eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2016-03-01
13
1
0
10.22111/ijfs.2016.2631
2631
Cover vol. 13, no. 1, February 2016
http://ijfs.usb.ac.ir/article_2631_dc98dadae6fef4885991297e38de7d91.pdf
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2016-02-28
13
1
1
23
10.22111/ijfs.2016.2284
2284
مقاله پژوهشی
Arithmetic Aggregation Operators for Interval-valued Intuitionistic Linguistic Variables and Application to Multi-attribute Group Decision Making
Jiuying Dong
jiuyingdong@126.com
1
Shu-Ping Wan
2
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
College of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China
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.
http://ijfs.usb.ac.ir/article_2284_a8c89f45da6d004df613f2dedf70b6f9.pdf
Multi-attribute group decision making
Interval-valued intuitionistic linguistic set
Intuitionistic fuzzy set
Arithmetic operators
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2016-02-28
13
1
25
44
10.22111/ijfs.2016.2285
2285
Decision making in medical investigations using new divergence measures for intuitionistic fuzzy sets
A. Srivastava
1
S. Maheshwari
2
Department of Mathematics, Jaypee Institute of Information Tech- nology, Noida, Uttar Pradesh
Department of Mathematics, Jaypee Institute of Information Tech- nology, Noida, Uttar Pradesh
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.
http://ijfs.usb.ac.ir/article_2285_c662f28b659682009004d67579186183.pdf
Fuzzy sets
Intuitionistic fuzzy sets
Divergence measure
Medical diagnosis
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2016-02-28
13
1
45
65
10.22111/ijfs.2016.2286
2286
Designing a model of intuitionistic fuzzy VIKOR in multi-attribute group decision-making problems
Seyed Meysam Mousavi
1
Behnam Vahdani
b.vahdani@ut.ac.ir
2
Shadan Sadigh Behzadi
3
Department of Industrial Engineering, Faculty of Engi- neering, Shahed University, Tehran, Iran
Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
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.
http://ijfs.usb.ac.ir/article_2286_459119c7ea81ef16c1dc2c156e716ea4.pdf
Intuitionistic fuzzy sets
VIKOR method
Group decision making
Portfolio selection
Material handling selection
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2016-02-28
13
1
67
76
10.22111/ijfs.2016.2287
2287
Piecewise cubic interpolation of fuzzy data based on B-spline basis functions
Masoumeh Zeinali
zeinali@tabrizu.ac.ir
1
Sedaghat Shahmorad
shahmorad@tabrizu.ac.ir
2
Kamal Mirnia
mirnia-kam@tabrizu.ac.ir
3
Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran
Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran
Faculty of mathematical sciences, University of Tabriz, Tabriz, Iran
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.
http://ijfs.usb.ac.ir/article_2287_4c7e790202a7257a98a74eed659ffe8c.pdf
Fuzzy number
Fuzzy interpolation
B-spline basis functions
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2016-02-28
13
1
77
92
10.22111/ijfs.2016.2289
2289
Further results on $L$-ordered fuzzifying convergence spaces
Bin Pang
pangbin1205@163.com
1
Yi Zhao
zhaoyisz420@sohu.com
2
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen- zhen, P.R. China
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen- zhen, P.R. China
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.
http://ijfs.usb.ac.ir/article_2289_7edf80dce877328f54e067a17901d97c.pdf
$L$-ordered fuzzifying convergence space
Stratified $L$-ordered convergence space
$L$-filter
Category theory
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2016-02-28
13
1
93
103
10.22111/ijfs.2016.2290
2290
On The Relationships Between Types of $L$-convergence Spaces
Qiu Jin
jinqiu79@126.com
1
Lingqiang Li
lilingqiang@126.com
2
Guangwu Meng
3
Department of Mathematics, Liaocheng University, Liaocheng, P.R.China
Department of Mathematics, Liaocheng University, Liaocheng, P.R.China
Department of Mathematics, Liaocheng University, Liaocheng, P.R.China
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.
http://ijfs.usb.ac.ir/article_2290_71de97e8ff22e4ed37bf0b947a19e70a.pdf
$L$-topology
Stratified $L$-filter
Stratified $L$-convergence space
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2016-02-28
13
1
105
114
10.22111/ijfs.2016.2291
2291
Correspondence between probabilistic norms and fuzzy norms
Hua-Peng Zhang
huapengzhang@163.com
1
School of Science, Nanjing University of Posts and Telecommuni- cations, Nanjing 210023, China
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.
http://ijfs.usb.ac.ir/article_2291_c21f5bbd1e1e97f9ce8d83b9838715be.pdf
Probabilistic norm
Fuzzy norm
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2016-02-28
13
1
115
129
10.22111/ijfs.2016.2292
2292
$L$-fuzzy approximation spaces and $L$-fuzzy topological spaces
A. A. Ramadan
1
E. H. Elkordy
2
M. El-Dardery
3
Department of Mathematics, Faculty of Science, Beni-Suef Univer- sity, Beni-Suef, Egypt
Department of Mathematics, Faculty of Science, Beni-Suef Univer- sity, Beni-Suef, Egypt
Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt
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.
http://ijfs.usb.ac.ir/article_2292_6313286d0ad372c6aaa06e50234658ed.pdf
Complete residuated lattice
$L$-fuzzy approximation spaces
$L$-fuzzy topology
Continuity
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2016-02-28
13
1
131
144
10.22111/ijfs.2016.2293
2293
Commutative pseudo BE-algebras
L. C. Ciungu
lcciungu@yahoo.com
1
Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242-1419, Usa
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.
http://ijfs.usb.ac.ir/article_2293_89fc397124e86bd8d36d0f72b59437ba.pdf
Pseudo BE-algebra
Pseudo BCK-algebra
Commutative pseudo BCK-algebra
Commutative pseudo BE-algebra
Pointed pseudo BE-algebra
Relative involutive pseudo BE-algebra
Relative Glivenko property
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2016-02-28
13
1
145
160
10.22111/ijfs.2016.2294
2294
Semi-G-filters, Stonean filters, MTL-filters, divisible filters, BL-filters and regular filters in residuated lattices
D. Busneag
1
D. Piciu
2
Department of Mathematics, Faculty of Mathematics and Natural Sci- ences, University of Craiova, Craiova, Romania
Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Craiova, Craiova, Romania
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.
http://ijfs.usb.ac.ir/article_2294_d8dfab9476be9a9b5c4b01faa4c2942b.pdf
Residuated lattice
Boolean algebra
BL-algebra
MV-algebra
MTL-algebra
Divisible residuated lattice
Regular residuated lattice
Deductive system
Filter
Boolean filter
MTL-filter
Divisible filter
BL-filter
MV-filter
Semi-G-filter
Stonean filter
Regular filter
eng
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
1735-0654
2016-03-01
13
1
162
172
10.22111/ijfs.2016.2632
2632
Persian-translation vol. 13, no. 1, February 2016
http://ijfs.usb.ac.ir/article_2632_c03568e8d3443db7f6176c58d18a986b.pdf