University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
03
01
Cover vol. 14, no. 1, February 2017
0
EN
10.22111/ijfs.2017.3088
http://ijfs.usb.ac.ir/article_3088.html
http://ijfs.usb.ac.ir/article_3088_dd2a325fd028a1ecba3efff967ef6955.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
02
28
Group Generalized Interval-valued Intuitionistic Fuzzy Soft Sets and Their Applications in\ Decision Making
1
21
EN
Hua
Wu
Key Laboratory of Ultrafast Photoelectric Diagnostics Technology,
Xi'an Institute of Optics and Precision Mechanics of Chinese Academy of Sciences, Xi'an, China and University of Chinese Academy of Sciences, Beijing, China.
sunshinesmilewh@gmail.com
Xiuqin
Su
Key Laboratory of Ultrafast Photoelectric Diagnostics Technology,
Xi'an Institute of Optics and Precision Mechanics of Chinese Academy of Sciences, Xi'an, China
suxiuqin@opt.ac.cn
10.22111/ijfs.2017.3034
Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decision-making preference. Hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (G-GIVIFSS) which contains the basic description by interval-valued intuitionistic fuzzy soft set (IVIFSS) on the alternatives and a group of experts' evaluation of it. It contributes the following threefold: 1) A generalized interval-valued intuitionistic fuzzy soft set (GIVIFSS) is proposed by introducing an interval-valued intuitionistic fuzzy parameter, which reflects a new and senior expert's opinion on the basic description. The operations, properties and aggregation operators of GIVIFSS are discussed. 2) Based on GIVIFSS, a G-GIVIFSS is then proposed to reduce the impact of decision-making preference by introducing more parameters by a group of experts. Its important operations, properties and the weighted averaging operator are also defined. 3) A multi-attribute group decision making model based on G-GIVIFSS weighted averaging operator is built to solve the group decision making problems in the more universal IVIF environment, and two practical examples are taken to validate the efficiency and effectiveness of the proposed model.
Group decision making,Interval-valued intuitionistic fuzzy set,Generalized interval-valued intuitionistic fuzzy soft set,Soft set
http://ijfs.usb.ac.ir/article_3034.html
http://ijfs.usb.ac.ir/article_3034_c764374b831ad45afb14a759482b14ed.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
02
28
Soft Computing Based on a Modified MCDM Approach under Intuitionistic Fuzzy Sets
23
41
EN
M. R.
Shahriari
Faculty of Management, South Tehran Branch, Islamic Azad University, Tehran, Iran
10.22111/ijfs.2017.3035
The current study set to extend a new VIKOR method as a compromise ranking approach to solve multiple criteria decision-making (MCDM) problems through intuitionistic fuzzy analysis. Using compromise method in MCDM problems contributes to the selection of an alternative as close as possible to the positive ideal solution and far away from the negative ideal solution, concurrently. Using Atanassov intuitionistic fuzzy sets (A-IFSs) may simultaneously express the degree of membership and non-membership to decision makers (DMs) to describe uncertain situations in decision-making problems. The proposed intuitionistic fuzzy VIKOR indicates the degree of satisfaction and dissatisfaction of each alternative with respect to each criterion and the relative importance of each criterion, respectively, by degrees of membership and non-membership. Thus, the ratings for the importance of criteria, DMs, and alternatives are in linguistic variables and expressed in intuitionistic fuzzy numbers. Using IFS aggregation operators and with respect to subjective judgment and objective information, the most suitable alternative is indicated among potential alternatives. Moreover, practical examples illustrate the procedure of the proposed method.
Multiple criteria decision making (MCDM),Decision makers (DMs),Atanassov intuitionistic fuzzy sets (A-IFSs),Intuitionistic fuzzy numbers
http://ijfs.usb.ac.ir/article_3035.html
http://ijfs.usb.ac.ir/article_3035_56c511a22322a3f72ffb46e35bb130df.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
02
28
Support vector regression with random output variable and probabilistic constraints
43
60
EN
Maryam
Abaszade
Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran
Sohrab
Effati
Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
s-effati.profcms@um.ac.ir
10.22111/ijfs.2017.3036
Support Vector Regression (SVR) solves regression problems based on the concept of Support Vector Machine (SVM). In this paper, a new model of SVR with probabilistic constraints is proposed that any of output data and bias are considered the random variables with uniform probability functions. Using the new proposed method, the optimal hyperplane regression can be obtained by solving a quadratic optimization problem. The proposedmethod is illustrated by several simulated data and real data sets for both models (linear and nonlinear) with probabilistic constraints.
