Cover vol. 13, no. 1, February 2016
text
article
2016
eng
Iranian Journal of Fuzzy Systems
University of Sistan and Baluchestan
1735-0654
13
v.
1
no.
2016
0
http://ijfs.usb.ac.ir/article_2631_dc98dadae6fef4885991297e38de7d91.pdf
dx.doi.org/10.22111/ijfs.2016.2631
Arithmetic Aggregation Operators for Interval-valued Intuitionistic Linguistic Variables and Application to Multi-attribute Group Decision Making
Jiuying
Dong
School of Statistics, Jiangxi University of Finance and Economics,
Nanchang 330013, China and Research Center of Applied Statistics, Jiangxi University
of Finance and Economics, Nanchang 330013, China
author
Shu-Ping
Wan
College of Information Technology, Jiangxi University of Finance
and Economics, Nanchang 330013, China
author
text
article
2016
eng
The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The operation law, score function, accuracy function , and certainty function for interval-valued intuitionistic linguistic varibales (IVILVs) are defined. Hereby a lexicographic method is proposed to rank the IVILVs. Then, three kinds of interval-valued intuitionistic linguistic arithmetic average operators are defined, including the interval-valued intuitionistic linguistic weighted arithmetic average (IVILWAA) operator, interval-valued intuitionistic linguistic ordered weighted arithmetic (IVILOWA) operator, and interval-valued intuitionistic linguistic hybrid arithmetic (IVILHA) operator, and their desirable properties are also discussed. Based on the IVILWAA and IVILHA operators, two methods are proposed for solving multi-attribute group decision making problems with IVILVs. Finally, an investment selection example is illustrated to demonstrate the applicability and validity of the methods proposed in this paper.
Iranian Journal of Fuzzy Systems
University of Sistan and Baluchestan
1735-0654
13
v.
1
no.
2016
1
23
http://ijfs.usb.ac.ir/article_2284_a8c89f45da6d004df613f2dedf70b6f9.pdf
dx.doi.org/10.22111/ijfs.2016.2284
Decision making in medical investigations using new divergence measures for intuitionistic fuzzy sets
A.
Srivastava
Department of Mathematics, Jaypee Institute of Information Tech-
nology, Noida, Uttar Pradesh
author
S.
Maheshwari
Department of Mathematics, Jaypee Institute of Information Tech-
nology, Noida, Uttar Pradesh
author
text
article
2016
eng
In recent times, intuitionistic fuzzy sets introduced by Atanassov has been one of the most powerful and flexible approaches for dealing with complex and uncertain situations of real world. In particular, the concept of divergence between intuitionistic fuzzy sets is important since it has applications in various areas such as image segmentation, decision making, medical diagnosis, pattern recognition and many more. The aim of this paper is to introduce a new divergence measure for Atanassov's intuitionistic fuzzy sets (textit{AIFS)}. The properties of the proposed divergence measure have been studied and the findings are applied in medical diagnosis of some diseases with a common set of symptoms.
Iranian Journal of Fuzzy Systems
University of Sistan and Baluchestan
1735-0654
13
v.
1
no.
2016
25
44
http://ijfs.usb.ac.ir/article_2285_c662f28b659682009004d67579186183.pdf
dx.doi.org/10.22111/ijfs.2016.2285
Designing a model of intuitionistic fuzzy VIKOR in multi-attribute group decision-making problems
Seyed Meysam
Mousavi
Department of Industrial Engineering, Faculty of Engi-
neering, Shahed University, Tehran, Iran
author
Behnam
Vahdani
Faculty of Industrial and Mechanical Engineering, Qazvin Branch,
Islamic Azad University, Qazvin, Iran
author
Shadan Sadigh
Behzadi
Department of Mathematics, Qazvin Branch, Islamic Azad
University, Qazvin, Iran
author
text
article
2016
eng
Multiple attributes group decision making (MAGDM) is regarded as the process of determining the best feasible solution by a group of experts or decision makers according to the attributes that represent different effects. In assessing the performance of each alternative with respect to each attribute and the relative importance of the selected attributes, quantitative/qualitative evaluations are often required to handle uncertainty, imprecise and inadequate information, which are well suited to represent with fuzzy values. This paper develops a VIKOR method based on intuitionistic fuzzy sets with multi-judges and multi-attributes in real-life situations. Intuitionistic fuzzy weighted averaging (IFWA) operator is used to aggregate individual judgments of experts to rate the importance of attributes and alternatives. Then, an intuitionistic ranking index is introduced to obtain a compromise solution to solve MAGDM problems. For application and validation, this paper presents two application examples and solves the practical portfolio selection and material handling selection problems to verify the proposed method. Finally, the intuitionistic fuzzy VIKOR method is compared with the existing intuitionistic fuzzy MAGDM method for two application examples, and their computational results are discussed.
