University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
29
Cover Special Issue vol. 8, no. 5, October 2011-
0
EN
10.22111/ijfs.2011.2866
http://ijfs.usb.ac.ir/article_2866.html
http://ijfs.usb.ac.ir/article_2866_7c95e1e920951e2eb9a6e5bcecdb68b0.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
06
FUZZY ORDERED SETS AND DUALITY FOR FINITE FUZZY
DISTRIBUTIVE LATTICES
1
12
EN
Abdelaziz
Amroune
Department of Mathematics, M’Sila University, P.O. Box 166,
M’Sila 28000, Algeria
aamrounedz@yahoo.fr
Bijan
Davvaz
Department of Mathematics, Yazd University, Yazd, Iran
davvaz@yazduni.ac.ir
10.22111/ijfs.2011.294
The starting point of this paper is given by Priestley’s papers,
where a theory of representation of distributive lattices is presented. The purpose
of this paper is to develop a representation theory of fuzzy distributive
lattices in the finite case. In this way, some results of Priestley’s papers are
extended. In the main theorem, we show that the category of finite fuzzy
Priestley spaces is equivalent to the dual of the category of finite fuzzy distributive
lattices. Several examples are also presented.
Fuzzy ordered relation,Fuzzy ordered set,Fuzzy lattice,Fuzzy Priestley
space,Homomorphism of fuzzy lattices,Homomorphism of fuzzy Priestley spaces
http://ijfs.usb.ac.ir/article_294.html
http://ijfs.usb.ac.ir/article_294_0585ff76677fb9b648afed68597a373f.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
06
ON ALGEBRAIC AND COALGEBRAIC CATEGORIES OF
VARIETY-BASED TOPOLOGICAL SYSTEMS
13
30
EN
Sergey A.
Solovyov
Department of Mathematics, University of Latvia, Zellu iela 8,
LV-1002 Riga, Latvia and Institute of Mathematics and Computer Science, University
of Latvia, Raina bulvaris 29, LV-1459 Riga, Latvia
solovjovs@fme.vutbr.cz
10.22111/ijfs.2011.295
Motivated by the recent study on categorical properties of latticevalued
topology, the paper considers a generalization of the notion of topological
system introduced by S. Vickers, providing an algebraic and a coalgebraic
category of the new structures. As a result, the nature of the category
TopSys
of S. Vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalued)
topology can be embedded into algebra.
Algebra,(Co)algebraic category,(Co)re
ective subcategory,Latticevalued
topology,Powerset operator,S-quantale,Topological category,Topological system,Variety
http://ijfs.usb.ac.ir/article_295.html
http://ijfs.usb.ac.ir/article_295_78807b744112194d3dde64cbaf1cf650.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
06
ALGEBRAIC GENERATIONS OF SOME FUZZY POWERSET
OPERATORS
31
58
EN
Qi-Ye
Zhang
School of Mathematics and Systems Science, Beihang University, Beijing
100191, China and LMIB of the Ministry of Education, Beijing 100191, China
zhangqiye@buaa.edu.cn
10.22111/ijfs.2011.296
In this paper, let $L$ be a completeresiduated lattice, and let {bf Set} denote the category of setsand mappings, $LF$-{bf Pos} denote the category of $LF$-posets and$LF$-monotone mappings, and $LF$-{bf CSLat}$(sqcup)$, $LF$-{bfCSLat}$(sqcap)$ denote the category of $LF$-completelattices and $LF$-join-preserving mappings and the category of$LF$-complete lattices and $LF$-meet-preserving mappings, respectively. It isproved that there are adjunctions between {bf Set} and $LF$-{bf CSLat}$(sqcup)$, between $LF$-{bfPos} and $LF$-{bf CSLat}$(sqcup)$, and between $LF$-{bf Pos} and$LF$-{bf CSLat}$(sqcap)$, that is, {bf Set}$dashv LF$-{bf CSLat}$(sqcup)$, $LF$-{bfPos}$dashv LF$-{bf CSLat}$(sqcup)$, and $LF$-{bf Pos}$dashv$$LF$-{bf CSLat}$(sqcap)$. And a usual mapping $f$ generates thetraditional Zadeh forward powerset operator $f_L^rightarrow$ andthe fuzzy forward powerset operators $widetilde{f}^rightarrow,widetilde{f}_ast^rightarrow, widetilde{f}^{astrightarrow}$defined by the author et al via these adjunctions. Moreover, it is also shownthat all the fuzzy powerset operators mentioned above can be generated by the underlying algebraic theories.
Complete residuated lattice,$L$-fuzzy poset,Category,Adjunction,Algebraic theory,Powerset theory,Algebraic generation
http://ijfs.usb.ac.ir/article_296.html
http://ijfs.usb.ac.ir/article_296_80d019c2a46e66b3c7ab1031e2569b3e.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
06
NEW DIRECTION IN FUZZY TREE AUTOMATA
59
68
EN
S.