Probabilistic constraints,Support Vector Machine,Support Vector Regression,Quadratic programming,Probability function,Monte Carlo simulation
http://ijfs.usb.ac.ir/article_3036.html
http://ijfs.usb.ac.ir/article_3036_7fa269af1f035bda8d625aada763cf7a.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
02
28
A Tauberian theorem for $(C,1,1)$ summable double sequences of fuzzy numbers
61
75
EN
Ibrahim
Canak
Department of Mathematics, Ege University, 35100, Izmir, Turkey
ibrahimcanak@yahoo.com
Umit
Totur
Department of Mathematics, Adnan Menderes University, 09100, Aydin,
Turkey
utotur@adu.edu.tr
Zerrin
Onder
Department of Mathematics, Ege University, 35100, Izmir, Turkey
zerrin.onder11@gmail.com
10.22111/ijfs.2017.3037
In this paper, we determine necessary and sufficient Tauberian conditions under which convergence in Pringsheim's sense of a double sequence of fuzzy numbers follows from its $(C,1,1)$ summability. These conditions are satisfied if the double sequence of fuzzy numbers is slowly oscillating in different senses. We also construct some interesting double sequences of fuzzy numbers.
Fuzzy numbers,Double sequences,Slow oscillation,Summability $(C,1,1)$,Tauberian theorems
http://ijfs.usb.ac.ir/article_3037.html
http://ijfs.usb.ac.ir/article_3037_e93bbd0f6b9452e82d1a57a8403f41d7.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
02
28
Some topological properties of spectrum of fuzzy submodules
77
87
EN
R.
Ameri
School of Mathematics, Statistics and Computer Science, College of
Sciences, University of Tehran, Teheran, Iran
rez_ameri@yahoo.com
R.
Mahjoob
Department of Mathematics, Semnan University, Semnan, Iran
ra−mahjoob@yahoo.com
10.22111/ijfs.2017.3038
Let $R$ be a commutative ring with identity and $M$ be an$R$-module. Let $FSpec(M)$ denotes the collection of all prime fuzzysubmodules of $M$. In this regards some basic properties of Zariskitopology on $FSpec(M)$ are investigated. In particular, we provesome equivalent conditions for irreducible subsets of thistopological space and it is shown under certain conditions$FSpec(M)$ is a $T_0-$space or Hausdorff.
Fuzzy prime submodule,Fuzzy prime spectrum,Zariski topology,Irreducible subset
http://ijfs.usb.ac.ir/article_3038.html
http://ijfs.usb.ac.ir/article_3038_cf0537ee7303573d6949705f2d57737a.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
02
28
ON LOCAL HUDETZ g-ENTROPY
89
97
EN
M.
Rahimi
Department of Mathematics, Faculty of Science, University of Qom, Qom,
Iran
m10.rahimi@gmail.com
10.22111/ijfs.2017.3041
In this paper, a local approach to the concept of Hudetz $g$-entropy is presented. The introduced concept is stated in terms of Hudetz $g$-entropy. This representation is based on the concept of $g$-ergodic decomposition which is a result of the Choquet's representation Theorem for compact convex metrizable subsets of locally convex spaces.
$g$-entropy,$g$-ergodic decomposision,Hudetz correction
http://ijfs.usb.ac.ir/article_3041.html
http://ijfs.usb.ac.ir/article_3041_ca853dd5bb21099ad707b1cc56ee9624.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
02
28
Probabilistic Normed Groups
99
113
EN
Kourosh
Nourouzi
Faculty of Mathematics, K.N.Toosi University of Technology,
P.O.Box 16315-1618, Tehran, Iran.
nourouzi@kntu.ac.ir
Alireza
Pourmoslemi
Department of Mathematics, Payame Noor University, P.O.BOX
19395-3697, Tehran, Iran.
a_pourmoslemy@pnu.ac.ir
10.22111/ijfs.2017.3045
In this paper, we introduce the probabilistic normed groups. Among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. We also study midconvex functions defined on probabilistic normed groups and give some results about locally boundedness of such functions.
Probabilistic normed groups,Invariant probabilistic metrics,Distributional-slowly varying functions,Midconvex functions
http://ijfs.usb.ac.ir/article_3045.html
http://ijfs.usb.ac.ir/article_3045_07ffef6232373ba99af3aa077fbf129e.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
02
28
Implications, coimplications and left semi-uninorms on a complete lattice
115
130
EN
Yuan
Wang
College of Information Engineering, Yancheng Teachers University,
Jiangsu 224002, People's Republic of China
yctuwangyuan@163.com
Keming
Tang
College of Information Engineering, Yancheng Teachers University,
Jiangsu 224002, People's Republic of China
tkmchina@126.com
Zhudeng
Wang
School of Mathematics and Statistics, Yancheng Teachers University, Jiangsu 224002, People's Republic of China
zhudengwang2004@163.com
10.22111/ijfs.2017.3046
In this paper, we firstly show that the $N$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $N$-dual operation. As a dual result, the $N$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge$-distributive left semi-uninorm, is the right residual implication induced by its $N$-dual operation. Then, we demonstrate that the $N$-dual operations of the left semi-uninorms induced by an implication and a coimplication, which satisfy the neutrality principle, are the left semi-uninorms. Finally, we reveal the relationships between conjunctive right arbitrary $vee$-distributive left semi-uninorms induced by implications and disjunctive right arbitrary $wedge$-distributive left semi-uninorms induced by coimplications, where both implications and coimplications satisfy the neutrality principle.
