University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
Cover Special Issue vol. 9, no. 4, October 2012--
0
EN
10.22111/ijfs.2012.2810
http://ijfs.usb.ac.ir/article_2810.html
http://ijfs.usb.ac.ir/article_2810_95ecbd1c9f5abcf931d13082bb1c90b7.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
CONVERGENCE APPROACH SPACES AND APPROACH
SPACES AS LATTICE-VALUED CONVERGENCE SPACES
1
16
EN
Gunther
Jager
Department of Statistics, Rhodes University, 6140 Grahamstown,
South Africa
g.jager@ru.ac.za
10.22111/ijfs.2012.129
We show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. Further we study the preservation of diagonal conditions, which characterize approach spaces. It is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued pretopological spaces and that the category of approach spaces is a coreective subcategory of a category of lattice-valued topological convergence spaces
L-fuzzy convergence,L-topology,L-filter,L-limit space,Approach
space,Convergence approach space,Pre-approach space
http://ijfs.usb.ac.ir/article_129.html
http://ijfs.usb.ac.ir/article_129_bd3ed7750b453af4c9a20fe2aa85c8eb.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
EFFICIENCY IN FUZZY PRODUCTION POSSIBILITY SET
17
30
EN
T.
Allahviranloo
Department of Mathematics, Science and Research Branch, Is-
lamic Azad University, Tehran, Iran
tofigh@allahviranloo.com
F.
Hosseinzadeh Lotfi
Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran
hosseinzadeh lotfi@yahoo.com
M.
AdabitabarFirozja
Department of Mathematics, Qaemshar Branch, Islamic Azad
University, Qaemshahr, Iran
mohamadsadega@yahoo.com
10.22111/ijfs.2012.130
The existing Data Envelopment Analysis models for evaluating the relative eciency of a set of decision making units by using various inputs to produce various outputs are limited to crisp data in crisp production possibility set. In this paper, rst of all the production possibility set is extended to the fuzzy production possibility set by extension principle in constant return to scale, and then the fuzzy model of Charnes, Cooper and Rhodes in input oriented is proposed so that it satis es the initial concepts with crisp data. Finally, the fuzzy model of Charnes, Cooper and Rhodes for evaluating decision making units is illustrated by solving two numerical examples.
Data Envelopment Analysis,Extension principle,Fuzzy number
http://ijfs.usb.ac.ir/article_130.html
http://ijfs.usb.ac.ir/article_130_291d4bcb1fedf08c29c53872ef51b618.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
CLASSIFYING FUZZY SUBGROUPS OF FINITE NONABELIAN
GROUPS
31
41
EN
Marius
Tarnauceanu
Faculty of Mathematics, Al.I. Cuza" University, Iasi, Romania
tarnauc@uaic.ro
10.22111/ijfs.2012.131
In this paper a rst step in classifying the fuzzy subgroups of a nite nonabelian group is made. We develop a general method to count the number of distinct fuzzy subgroups of such groups. Explicit formulas are obtained in the particular case of dihedral groups.
Fuzzy subgroups,Chains of subgroups,Maximal chains of subgroups,Dihedral groups,Recurrence relations
http://ijfs.usb.ac.ir/article_131.html
http://ijfs.usb.ac.ir/article_131_a85ac48a21fd8e1c3315ef08068da1fe.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
SOME FIXED POINT THEOREMS IN LOCALLY CONVEX
TOPOLOGY GENERATED BY FUZZY N-NORMED SPACES
43
54
EN
S. K.
Elagan
Mathematics and statistics Department, Faculty of Science, Taif Uni-
versity (P.O.888), Zip Code 21974, Kingdom of Saudi Arabia (KSA) and Department of
Mathematics, Faculty of Science, Menofiya University, Shebin Elkom, Egypt
sayed khalil2000@yahoo.com
M. R.
Segi Rahmat
School of Applied Mathematics, University of Nottingham Malaysia
Campus, Jalan Broga, 43500, Semenyih, Selangor D.E, Malaysia
Mohd.Rafi@nottingham.edu.my
10.22111/ijfs.2012.132
The main purpose of this paper is to study the existence of afixed point in locally convex topology generated by fuzzy n-normed spaces.We prove our main results, a fixed point theorem for a self mapping and acommon xed point theorem for a pair of weakly compatible mappings inlocally convex topology generated by fuzzy n-normed spaces. Also we givesome remarks in locally convex topology generated by fuzzy n-normed spaces.
