University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
29
Cover Vol. 7, No.2, June 2010
0
EN
10.22111/ijfs.2010.2880
http://ijfs.usb.ac.ir/article_2880.html
http://ijfs.usb.ac.ir/article_2880_b5fa2ee8d514bfd718b3763a5e9e2d54.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
05
Exact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the ABS approach
1
18
EN
Reza
Ghanbari
Department of Mathematics,
Ferdowsi University of Mashhad,
Mashhad, Iran
rghanbari@matr.um.ac.ir
Nezam
Mahdavi-Amiri
Faculty of Mathematical Sciences,
Sharif University of Technology,
Tehran, Iran
nezamm@sharif.edu
Rohollah
Yousefpour
Department of Mathematics,
Mazandaran University,
Babolsar, Iran
yosefpoor@mehr.sharif.edu
10.22111/ijfs.2010.167
We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy LR system lacks exact solutions. We show that the fuzzy LR system has an exact solution if and only if the corresponding crisp system is compatible (has a solution) and the solution of the corresponding least squares problem is equal to zero. In this case, the exact solution is determined by the solutions of the two corresponding problems. On the other hand, if the corresponding crisp system is compatible and the optimal value of the corresponding constrained least squares problem is nonzero, then we characterize approximate solutions of the fuzzy system by solution of the least squares problem. Also, we characterize solutions by defining an appropriate membership function so that an exact solution is a fuzzy LR vector having the membership function value equal to one and, when an exact solution does not exist, an approximate solution is a fuzzy LR vector with a maximal membership function value. We propose a class of algorithms based on ABS algorithm for solving the LR fuzzy systems. The proposed algorithms can also be used to solve the extended dual fuzzy linear systems. Finally, we show that, when the system has more than one solution, the proposed algorithms are flexible enough to compute special solutions of interest. Several examples are worked out to demonstrate the various possible scenarios for the solutions of fuzzy LR linear systems.
Fuzzy linear system,Fuzzy LR solution,ABS algorithm,Least squares
approximation
http://ijfs.usb.ac.ir/article_167.html
http://ijfs.usb.ac.ir/article_167_fe7dee7c3aebbf868f6740e4d0784901.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
05
Fuzzy linear regression model with crisp coefficients: A goal programming approach
1
153
EN
H
Hassanpour
Department of Mathematics,
University of Birjand,
Birjand, Iran
hhassanpur@birjand.ac.ir
H. R
Maleki
Faculty of Basic Sciences,
Shiraz University of Technology,
Shiraz, Iran
maleki@sutech.ac.ir
M. A
Yaghoobi
Department of Statistics,
Shahid Bahonar University of Kerman,
Kerman, Iran
yaghoobi@mail.uk.ac.ir
10.22111/ijfs.2010.168
The fuzzy linear regression model with fuzzy input-output data andcrisp coefficients is studied in this paper. A linear programmingmodel based on goal programming is proposed to calculate theregression coefficients. In contrast with most of the previous works, theproposed model takes into account the centers of fuzzy data as animportant feature as well as their spreads in the procedure ofconstructing the regression model. Furthermore, the model can dealwith both symmetric and non-symmetric triangular fuzzy data as wellas trapezoidal fuzzy data which have rarely been considered in theprevious works. To show the efficiency of the proposed model, somenumerical examples are solved and a simulation study is performed.The computational results are compared with some earlier methods.
Fuzzy linear regression,Goal programming,Linear programming,Fuzzy number
http://ijfs.usb.ac.ir/article_168.html
http://ijfs.usb.ac.ir/article_168_ed17b26f4193ed675c09ed1962d21f3b.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
06
FUZZY CONVEX SUBALGEBRAS OF COMMUTATIVE
RESIDUATED LATTICES
41
54
EN
Shokoofeh
Ghorbani
Department of Mathematics of Bam, Shahid Bahonar University
of Kerman, Kerman, Iran
sh.ghorbani@mail.uk.ac.ir
Abbas
Hasankhani
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
abhasan@mail.uk.ac.ir
10.22111/ijfs.2010.171
In this paper, we define the notions of fuzzy congruence relations
and fuzzy convex subalgebras on a commutative residuated lattice and we obtain
some related results. In particular, we will show that there exists a one
to one correspondence between the set of all fuzzy congruence relations and
the set of all fuzzy convex subalgebras on a commutative residuated lattice.
Then we study fuzzy convex subalgebras of an integral commutative residuated
lattice and will prove that fuzzy filters and fuzzy convex subalgebras of
an integral commutative residuated lattice coincide.