Moghari
Department of Mathematics, Science Faculty, Alzahra University,
Vanak, Tehran, Iran
s moghari@student.alzahra.ac.ir
M. M.
Zahedi
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
zahedi mm@mail.uk.ac.ir
R.
Ameri
College of Sciences, Tehran University, P.O. Box 14155-6455, Tehran, Iran
ameri@umz.ac.ir
10.22111/ijfs.2011.297
In this paper, our focus of attention is the proper propagationof fuzzy degrees in determinization of $Nondeterministic$ $Fuzzy$$Finite$ $Tree$ $Automata$ (NFFTA). Initially, two determinizationmethods are introduced which have some limitations (one inbehavior preserving and other in type of fuzzy operations). Inorder to eliminate these limitations and increasing theefficiency of FFTA, we define the notion of fuzzy complex stateand $Complex$ $FFTA$ (CFFTA). Also, we define$nabla$-normalization operation in algebra of fuzzy complexstate to solve the multi membership state problem in fuzzyautomata. Furthermore, we discuss the relationship between FFTAand CFFTA. Finally, determinization of CFFTA is presented.
Fuzzy tree automata,Complex fuzzy tree automata,Determinization
http://ijfs.usb.ac.ir/article_297.html
http://ijfs.usb.ac.ir/article_297_0c27ea3b6611895f9ba1d96628fb269a.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
06
THE CONNECTION BETWEEN SOME EQUIVALENCE
RELATIONS ON FUZZY SUBGROUPS
69
80
EN
Ali
Iranmanesh
Department of Mathematics, Tarbiat Modares University, P.O.
Box: 14115-137, Tehran, Iran
iranmana@modares.ac.ir
Hossein
Naraghi
Tarbiat Modares University, P.O. Box: 14115-137, Tehran, Iran
h.naraghi56@gmail.com
10.22111/ijfs.2011.298
This paper, deals with some equivalence relations in fuzzy subgroups.
Further the probability of commuting two fuzzy subgroups of some
finite abelian groups is defined.
Dihedral group,Equivalence relation,Fuzzy subgroups,Finite cyclic
group,p − group,Probability
http://ijfs.usb.ac.ir/article_298.html
http://ijfs.usb.ac.ir/article_298_9700a0526c25c8f4d3ca42e4af01ae3f.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
06
A NEW WAY TO FUZZY h-IDEALS OF HEMIRINGS
81
101
EN
Yunqiang
Yin
School of Sciences, East China Institute of Technology, Fuzhou,
Jiangxi 344000, China
yunqiangyin@gmail.com
Jianming
Zhan
Department of Mathematics, Hubei Institute for Nationalities, Enshi,
Hubei Province 445000, China
zhanjianming@hotmail.com
Xiaokun
Huang
Department of Mathematics, Honghe University, Mengzi, Yunnan
661100, China
boyhxk@163.com
10.22111/ijfs.2011.299
By means of a kind of new idea, we consider the $(in,ivq)$-fuzzy$h$-ideals of a hemiring. First, the concepts of $(in,ivq)$-fuzzyleft(right) $h$-ideals of a hemiring are provided and some relatedproperties are investigated. Then, a kind of quotient hemiring ofa hemiring by an $(in,ivq)$-fuzzy $h$-ideal is presented andstudied. Moreover, the notions of generalized $varphi$-compatible$(in,ivq)$-fuzzy left(right) $h$-ideals of a hemiring areintroduced and some properties of them are provided. Finally, therelationships among $(in,ivq)$-fuzzy $h$-ideals, quotienthemirings and homomorphisms are explored and several homomorphismtheorems are provided.
Hemiring,$(\in,\ivq)$-fuzzy
left(right) $h$-ideals,Generalized $\varphi$-compatible
$(\in,\ivq)$-fuzzy left(right) $h$-ideals
http://ijfs.usb.ac.ir/article_299.html
http://ijfs.usb.ac.ir/article_299_aaa3f3b3c23fef1a9e66044b328b54d2.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
06
FUZZY REFLEXIVITY OF FELBIN'S TYPE FUZZY NORMED
LINEAR SPACES AND FIXED POINT THEOREMS
IN SUCH SPACES
103
115
EN
T.
Bag
Department of Mathematics, Visva-Bharati, Santiniketan-731235, West Ben-
gal, India
tarapadavb@gmail.com
S. K.
Samanta
Department of Mathematics, Visva-Bharati, Santiniketan-731235, West
Bengal, India
syamal 123@yahoo.co.in
10.22111/ijfs.2011.300
An idea of fuzzy reexivity of Felbin's type fuzzy normed linear
spaces is introduced and its properties are studied. Concept of fuzzy uniform
normal structure is given and using the geometric properties of this concept
xed point theorems are proved in fuzzy normed linear spaces.