Fuzzy n-normed spaces,n-seminorm,Fixed points
http://ijfs.usb.ac.ir/article_132.html
http://ijfs.usb.ac.ir/article_132_837208a7dd5fddbb57bd0b81a873f2a3.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
Fuzzy $h$-ideal of Matrix Hemiring $S_{2}=left(
begin{array}{cc}
R & Gamma
S & L
end{array}
right)$
55
70
EN
S. K.
Sardar
Department of Mathematics, Jadavpur University, Kolkata, India
sksardarjumath@gmail.com
D.
Mandal
Department of Mathematics, Jadavpur University, Kolkata, India
dmandaljumath@gmail.com
B.
Davvaz
Department of Mathematics, Yazd University, Yazd, Iran
davvaz@yazduni.ac.ir
10.22111/ijfs.2012.133
The purpose of this paper is to study matrix hemiring $S_{2}$ via fuzzy subsets and fuzzy $h$-ideals.
$Gamma$-hemiring,Fuzzy $h$-ideal,$h$-hemiregular,Matrix hemiring,Operator hemirings
http://ijfs.usb.ac.ir/article_133.html
http://ijfs.usb.ac.ir/article_133_ab7b86c21df96936081a587cc5bade03.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
ATANASSOV'S INTUITIONISTIC FUZZY GRADE OF I.P.S.
HYPERGROUPS OF ORDER LESS THAN OR EQUAL TO 6
71
97
EN
B.
Davvaz
Department of Mathematics, Yazd University, Yazd, Iran
davvaz@yazduni.ac.ir
E.
Hassani Sadrabadi
Department of Mathematics, Yazd University, Yazd, Iran
hassanipma@yahoo.com
I.
Cristea
University of Udine, Via delle Scienze 206, 33100 Udine, Italy
irinacri@yahoo.co.uk
10.22111/ijfs.2012.134
In this paper we determine the sequences of join spaces and Atanassov's intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than or equal to 6, focusing on the calculation of their lengths.
Fuzzy set,Atanassov's intuitionistic fuzzy set,i.p.s. hypergroup,Fuzzy grade,Join space
http://ijfs.usb.ac.ir/article_134.html
http://ijfs.usb.ac.ir/article_134_d4fa23b3ec49455af1d2d822746a7833.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
More General Forms of $(alpha, beta )$-fuzzy Ideals of Ordered Semigroups
99
113
EN
Yunqiang
Yin
State Key Laboratory, Breeding Base of Nuclear Resources and
Environment, East China Institute of Technology, Nanchang, 330013, China
yunqiangyin@gmail.com
Young Bae
Jun
Department of Mathematics Education (and RINS), Gyeongsang Na-
tional University, Chinju 660-701, Korea
skywine@gmail.com
Zhihui
Yang
School of Mathematics and Information Sciences, East China Institute
of Technology, Fuzhou, Jiangxi 344000, China
zhhyang75@gmail.com
10.22111/ijfs.2012.135
This paper consider the general forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. Special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related properties are investigated. Thecharacterization of regular ordered semigroups in terms of$(in_{gamma},ivq)$-fuzzy left (right) ideals,$(in_{gamma},ivq)$-fuzzy bi-ideals and$(in_{gamma},ivq)$-fuzzy interior ideals is also investigated.
Ordered
semigroups,$(\alpha,beta)$-fuzzy left (right) ideals,$(in_{gamma},ivq)$-fuzzy bi-ideals,ivq)$-fuzzy
interior ideals
http://ijfs.usb.ac.ir/article_135.html
http://ijfs.usb.ac.ir/article_135_cbe7d4b32ae35a4d34772c5395e4b648.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
L-FUZZIFYING TOPOLOGICAL GROUPS
115
132
EN
Shai-yan
Zhang
School of Science, Southern Yangtze University, Wuxi, Jiangsu
214122, People0 s Republic of China
syzhang79@126.com
Cong-hua
Yan
school of Math. Sciences, Nanjing Normal Uni-
versity, Nanjing Jiangsu 210046, People0 s Republic of China
chyan@njnu.edu.cn
10.22111/ijfs.2012.136
The main purpose of this paper is to introduce a concept of$L$-fuzzifying topological groups (here $L$ is a completelydistributive lattice) and discuss some of their basic properties andthe structures. We prove that its corresponding $L$-fuzzifyingneighborhood structure is translation invariant. A characterizationof such topological groups in terms of the corresponding$L$-fuzzifying neighborhood structure of the unit is given. It isshown that the category of $L$-fuzzifying topological groups$L$-{bf FYTPG} is topological over the category of groups {bf GRP}with respect to the forgetful functor. As an application, theconclusion that the product of $L$-fuzzifying topological groups isalso an $L$-fuzzifying topological group is proved. Finally, it isproved the forgetful functor preserves the product.