(Integral) Commutative residuated lattice,Fuzzy convex subalgebra,Fuzzy congruence relation,Fuzzy filter
http://ijfs.usb.ac.ir/article_171.html
http://ijfs.usb.ac.ir/article_171_1370a93bbd457a39fefc4b221aa47ddf.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
06
Ordered semigroups characterized by their intuitionistic fuzzy
bi-ideals
55
69
EN
Asghar
Khan
Department of Mathematics,
COMSATS Institute of IT Abbottabad, Pakistan
azhar4set@yahoo.com
Young Bae
Jun
Department of Mathematics Educations and RINS ,
Gyengsang National University ,
Chinju 660-701, Korea
skywine@gmail.com
Muhammad
Shabir
Department of Mathematics Quaid-i-Azam University,
Islamabad, Pakistan
mshabirbhatti@yahoo.co.uk
10.22111/ijfs.2010.172
Fuzzy bi-ideals play an important role in the study of ordered semigroupstructures. The purpose of this paper is to initiate and study theintiuitionistic fuzzy bi-ideals in ordered semigroups and investigate thebasic theorem of intuitionistic fuzzy bi-ideals. To provide thecharacterizations of regular ordered semigroups in terms of intuitionisticfuzzy bi-ideals and to discuss the relationships of left(resp. right andcompletely regular) ordered semigroups in terms intuitionistic fuzzybi-ideals.
Intuitionistic fuzzy sets,Intuitionistic fuzzy bi-ideals,Regular,Left (resp. right) regular ordered semigroups,Semilattices of left and right simple ordered semigroups
http://ijfs.usb.ac.ir/article_172.html
http://ijfs.usb.ac.ir/article_172_1c617c3ed60238508136f81e9795a7ac.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
06
M-FUZZIFYING DERIVED OPERATORS AND DIFFERENCE
DERIVED OPERATORS
71
81
EN
Xiu
Xin
Department of Mathematics, Tianjin University of Technology, Tianjin,300384, P.R.China
xinxiu518@163.com
Fu-Gui
Shi
Department of Mathematics, Beijing Institute of Technology, Beijing,
100081, P.R.China
fuguishi@bit.edu.cn
Sheng-Gang
Li
College of Mathematics and Information Science, Shaanxi Normal
University, Xi’an, 710062, P.R.China
shenggangli@yahoo.com.cn
10.22111/ijfs.2010.176
This paper presents characterizations of M-fuzzifying matroids bymeans of two kinds of fuzzy operators, called M-fuzzifying derived operatorsand M-fuzzifying difference derived operators.
M-fuzzifying matroid,M-fuzzifying closure operator,M-fuzzifying
derived operator,M-fuzzifying difference derived operator
http://ijfs.usb.ac.ir/article_176.html
http://ijfs.usb.ac.ir/article_176_bf29768647d8ad71714eade86704756a.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
06
LOCAL BASES WITH STRATIFIED STRUCTURE IN $I$-TOPOLOGICAL VECTOR SPACES
83
93
EN
Jin-Xuan
Fang
School of Mathematical Science,
Nanjing Normal University,
Nanjing, Jiangsu 210097,
P. R. China
jxfang@njnu.edu.cn
10.22111/ijfs.2010.177
In this paper, the concept of {sl local base with stratifiedstructure} in $I$-topological vector spaces is introduced. Weprove that every $I$-topological vector space has a balanced localbase with stratified structure. Furthermore, a newcharacterization of $I$-topological vector spaces by means of thelocal base with stratified structure is given.
$I$-topological vector spaces,$Q$-neighborhood base,$W$-neighborhood base,Local base with stratified structure
http://ijfs.usb.ac.ir/article_177.html
http://ijfs.usb.ac.ir/article_177_3e022aede8e3ab245bf67a59a25d7598.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
06
About the fuzzy grade of the direct product of two hypergroupoids
95
108
EN
Irina
Cristea
DIEA, University of Udine,
Via delle Scienze 2008, 33100 Udine, Italy
irinacri@yahoo.co.uk
10.22111/ijfs.2010.178
The aim of this paper is the study of the sequence of join spacesand fuzzy subsets associated with a hypergroupoid. In thispaper we give some properties of the membership function$widetildemu_{otimes}$ corresponding to the direct pro-duct oftwo hypergroupoids and we determine the fuzzy grade of thehypergroupoid $langle Htimes H, otimesrangle$ in a particularcase.
Fuzzy set,Hypergroup,Join space,Fuzzy grade. }
newlineindent{footnotesize This work was partially supported by the Grant no.88/2008 of the Romanian Academy
http://ijfs.usb.ac.ir/article_178.html
http://ijfs.usb.ac.ir/article_178_e94ca66d8a7055112f67e19bcab455cb.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
06
A new perspective to the Mazur-Ulam problem in $2$-fuzzy $2$-normed linear spaces
109
119
EN
Cihangir
Alaca
Department of Mathematics,
Faculty of Science and Arts, Sinop University,
57000 Sinop, Turkey
cihangiralaca@yahoo.com.tr
10.22111/ijfs.2010.179
In this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-Lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. Also, we give anew generalization of the Mazur-Ulam theorem when $X$ is a $2$-fuzzy $2$%-normed linear space or $Im (X)$ is a fuzzy $2$-normed linear space, thatis, the Mazur-Ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space is affine.