Fuzzy normed linear space,Fuzzy re
exive space,Fuzzy uniform
normal structure,Fixed point theorem
http://ijfs.usb.ac.ir/article_300.html
http://ijfs.usb.ac.ir/article_300_624227350b1d0dcbab964c4fb90430d5.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
06
ON FELBIN’S-TYPE FUZZY NORMED LINEAR SPACES AND
FUZZY BOUNDED OPERATORS
117
130
EN
Mohammad
Janfada
Department of Mathematics, Sabzevar Tarbiat Moallem University,
Sabzevar, Iran
mjanfada@gmail.com
Hamid
Baghani
Department of Mathematics, Semnan University, Semnan, Iran
baghani@gmail.com
Omid
Baghani
Department of Mathematics, Ferdowsi University of Mashhad, Mashhad,
Iran
omid.baghani@gmail.com
10.22111/ijfs.2011.301
In this note, we aim to present some properties of the space of all
weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator
norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness
of this space is studied. By some counterexamples, it is shown that the inverse
mapping theorem and the Banach-Steinhaus’s theorem, are not valid for
this fuzzy setting. Also finite dimensional normed fuzzy spaces are considered
briefly. Next, a Hahn-Banach theorem for weakly fuzzy bounded linear
functional with some of its applications are established.
Fuzzy analysis,Fuzzy number,Fuzzy relations
http://ijfs.usb.ac.ir/article_301.html
http://ijfs.usb.ac.ir/article_301_74ebb1ab54f2a83281a4bc5d5a3a8241.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
06
GRADUAL NORMED LINEAR SPACE
131
139
EN
I.
Sadeqi
Department of Mathematics, Sahand university of technology, Tabriz-
Iran
esadeqi@sut.ac.ir
F. Y.
Azari
Department of Mathematics, Sahand university of technology, Tabriz-
Iran
fyaqubazari@gmail.com
10.22111/ijfs.2011.302
In this paper, the gradual real numbers are considered and the
notion of the gradual normed linear space is given. Also some topological
properties of such spaces are studied, and it is shown that the gradual normed
linear space is a locally convex space, in classical sense. So the results in locally
convex spaces can be translated in gradual normed linear spaces. Finally, we
give an example of a gradual normed linear space which is not normable in
classical analysis.
Fuzzy interval,Gradual real number,Locally convex space
http://ijfs.usb.ac.ir/article_302.html
http://ijfs.usb.ac.ir/article_302_6ea1e8a077e90219b672804fb0f85ca4.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
06
$psi -$weak Contractions in Fuzzy Metric Spaces
141
148
EN
Mujahid
Abbas
Department of Mathematics, Lahore University of Management Sci-
ences, 54792- Lahore, Pakistan
mujahid@lums.edu.pk
M.
Imdad
Department of Mathematics, Aligarh Muslim University, 202002, Aligarh,
India
mhimdad@yahoo.com
D.
Gopal
Department of Mathematics and Humanities, S. V. National Institute of
Technology, Surat, 395007, Gujarat, India
gopal.dhananjay@rediffmail.com
10.22111/ijfs.2011.303
In this paper, the notion of $psi -$weak contraction cite{Rhoades} isextended to fuzzy metric spaces. The existence of common fixed points fortwo mappings is established where one mapping is $psi -$weak contractionwith respect to another mapping on a fuzzy metric space. Our resultgeneralizes a result of Gregori and Sapena cite{Gregori}.
Weekly compatible mappings,Fuzzy metric spaces,Common fixed
point,$\psi-$weak contractions
http://ijfs.usb.ac.ir/article_303.html
http://ijfs.usb.ac.ir/article_303_a705fe8411d5fcf87c600a6746d0841a.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
06
DIMENSION OF FUZZY HYPERVECTOR SPACES
149
166
EN
Reza
Ameri
School of Mathematics, Statistics and Computer Science, College of
Sciences, University of Tehran, P. O. Box 14155-6455, Teheran, Iran
rameri@ut.ac.ir
Omid Reza
Dehghan
Department of Mathematics, Faculty of Basic Sciences, University
of Bojnourd, Bojnourd, Iran
dehghan@umz.ac.ir
10.22111/ijfs.2011.304
In this paper we investigate the algebraic properties of dimension
of fuzzy hypervector spaces. Also, we prove that two isomorphic fuzzy
hypervector spaces have the same dimension.
Fuzzy hypervector space,Fuzzy linear independence,Fuzzy basis,Dimension
http://ijfs.usb.ac.ir/article_304.html
http://ijfs.usb.ac.ir/article_304_14bfdec4c43880bdbfe530d2df936bd0.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
8
5
2011
10
29
Persian-translation Special Issue vol. 8, no. 5, October 2011
169
179
EN
10.22111/ijfs.2011.2867
http://ijfs.usb.ac.ir/article_2867.html
http://ijfs.usb.ac.ir/article_2867_f04ea4312ef08393949d183a3d63641f.pdf