University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
5
2012
12
01
Cover Special Issue vol. 9, no. 5, December 2012 --
0
EN
10.22111/ijfs.2012.2808
http://ijfs.usb.ac.ir/article_2808.html
http://ijfs.usb.ac.ir/article_2808_826d21ec51e18d3df0a93b006f7e67a8.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
5
2014
02
20
EXTENSION OF FUZZY CONTRACTION MAPPINGS
1
6
EN
H
VOSOUGHI
Department of Mathematics, Faculty of Science, Islamshahr Branch,
Islamic Azad University, Islamshahr, Tehran, Iran
vosughi@iiau.ac.ir
S. J
Hosseini Ghoncheh
Department of mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran
10.22111/ijfs.2014.85
In a fuzzy metric space (X;M; *), where * is a continuous t-norm,a locally fuzzy contraction mapping is de ned. It is proved that any locally fuzzy contraction mapping is a global fuzzy contractive. Also, if f satis es the locally fuzzy contractivity condition then it satis es the global fuzzy contrac-tivity condition.
Fuzzy metric space,Fuzzy contraction,Fuzzy contractivity
http://ijfs.usb.ac.ir/article_85.html
http://ijfs.usb.ac.ir/article_85_de05589897c8a0532907b3e4386dff22.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
5
2012
12
26
(T,S)-BASED INTERVAL-VALUED INTUITIONISTIC FUZZY
COMPOSITION MATRIX AND ITS APPLICATION FOR
CLUSTERING
7
19
EN
H. L
HUANG
Department of Mathematics and Information Science, Zhangzhou
Normal University, Zhangzhou 363000, China
hl huang1980.student@sina.com
10.22111/ijfs.2012.101
In this paper, the notions of $(T,S)$-composition matrix and$(T,S)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(T,S)$ is a dual pair of triangular module. Theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. Furthermore, theirproperties and characterizations are presented. Then a new methodbased on $tilde{alpha}-$matrix for clustering is developed.Finally, an example is given to demonstrate our method.
Clustering,Interval-valued intuitionistic fuzzy set,Interval-valued
intuitionistic fuzzy number,Interval-valued intuitionistic fuzzy matrix,Triangular dual module
http://ijfs.usb.ac.ir/article_101.html
http://ijfs.usb.ac.ir/article_101_ed10b9c13fc14775b97c1a61deea60cc.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
5
2012
12
28
A FIXED POINT APPROACH TO THE INTUITIONISTIC
FUZZY STABILITY OF QUINTIC AND SEXTIC
FUNCTIONAL EQUATIONS
21
40
EN
Tian Zhou
Xu
School of Mathematics, Beijing Institute of Technology, Beijing
100081, People's Republic of China
xutianzhou@bit.edu.cn
Matina John
Rassias
Department of Statistical, University College London, Science
1-19 Torrington Place, London WC1E 7HB, United Kingdom
matina@stats.ucl.ac.uk
Wan
Xin Xu
Department of Electrical and Computer Engineering, College of En-
gineering, University of Kentucky, Lexington 40506, Usa and School of Communica-
tion and Information Engineering, University of Electronic Science and Technology
of China
wxbit0930@gmail.com
10.22111/ijfs.2012.102
The fixed point alternative methods are implemented to giveHyers-Ulam stability for the quintic functional equation $ f(x+3y)- 5f(x+2y) + 10 f(x+y)- 10f(x)+ 5f(x-y) - f(x-2y) = 120f(y)$ and thesextic functional equation $f(x+3y) - 6f(x+2y) + 15 f(x+y)- 20f(x)+15f(x-y) - 6f(x-2y)+f(x-3y) = 720f(y)$ in the setting ofintuitionistic fuzzy normed spaces (IFN-spaces). This methodintroduces a metrical context and shows that the stability isrelated to some fixed point of a suitable operator. Furthermore, theinterdisciplinary relation among the fuzzy set theory, the theoryof intuitionistic spaces and the theory of functional equations arealso presented in the paper.
http://ijfs.usb.ac.ir/article_102.html
http://ijfs.usb.ac.ir/article_102_8ee321bf3524ad5d9b61a7ebca651dc9.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
5
2012
12
28
ON (L;M)-FUZZY CLOSURE SPACES
41
62
EN
Halis
Aygun
Department of Mathematics, Kocaeli University, 41380, Kocaeli, Turkey.
halis@kocaeli.edu.tr
Vildan
Cetkin
Department of Mathematics, Kocaeli University, 41380, Kocaeli,
Turkey.
vildan.cetkin@kocaeli.edu.tr
S. E.
Abbas
Department of Mathematics, Faculty of Science, Sohag 82524, Egypt.
