eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-29
7
2
0
10.22111/ijfs.2010.2880
2880
Cover Vol. 7, No.2, June 2010
http://ijfs.usb.ac.ir/article_2880_b5fa2ee8d514bfd718b3763a5e9e2d54.pdf
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-05
7
2
1
18
10.22111/ijfs.2010.167
167
مقاله پژوهشی
Exact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the ABS approach
Reza Ghanbari
rghanbari@matr.um.ac.ir
1
Nezam Mahdavi-Amiri
nezamm@sharif.edu
2
Rohollah Yousefpour
yosefpoor@mehr.sharif.edu
3
Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran
Department of Mathematics, Mazandaran University, Babolsar, Iran
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.
http://ijfs.usb.ac.ir/article_167_fe7dee7c3aebbf868f6740e4d0784901.pdf
Fuzzy linear system
Fuzzy LR solution
ABS algorithm
Least squares
approximation
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-05
7
2
1
153
10.22111/ijfs.2010.168
168
مقاله پژوهشی
Fuzzy linear regression model with crisp coefficients: A goal programming approach
H Hassanpour
hhassanpour@birjand.ac.ir
1
H. R Maleki
maleki@sutech.ac.ir
2
M. A Yaghoobi
yaghoobi@mail.uk.ac.ir
3
Department of Mathematics,
University of Birjand,
Birjand, Iran
Faculty of Basic Sciences,
Shiraz University of Technology,
Shiraz, Iran
Department of Statistics,
Shahid Bahonar University of Kerman,
Kerman, Iran
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.
http://ijfs.usb.ac.ir/article_168_ed17b26f4193ed675c09ed1962d21f3b.pdf
Fuzzy linear regression
Goal programming
Linear programming
Fuzzy number
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-06
7
2
41
54
10.22111/ijfs.2010.171
171
مقاله پژوهشی
FUZZY CONVEX SUBALGEBRAS OF COMMUTATIVE
RESIDUATED LATTICES
Shokoofeh Ghorbani
sh.ghorbani@mail.uk.ac.ir
1
Abbas Hasankhani
abhasan@mail.uk.ac.ir
2
Department of Mathematics of Bam, Shahid Bahonar University
of Kerman, Kerman, Iran
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
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.
http://ijfs.usb.ac.ir/article_171_1370a93bbd457a39fefc4b221aa47ddf.pdf
(Integral) Commutative residuated lattice
Fuzzy convex subalgebra
Fuzzy congruence relation
Fuzzy filter
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-06
7
2
55
69
10.22111/ijfs.2010.172
172
مقاله پژوهشی
Ordered semigroups characterized by their intuitionistic fuzzy
bi-ideals
Asghar Khan
azhar4set@yahoo.com
1
Young Bae Jun
skywine@gmail.com
2
Muhammad Shabir
mshabirbhatti@yahoo.co.uk
3
Department of Mathematics,
COMSATS Institute of IT Abbottabad, Pakistan
Department of Mathematics Educations and RINS ,
Gyengsang National University ,
Chinju 660-701, Korea
Department of Mathematics Quaid-i-Azam University,
Islamabad, Pakistan
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.
http://ijfs.usb.ac.ir/article_172_1c617c3ed60238508136f81e9795a7ac.pdf
Intuitionistic fuzzy sets
Intuitionistic fuzzy bi-ideals
Regular
Left (resp. right) regular ordered semigroups
Semilattices of left and right simple ordered semigroups
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-06
7
2
71
81
10.22111/ijfs.2010.176
176
مقاله پژوهشی
M-FUZZIFYING DERIVED OPERATORS AND DIFFERENCE
DERIVED OPERATORS
Xiu Xin
xinxiu518@163.com
1
Fu-Gui Shi
fuguishi@bit.edu.cn
2
Sheng-Gang Li
shenggangli@yahoo.com.cn
3
Department of Mathematics, Tianjin University of Technology, Tianjin,300384, P.R.China
Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, P.R.China
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, P.R.China
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.
http://ijfs.usb.ac.ir/article_176_bf29768647d8ad71714eade86704756a.pdf
M-fuzzifying matroid
M-fuzzifying closure operator
M-fuzzifying
derived operator
M-fuzzifying difference derived operator
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-06
7
2
83
93
10.22111/ijfs.2010.177
177
مقاله پژوهشی
LOCAL BASES WITH STRATIFIED STRUCTURE IN $I$-TOPOLOGICAL VECTOR SPACES
Jin-Xuan Fang
jxfang@njnu.edu.cn
1
School of Mathematical Science, Nanjing Normal University, Nanjing, Jiangsu 210097, P. R. China
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.