Fuzzy connective,Implication,Coimplication,Left semi-uninorm,Neutrality principle
http://ijfs.usb.ac.ir/article_3046.html
http://ijfs.usb.ac.ir/article_3046_01bd93593faf02d51d0a59def6a543fe.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
02
28
Structural properties of fuzzy graphs
131
144
EN
Xiaonan
Li
School of Mathematics and Statistics, Xidian University, Xi'an, 710071,
Shaanxi, China
xnli@xidian.edu.cn
Huangjian
Yi
School of Information and Technology, Northwest University, Xi'an,
710069, Shaanxi, China
yhj255@163.com
10.22111/ijfs.2017.3048
Matroids are important combinatorial structures and connect close-lywith graphs. Matroids and graphs were all generalized to fuzzysetting respectively. This paper tries to study connections betweenfuzzy matroids and fuzzy graphs. For a given fuzzy graph, we firstinduce a sequence of matroids from a sequence of crisp graph, i.e.,cuts of the fuzzy graph. A fuzzy matroid, named graph fuzzy matroid,is then constructed by using the sequence of matroids. An equivalentdescription of graphic fuzzy matroids is given and their propertiesof fuzzy bases and fuzzy circuits are studied.
Fuzzy graph,Partial fuzzy subgraph,Cycle,Fuzzy matroid
http://ijfs.usb.ac.ir/article_3048.html
http://ijfs.usb.ac.ir/article_3048_b36fae2bb90f788b2a7a140802ec8baa.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
02
28
M-FUZZIFYING INTERVAL SPACES
145
162
EN
Zhen-Yu
Xiu
College of Applied Mathematics, Chengdu University of Information
Technology, Chengdu 610000, P.R. China
xyz198202@163.com
Fu-Gui
Shi
chool of Mathematics and Statistics, Beijing Institute of Technology,
Beijing 100081, P.R. China
fugushi@bit.edu.cn
10.22111/ijfs.2017.3050
In this paper, we introduce the notion of $M$-fuzzifying interval spaces, and discuss the relationship between $M$-fuzzifying interval spaces and $M$-fuzzifying convex structures.It is proved that the category {bf MYCSA2} can be embedded in the category {bf MYIS} as a reflective subcategory, where {bf MYCSA2} and {bf MYIS} denote the category of $M$-fuzzifying convex structures of $M$-fuzzifying arity $leq 2$ and the category of $M$-fuzzifying interval spaces, respectively. Under the framework of $M$-fuzzifying interval spaces, subspaces and product spaces are presented and some of their fundamental properties are obtained.
$M$-fuzzifying interval spaces,$M$-fuzzifying convex structures,$M$-fuzzifying interval preserving functions,Subspaces,Product spaces
http://ijfs.usb.ac.ir/article_3050.html
http://ijfs.usb.ac.ir/article_3050_199fd4b0125cf88df6ef7f1e2066dd5c.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
02
28
COUNTING DISTINCT FUZZY SUBGROUPS OF SOME RANK-3 ABELIAN GROUPS
163
181
EN
Isaac K.
Appiah
Department of Mathematics, University of Fort Hare, ALICE, 5700,
South Africa
B. B.
Makamba
Department of Mathematics, University of Fort Hare, ALICE, 5700,
South Africa
bbmakamba@ufh.ac.za
10.22111/ijfs.2017.3051
In this paper we classify fuzzy subgroups of a rank-3 abelian group $G = mathbb{Z}_{p^n} + mathbb{Z}_p + mathbb{Z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorphic maximal chains of subgroups and (v) classes of isomorphic fuzzy subgroups of $G$. Illustrative examples are provided.
Equivalence,Fuzzy subgroup,Maximal chain,Keychain,Distinguishing factor,Isomorphism
http://ijfs.usb.ac.ir/article_3051.html
http://ijfs.usb.ac.ir/article_3051_d9c53364056080d2ad2e5d2af478926e.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
14
1
2017
03
01
Persian-translation vol. 14, no. 1, February 2017
185
195
EN
10.22111/ijfs.2017.3089
http://ijfs.usb.ac.ir/article_3089.html
http://ijfs.usb.ac.ir/article_3089_96891c6b02f1f2f16c91eec6e6a77e02.pdf