sabbas73@yahoo.com
10.22111/ijfs.2012.103
The aim of this paper is to introduce $(L,M)$-fuzzy closurestructure where $L$ and $M$ are strictly two-sided, commutativequantales. Firstly, we define $(L,M)$-fuzzy closure spaces and getsome relations between $(L,M)$-double fuzzy topological spaces and$(L,M)$-fuzzy closure spaces. Then, we introduce initial$(L,M)$-fuzzy closure structures and we prove that the category$(L,M)$-{bf FC} of $(L,M)$-fuzzy closure spaces and$(L,M)$-$mathcal{C}$-maps is a topological category over thecategory {bf SET}. From this fact, we define products of$(L,M)$-fuzzy closure spaces. Finally, we show that an initialstructure of $(L,M)$-double fuzzy topological spaces can be obtainedby the initial structure of $(L,M)$-fuzzy closure spaces induced bythem.
Double fuzzy topological space,Fuzzy closure space,Initial fuzzy
closure space
http://ijfs.usb.ac.ir/article_103.html
http://ijfs.usb.ac.ir/article_103_536f9823347996d1b8deb9dee5ec4124.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
5
2012
12
28
A NOTE ON INTUITIONISTIC FUZZY MAPPINGS
63
76
EN
Yong-hong
Shen
School of Mathematics and Statistics, Tianshui Normal Univer-
sity, Tianshui 741001, People's Republic of China
shenyonghong2008@hotmail.com
Fa-xing
Wang
Tongda College, Nanjing University of Posts and Telecommunica-
tions, Nanjing, 210046, People's Republic of China
fxwangcaptain@126.com
Wei
Chen
School of Information, Capital University of Economics and Business,
Beijing, 100070, People's Republic of China
chenwei@cueb.edu.cn
10.22111/ijfs.2012.104
In this paper, the concept of intuitionistic fuzzy mapping as a generalization of fuzzy mapping is presented, and its' relationship with intuitionistic fuzzy relations is derived. Moreover, some basicoperations of intuitionistic fuzzy mappings are defined, hence we can conclude that all of intuitionistic fuzzy mappings constitute a soft algebrawith respect to these operations. Afterwards, the Atanassov'soperator is applied to intuitionistic fuzzy mappings and thecorresponding properties are examined. Finally, the decompositionand representation theorems of intuitionistic fuzzy mappings areestablished.
Truncation projection,Intuitionistic fuzzy mapping,Truncation map-
ping,Decomposition theorem,Representation theorem
http://ijfs.usb.ac.ir/article_104.html
http://ijfs.usb.ac.ir/article_104_b8eee8be1022c4052be689163c79088f.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
5
2012
12
28
COMMON FIXED POINT THEOREMS IN MODIFIED
INTUITIONISTIC FUZZY METRIC SPACES
77
92
EN
M.
Imdad
Department of Mathematics, Aligarh Muslim University, Aligarh 202002,
India
mhimdad@yahoo.co.in
Javid
Ali
Departament de Matematica Aplicada III (MA3), Universitat Politecnica
de Catalunya, Colom 1, 08222 Terrassa (Barcelona), Spain
javid@math.com
M.
Hasan
Department of Applied Mathematics, Aligarh Muslim University, Aligarh
202002, India
hasan352000@gmail.com
10.22111/ijfs.2012.105
In this paper, we introduce a new class of implicit functions and also common property (E.A) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. We are not aware of any paper dealing with such implicit functions in modified intuitionistic fuzzy metric spaces.
Fuzzy metric space,Modied intuitionistic fuzzy metric space,Prop-
erty (E.A),Common property (E.A)
http://ijfs.usb.ac.ir/article_105.html
http://ijfs.usb.ac.ir/article_105_c515b1a8b53ad4410978aa4136bf1270.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
5
2012
12
28
ON LOCAL BOUNDEDNESS OF I-TOPOLOGICAL
VECTOR SPACES
93
104
EN
Jin-Xuan
Fang
School of Mathematical Science, Nanjing Normal University, Nan-
jing, Jiangsu 210023, P. R. China
jxfang@njnu.edu.cn
Hui
Zhang
Department of Mathematics, Anhui NormalUniversity, Wuhu, Anhui 241000,
P. R. China
zh9907084@sohu.com
10.22111/ijfs.2012.106
The notion of generalized locally bounded $I$-topological vectorspaces is introduced. Some of their important properties arestudied. The relationship between this kind of spaces and thelocally bounded $I$-topological vector spaces introduced by Wu andFang [Boundedness and locally bounded fuzzy topological vectorspaces, Fuzzy Math. 5 (4) (1985) 87$-$94] is discussed. Moreover, wealso use the family of generalized fuzzy quasi-norms to characterizethe generalized locally bounded $I$-topological vector spaces, andgive some applications of this characterization.