http://ijfs.usb.ac.ir/article_177_3e022aede8e3ab245bf67a59a25d7598.pdf
$I$-topological vector spaces
$Q$-neighborhood base
$W$-neighborhood base
Local base with stratified structure
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-06
7
2
95
108
10.22111/ijfs.2010.178
178
مقاله پژوهشی
About the fuzzy grade of the direct product of two hypergroupoids
Irina Cristea
irinacri@yahoo.co.uk
1
DIEA, University of Udine, Via delle Scienze 2008, 33100 Udine, Italy
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.
http://ijfs.usb.ac.ir/article_178_e94ca66d8a7055112f67e19bcab455cb.pdf
Fuzzy set
Hypergroup
Join space
Fuzzy grade. }
newlineindent{footnotesize This work was partially supported by the Grant no.88/2008 of the Romanian Academy
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-06
7
2
109
119
10.22111/ijfs.2010.179
179
مقاله پژوهشی
A new perspective to the Mazur-Ulam problem in $2$-fuzzy $2$-normed linear spaces
Cihangir Alaca
cihangiralaca@yahoo.com.tr
1
Department of Mathematics, Faculty of Science and Arts, Sinop University, 57000 Sinop, Turkey
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.
http://ijfs.usb.ac.ir/article_179_8adc6821d9faa0742f04eaa70deb7f43.pdf
$alpha $-$2$-Norm
$2$-Fuzzy $2$-Normed linear spaces
$2$-Isometry
$2$-Lipschitz mapping
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-06
7
2
121
140
10.22111/ijfs.2010.180
180
مقاله پژوهشی
Regular ordered semigroups and intra-regular ordered
semigroups in terms of fuzzy subsets
Xiang-Yun Xie
xyxie@wyu.edu.cn
1
Jian Tang
tangjian0901@126.com
2
Department of Mathematics and Physics, Wuyi University , Jiangmen, Guangdong, 529020, P.R.China
Jian Tang\\ School of Mathematics and Computational Science, Fuyang Normal College, Fuyang, Anhui, 236041, P.R.China
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.
http://ijfs.usb.ac.ir/article_180_8923887933d3e5df3691f5dcf3db83d6.pdf
Ordered semigroup
Regular ordered semigroup
Intra-regular ordered semigroup
Fuzzy left (right) ideal
Fuzzy (generalized) bi-ideal
Fuzzy quasi-ideal
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-06
7
2
141
147
10.22111/ijfs.2010.182
182
مقاله پژوهشی
Actions, Norms, Subactions and Kernels of (Fuzzy) Norms
Jeong Soon Han
han@hanyang.ac.kr
1
Hee Sik Kim
heekim@hanyang.ac.kr
2
J Neggers
jneggers@as.ua.edu
3
Department of Applied Mathematics, Hanyang University , Ahnsan, 426-791, Korea
Department of Mathematics, Hanyang University , Seoul, 133-791, Korea
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U. S. A
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 $Y_X$.
http://ijfs.usb.ac.ir/article_182_12583be5a7b08dcb03ed1386fea3d7d7.pdf
(Fuzzy) norm
(Sub) action
Kernel
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-06
7
2
149
153
10.22111/ijfs.2010.183
183
مقاله پژوهشی
Fuzzy Subgroups of Rank Two Abelian p-Group
S Ngcibi
sngcibi@ufh.ac.za
1
V Murali
v.murali@ru.ac.za
2
B. B Makamba
bmakamba@ufh.ac.za
3
Department of Mathematics (P\&A), University of Fort Hare, Alice, 5700, South Africa
Department of Mathematics (P\&A), Rhodes University, Grahamstown, 6140, South Africa
B. B. Makamba, Department of Mathematics (P\&A), University of Fort Hare, Alice, 5700, South Africa
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.
http://ijfs.usb.ac.ir/article_183_abcc8ea6ca2ad50f2a5cd5f052d2e9d5.pdf
Equivalence
Fuzzy subgroup
p-groups
Keychain
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2010-06-30
7
2
157
167
10.22111/ijfs.2010.2881
2881
Persian-translation Vol. 7, No.2, June 2010
http://ijfs.usb.ac.ir/article_2881_decd549ebe986c38348b397fc6aa0204.pdf