Iranian Journal of Fuzzy Systems
University of Sistan and Baluchestan
1735-0654
13
v.
1
no.
2016
45
65
http://ijfs.usb.ac.ir/article_2286_459119c7ea81ef16c1dc2c156e716ea4.pdf
dx.doi.org/10.22111/ijfs.2016.2286
Piecewise cubic interpolation of fuzzy data based on B-spline basis functions
Masoumeh
Zeinali
Faculty of mathematical sciences, University of Tabriz, Tabriz,
Iran
author
Sedaghat
Shahmorad
Faculty of mathematical sciences, University of Tabriz, Tabriz,
Iran
author
Kamal
Mirnia
Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran
author
text
article
2016
eng
In this paper fuzzy piecewise cubic interpolation is constructed for fuzzy data based on B-spline basis functions. We add two new additional conditions which guarantee uniqueness of fuzzy B-spline interpolation.Other conditions are imposed on the interpolation data to guarantee that the interpolation function to be a well-defined fuzzy function. Finally some examples are given to illustrate the proposed method.
Iranian Journal of Fuzzy Systems
University of Sistan and Baluchestan
1735-0654
13
v.
1
no.
2016
67
76
http://ijfs.usb.ac.ir/article_2287_4c7e790202a7257a98a74eed659ffe8c.pdf
dx.doi.org/10.22111/ijfs.2016.2287
Further results on $L$-ordered fuzzifying convergence spaces
Bin
Pang
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
author
Yi
Zhao
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
author
text
article
2016
eng
In this paper, it is shown that the category of $L$-ordered fuzzifying convergence spaces contains the category of pretopological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory and the latter contains the category of topological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory. Also, it is proved that the category of $L$-ordered fuzzifying convergence spaces can be embedded in the category of stratified $L$-ordered convergence spaces as a coreflective subcategory.
Iranian Journal of Fuzzy Systems
University of Sistan and Baluchestan
1735-0654
13
v.
1
no.
2016
77
92
http://ijfs.usb.ac.ir/article_2289_7edf80dce877328f54e067a17901d97c.pdf
dx.doi.org/10.22111/ijfs.2016.2289
On The Relationships Between Types of $L$-convergence Spaces
Qiu
Jin
Department of Mathematics, Liaocheng University, Liaocheng, P.R.China
author
Lingqiang
Li
Department of Mathematics, Liaocheng University, Liaocheng, P.R.China
author
Guangwu
Meng
Department of Mathematics, Liaocheng University, Liaocheng, P.R.China
author
text
article
2016
eng
This paper focuses on the relationships between stratified $L$-conver-gence spaces, stratified strong $L$-convergence spaces and stratifiedlevelwise $L$-convergence spaces. It has been known that: (1) astratified $L$-convergence space is precisely a left-continuousstratified levelwise $L$-convergence space; and (2) a stratifiedstrong $L$-convergence space is naturally a stratified $L$-convergence space, but the converse is not true generally.In this paper, a strong left-continuity condition for stratified levelwise $L$-convergence space is given. It is proved that a stratified strong $L$-convergence space is precisely a strongly left-continuous stratifiedlevelwise $L$-convergence space. Then a sufficient and necessary condition for a stratified $L$-convergence space to be a stratified strong $L$-convergence space is presented.
Iranian Journal of Fuzzy Systems
University of Sistan and Baluchestan
1735-0654
13
v.
1
no.
2016
93
103
http://ijfs.usb.ac.ir/article_2290_71de97e8ff22e4ed37bf0b947a19e70a.pdf
dx.doi.org/10.22111/ijfs.2016.2290
Correspondence between probabilistic norms and fuzzy norms
Hua-Peng
Zhang
School of Science, Nanjing University of Posts and Telecommuni-
cations, Nanjing 210023, China
author
text
article
2016
eng
In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.