I-topological vector spaces,Generalized locally bounded I-topological
vector spaces,Family of generalized fuzzy quasi-norms
http://ijfs.usb.ac.ir/article_106.html
http://ijfs.usb.ac.ir/article_106_be86b18ee0bf485a237b60562493a9cb.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
5
2012
12
28
NEW TYPES OF FUZZY n-ARY SUBHYPERGROUPS OF AN
n-ARY HYPERGROUP
105
124
EN
Yunqiang
Yin
College of Mathematics and Information Sciences, East China Insti-
tute of Technology, Fuzhou, Jiangxi 344000, China
yinyunqiang@126.com
Jianming
Zhan
Department of Mathematics, Hubei Institute for Nationalities, Enshi,
Hubei Province 445000, China
zhanjianming@hotmail.com
Bijan
Davvaz
Department of Mathematics, Yazd University, Yazd, Iran
davvaz@yazduni.ac.ir
10.22111/ijfs.2012.107
In this paper, the new notions of ``belongingness ($in_{gamma}$)"and ``quasi-coincidence ($q_delta$)" of a fuzzy point with a fuzzyset are introduced. By means of this new idea, the concept of$(alpha,beta)$-fuzzy $n$-ary subhypergroup of an $n$-aryhypergroup is given, where $alpha,betain{in_{gamma}, q_{delta},in_{gamma}wedge q_{delta}, ivq}$, andit is shown that, in 16 kinds of $(alpha,beta)$-fuzzy $n$-arysubhypergroups, the significant ones are the$(in_{gamma},in_{gamma})$-fuzzy $n$-ary subhypergroups,$(in_{gamma},ivq)$-fuzzy $n$-ary subhypergroups and the$(in_{gamma}wedge q_{delta},in_{gamma})$-fuzzy $n$-arysubhypergroups.
n-ary subhypergroup,$(\in_{\gamma},in_{gamma})$-fuzzy $n$-ary subhypergroups,ivq)$-fuzzy $n$-ary subhypergroups and the
$(in_{gamma}wedge q_{delta},in_{gamma})$-fuzzy $n$-ary
subhypergroups
http://ijfs.usb.ac.ir/article_107.html
http://ijfs.usb.ac.ir/article_107_46055ab13bf60c1e2bce3c93b56e5935.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
5
2012
12
28
MIXED VARIATIONAL INCLUSIONS INVOLVING INFINITE
FAMILY OF FUZZY MAPPINGS
125
135
EN
R.
Ahmad
Department of Mathematics, Aligarh Muslim University, Aligarh 202002,
India
raisain 123@rediffmail.com
M.
Dilshad
Department of Mathematics, Aligarh Muslim University, Aligarh 202002,
India
mdilshaad@gmail.com
J. C.
YAO
Center for General Education, Kaohsiung Medical University, Kaohsiung
807, Taiwan
yaojc@kmu.edu.tw
10.22111/ijfs.2012.108
In this paper, we introduce and study a mixed variational inclusion problem involving infinite family of fuzzy mappings. An iterative algorithm is constructed for solving a mixed variational inclusion problem involving infinite family of fuzzy mappings and the convergence of iterative sequences generated by the proposed algorithm is proved. Some illustrative examples are also given.
Mixed variational inclusions,Innite family,Fuzzy mappings,Algo-
rithm
http://ijfs.usb.ac.ir/article_108.html
http://ijfs.usb.ac.ir/article_108_94216fc2ba0c05bf29a5f76466376555.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
5
2012
12
28
SOME RESULTS ON t-BEST APPROXIMATION IN FUZZY
n-NORMED SPACES
137
146
EN
Serkan
Gumus
Turkish Military Academy, Cankaya, 06580, Ankara, Turkey
sgumus@kho.edu.tr, serkangumus06@yahoo.com
Hakan
Efe
Department of Mathematics, Faculty of Science and Arts, Gazi University,
Teknikokullar, 06500 Ankara, Turkey
hakanefe@gazi.edu.tr, hakanefe1972@yahoo.com.tr
Cemil
Yildiz
Department of Mathematics, Faculty of Science and Arts, Gazi University,
Teknikokullar, 06500 Ankara, Turkey
cyildiz@gazi.edu.tr
10.22111/ijfs.2012.109
The aim of this paper is to give the set of all t -best approximations on fuzzy n-normed spaces and prove some theorems in the sense of Vaezpour and Karimi [13].
n-normed spaces,Fuzzy n-norms,Best approximation.
2000 Mathematics Subject Classication. 46A30,46A70,54A40
http://ijfs.usb.ac.ir/article_109.html
http://ijfs.usb.ac.ir/article_109_7a1b1b483a2916fff5e951fc17b9cfef.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
9
5
2012
12
01
Persian-translation vol. 9, no. 5, December 2012
149
158
EN
10.22111/ijfs.2012.2809
http://ijfs.usb.ac.ir/article_2809.html
http://ijfs.usb.ac.ir/article_2809_fed88bc5fe03e6c7cedb889296a30126.pdf