERTIES OF T-FUZZY GENERALIZED SUBGROUPS
73
87
EN
Mahmood
Bakhshi
Department of Mathematics, University of Bojnord, Bojnord,
Iran
bakhshi@ub.ac.ir, bakhshimahmood@yahoo.com
Rajab Ali
Borzooei
Department of Mathematics, Shahid Beheshti University, Tehran,
Iran
borzooei@sbu.ac.ir
10.22111/ijfs.2009.542
In this paper, we deal with Molaeiās 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.
Generalized groups,Fuzzy generalized subgroups,t-norm,Heyting
algebra
http://ijfs.usb.ac.ir/article_542.html
http://ijfs.usb.ac.ir/article_542_29a3205d0a54855da6b624d09f45be58.pdf