Iranian Journal of Fuzzy Systems
University of Sistan and Baluchestan
1735-0654
13
v.
1
no.
2016
105
114
http://ijfs.usb.ac.ir/article_2291_c21f5bbd1e1e97f9ce8d83b9838715be.pdf
dx.doi.org/10.22111/ijfs.2016.2291
$L$-fuzzy approximation spaces and $L$-fuzzy topological spaces
A. A.
Ramadan
Department of Mathematics, Faculty of Science, Beni-Suef Univer-
sity, Beni-Suef, Egypt
author
E. H.
Elkordy
Department of Mathematics, Faculty of Science, Beni-Suef Univer-
sity, Beni-Suef, Egypt
author
M.
El-Dardery
Department of Mathematics, Faculty of Science, Fayoum University,
Fayoum, Egypt
author
text
article
2016
eng
The $L$-fuzzy approximation operator associated with an $L$-fuzzy approximation space $(X,R)$ turns out to be a saturated $L$-fuzzy closure (interior) operator on a set $X$ precisely when the relation $R$ is reflexive and transitive. We investigate the relations between $L$-fuzzy approximation spaces and $L$-(fuzzy) topological spaces.
Iranian Journal of Fuzzy Systems
University of Sistan and Baluchestan
1735-0654
13
v.
1
no.
2016
115
129
http://ijfs.usb.ac.ir/article_2292_6313286d0ad372c6aaa06e50234658ed.pdf
dx.doi.org/10.22111/ijfs.2016.2292
Commutative pseudo BE-algebras
L. C.
Ciungu
Department of Mathematics, University of Iowa, 14 MacLean Hall,
Iowa City, Iowa 52242-1419, Usa
author
text
article
2016
eng
The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-algebras also hold for commutative pseudo BE-algebras. For example, any finite commutative pseudo BE-algebra is a BE-algebra, and any commutative pseudo BE-algebra is a join-semilattice. Moreover, if a commutative pseudo BE-algebra is a meet-semilattice, then it is a distributive lattice. We define the pointed pseudo-BE algebras, and introduce and study the relative negations on pointed pseudo BE-algebras. Based on the relative negations we construct two closure operators on a pseudo BE-algebra.We also define relative involutive pseudo BE-algebras, we investigate their properties and prove equivalent conditions for a relative involutive pseudo BE-algebra.We define the relative Glivenko property for a relative good pseudo BE-algebra and show that any relativeinvolutive pseudo BE-algebra has the relative Glivenko property.
Iranian Journal of Fuzzy Systems
University of Sistan and Baluchestan
1735-0654
13
v.
1
no.
2016
131
144
http://ijfs.usb.ac.ir/article_2293_89fc397124e86bd8d36d0f72b59437ba.pdf
dx.doi.org/10.22111/ijfs.2016.2293
Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices
D.
Busneag
Department of Mathematics, Faculty of Mathematics and Natural Sci-
ences, University of Craiova, Craiova, Romania
author
D.
Piciu
Department of Mathematics, Faculty of Mathematics and Natural Sciences,
University of Craiova, Craiova, Romania
author
text
article
2016
eng
At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that filters are also characterized byvarious types of fuzzy sets. Most of such characterizations is trivial butsome are nontrivial, for example characterizations obtained in cite{xm}.Both situation have revealed a rich range of classes of filters: Boolean,implicative, Heyting, positive implicative, fantastic (or MV-filter), etc.In this paper we work in the general cases of residuated lattices and put inevidence new types of filters in a residuated lattice (in the spirit of cite{mvl}): semi-G-filterstextit{, }Stonean filters, divisible filters,BL-filters and regular filters.
Iranian Journal of Fuzzy Systems
University of Sistan and Baluchestan
1735-0654
13
v.
1
no.
2016
145
160
http://ijfs.usb.ac.ir/article_2294_d8dfab9476be9a9b5c4b01faa4c2942b.pdf
dx.doi.org/10.22111/ijfs.2016.2294
Persian-translation vol. 13, no. 1, February 2016
text
article
2016
eng
Iranian Journal of Fuzzy Systems
University of Sistan and Baluchestan
1735-0654
13
v.
1
no.
2016
162
172
http://ijfs.usb.ac.ir/article_2632_c03568e8d3443db7f6176c58d18a986b.pdf
dx.doi.org/10.22111/ijfs.2016.2632