L-fuzzifying topological groups,L-fuzzifying topology,L-fuzzifying
neighborhood structure,Category
http://ijfs.usb.ac.ir/article_136.html
http://ijfs.usb.ac.ir/article_136_5aec0b42a085eb0d15775832efc7139a.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
FUZZY INTEGRAL OF MEASURABLE MULTIFUNCTIONS
133
140
EN
Anca
Croitoru
"Al.I. Cuza" University, Faculty of Mathematics, Bd. Carol I, No.
11, Iasi, 700506, Romania
croitoru@uaic.ro
10.22111/ijfs.2012.137
We study a fuzzy type integral for measurable multifunctions with respect to a fuzzy measure. Some classical properties and convergence theorems are presented.
Fuzzy integral,Fuzzy measure,Measurable multifunction
http://ijfs.usb.ac.ir/article_137.html
http://ijfs.usb.ac.ir/article_137_bae43e24655cf7f43dd488e58f3d5596.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
ON THE FUZZY DIMENSIONS OF FUZZY VECTOR SPACES
141
150
EN
Chun-E
Huang
Biochemical engineering college, Beijing Union University, Beijing
100023, P. R. China
hce 137@163.com, hchune@yahoo.com
Fu-Gui
Shi
Department of Mathematics, School of Science, Beijing Institute of
Technology, Beijing 100081, P. R. China
fuguishi@bit.edu.cn, f.g.shi@263.net
10.22111/ijfs.2012.138
In this paper, rstly, it is proved that, for a fuzzy vector space, the set of its fuzzy bases de ned by Shi and Huang, is equivalent to the family of its bases de ned by P. Lubczonok. Secondly, for two fuzzy vector spaces, it is proved that they are isomorphic if and only if they have the same fuzzy dimension, and if their fuzzy dimensions are equal, then their dimensions are the same, however, the converse is not true. Finally, fuzzy dimension of direct sum is considered, for a nite number of fuzzy vector spaces and it is proved that fuzzy dimension of their direct sum is equal to the sum of fuzzy dimensions of fuzzy vector spaces.
Fuzzy vector space,Fuzzy basis,Fuzzy dimension,Direct sum
http://ijfs.usb.ac.ir/article_138.html
http://ijfs.usb.ac.ir/article_138_f039ecb754d89261c9c1e68ef58032fc.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
ON COMPACTNESS AND G-COMPLETENESS IN FUZZY
METRIC SPACES
151
158
EN
Pedro
Tirado
Instituto Universitario de Matematica Pura y Aplicada, Universidad
Politecnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
pedtipe@mat.upv.es
10.22111/ijfs.2012.139
In [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case, for which we present an example of a compact fuzzy metric space that is not complete in Grabiecs sense. On the other hand, Grabiec used a notion of compactness to obtain a fuzzy version of Edelstein s contraction principle. We present here a generalized version of Grabiecs version of the Edelstein xed point theorem and dierent interesting facts on the topology of fuzzy metric spaces.
Fuzzy metric space,Cauchy sequence,G-completeness,Compactness,Fixed point theorem
http://ijfs.usb.ac.ir/article_139.html
http://ijfs.usb.ac.ir/article_139_bcc0473d0d21e8f848502062a387e278.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
4
2012
10
01
Persian-translation vol. 9, no. 4, October 2012
161
171
EN
10.22111/ijfs.2012.2811
http://ijfs.usb.ac.ir/article_2811.html
http://ijfs.usb.ac.ir/article_2811_1713f6a89b3a4f736a6bda87ff922381.pdf