$alpha $-$2$-Norm,$2$-Fuzzy $2$-Normed linear spaces,$2$-Isometry,$2$-Lipschitz mapping
http://ijfs.usb.ac.ir/article_179.html
http://ijfs.usb.ac.ir/article_179_8adc6821d9faa0742f04eaa70deb7f43.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
06
Regular ordered semigroups and intra-regular ordered
semigroups in terms of fuzzy subsets
121
140
EN
Xiang-Yun
Xie
Department of Mathematics and Physics,
Wuyi University ,
Jiangmen, Guangdong, 529020, P.R.China
xyxie@wyu.edu.cn
Jian
Tang
Jian Tang\\
School of
Mathematics and Computational Science,
Fuyang Normal College,
Fuyang, Anhui, 236041, P.R.China
tangjian0901@126.com
10.22111/ijfs.2010.180
Let $S$ be an ordered semigroup. A fuzzy subset of $S$ is anarbitrary mapping from $S$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. In this paper, the concept of fuzzygeneralized bi-ideals of an ordered semigroup $S$ is introduced.Regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.Finally, two main theorems which characterize regular orderedsemigroups and intra-regular ordered semigroups in terms of fuzzyleft ideals, fuzzy right ideals, fuzzy bi-ideals or fuzzyquasi-ideals are given. The paper shows that one can pass fromresults in terms of fuzzy subsets in semigroups to orderedsemigroups. The corresponding results of unordered semigroups arealso obtained.
Ordered semigroup,Regular ordered semigroup,Intra-regular ordered semigroup,Fuzzy left (right) ideal,Fuzzy (generalized) bi-ideal,Fuzzy quasi-ideal
http://ijfs.usb.ac.ir/article_180.html
http://ijfs.usb.ac.ir/article_180_8923887933d3e5df3691f5dcf3db83d6.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
06
Actions, Norms, Subactions and Kernels of (Fuzzy) Norms
141
147
EN
Jeong Soon
Han
Department of Applied Mathematics,
Hanyang University ,
Ahnsan, 426-791, Korea
han@hanyang.ac.kr
Hee Sik
Kim
Department of Mathematics,
Hanyang University ,
Seoul, 133-791, Korea
heekim@hanyang.ac.kr
J
Neggers
Department of Mathematics,
University of Alabama,
Tuscaloosa, AL 35487-0350, U. S. A
jneggers@as.ua.edu
10.22111/ijfs.2010.182
In this paper, we introduce the notion of an action $Y_X$as a generalization of the notion of a module,and the notion of a norm $vt: Y_Xto F$, where $F$ is a field and $vartriangle(xy)vartriangle(y') =$ $ vartriangle(y)vartriangle(xy')$ as well as the notion of fuzzy norm, where $vt: Y_Xto [0, 1]subseteq {bf R}$, with $bf R$ the set of all real numbers. A great many standard mappings on algebraic systems can be modeled on norms as shown in the examples and it is seen that $mathrm{Ker}vt ={y|vt(y)=0}$ has many useful properties. Some are explored, especially in the discussion of fuzzy norms as they relate to the complements of subactions $N_X$ of $Y_X$.
(Fuzzy) norm,(Sub) action,Kernel
http://ijfs.usb.ac.ir/article_182.html
http://ijfs.usb.ac.ir/article_182_12583be5a7b08dcb03ed1386fea3d7d7.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
06
Fuzzy Subgroups of Rank Two Abelian p-Group
149
153
EN
S
Ngcibi
Department of Mathematics (P\&A),
University of Fort Hare,
Alice, 5700, South Africa
sngcibi@ufh.ac.za
V
Murali
Department of Mathematics (P\&A),
Rhodes University,
Grahamstown, 6140, South Africa
v.murali@ru.ac.za
B. B
Makamba
B. B. Makamba,
Department of Mathematics (P\&A),
University of Fort Hare,
Alice, 5700, South Africa
bmakamba@ufh.ac.za
10.22111/ijfs.2010.183
In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the subgroups of maximal chains in a special way which enables us to count the number of fuzzy subgroups.
Equivalence,Fuzzy subgroup,p-groups,Keychain
http://ijfs.usb.ac.ir/article_183.html
http://ijfs.usb.ac.ir/article_183_abcc8ea6ca2ad50f2a5cd5f052d2e9d5.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
7
2
2010
06
30
Persian-translation Vol. 7, No.2, June 2010
157
167
EN
10.22111/ijfs.2010.2881
http://ijfs.usb.ac.ir/article_2881.html
http://ijfs.usb.ac.ir/article_2881_decd549ebe986c38348b397fc6aa0204.pdf