ORIGINAL_ARTICLE
Cover for Volume.13, No.4
http://ijfs.usb.ac.ir/article_2622_62f46e0d5b4bbe46365d43f6b7ed13cd.pdf
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10.22111/ijfs.2016.2622
ORIGINAL_ARTICLE
Hesitant Fuzzy Linguistic Arithmetic Aggregation Operators in Multiple Attribute Decision Making
In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with hesitant fuzzy linguistic information. Then, motivated by the idea of traditional arithmetic operation, we have developed some aggregation operators for aggregating hesitant fuzzy linguistic information: hesitant fuzzy linguistic weighted average (HFLWA) operator, hesitant fuzzy linguistic ordered weighted average (HFLOWA) operator and hesitant fuzzy linguistic hybrid average (HFLHA) operator. Furthermore, we propose the concept of the dual hesitant fuzzy linguistic set and develop some aggregation operators with dual hesitant fuzzy linguistic information. Then, we have utilized these operators to develop some approaches to solve the hesitant fuzzy linguistic multiple attribute decision making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.
http://ijfs.usb.ac.ir/article_2592_619f4e19e93b5824c3f4b46437720286.pdf
2016-08-30T11:23:20
2019-02-16T11:23:20
1
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10.22111/ijfs.2016.2592
Multiple attribute decision making (MADM)
Hesitant fuzzy linguistic values
Hesitant fuzzy linguistic hybrid average (HFLHA) operator
Dual hesitant fuzzy linguistic set
Guiwu
Wei
weiguiwu@163.com
true
1
School of Business, Sichuan Normal University, Chengdu, 610101, P.R.
China; Communications Systems and Networks (CSN) Research Group, Department of
Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
School of Business, Sichuan Normal University, Chengdu, 610101, P.R.
China; Communications Systems and Networks (CSN) Research Group, Department of
Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
School of Business, Sichuan Normal University, Chengdu, 610101, P.R.
China; Communications Systems and Networks (CSN) Research Group, Department of
Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
LEAD_AUTHOR
Fuad E.
Alsaadi
true
2
Communications Systems and Networks (CSN) Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Communications Systems and Networks (CSN) Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Communications Systems and Networks (CSN) Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
AUTHOR
Tasawar
Hayat
true
3
Department of Mathematics, QuaidI-Azam University 45320, Islam-
abad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research
Group, Department of Mathematics, Faculty of Science, King Abdulaziz University,
Jeddah 21589, Saudi Arabia
Department of Mathematics, QuaidI-Azam University 45320, Islam-
abad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research
Group, Department of Mathematics, Faculty of Science, King Abdulaziz University,
Jeddah 21589, Saudi Arabia
Department of Mathematics, QuaidI-Azam University 45320, Islam-
abad 44000, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research
Group, Department of Mathematics, Faculty of Science, King Abdulaziz University,
Jeddah 21589, Saudi Arabia
AUTHOR
Ahmed
Alsaedi
true
4
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group,
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group,
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group,
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
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ORIGINAL_ARTICLE
A satisfactory strategy of multiobjective two person matrix games with fuzzy payoffs
The multiobjective two person matrix game problem with fuzzy payoffs is considered in this paper. It is assumed that fuzzy payoffs are triangular fuzzy numbers. The problem is converted to several multiobjective matrix game problems with interval payoffs by using the $alpha$-cuts of fuzzy payoffs. By solving these problems some $alpha$-Pareto optimal strategies with some interval outcomes are obtained. An interactive algorithm is presented to obtain a satisfactory strategy of players. Validity and applicability of the method is illustrated by a practical example.
http://ijfs.usb.ac.ir/article_2593_a3f6078e1878f648f551e48322f3dde9.pdf
2016-08-30T11:23:20
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33
10.22111/ijfs.2016.2593
Fuzzy multiobjective game
Interval multiobjective programming
Satisfactory strategy
Security level
Hamid
Bigdeli
true
1
Department of Mathematics, University of Birjand, Birjand, I.R. Iran
Department of Mathematics, University of Birjand, Birjand, I.R. Iran
Department of Mathematics, University of Birjand, Birjand, I.R. Iran
LEAD_AUTHOR
Hassan
Hassanpour
true
2
Department of Mathematics, University of Birjand, Birjand,
I.R. Iran
Department of Mathematics, University of Birjand, Birjand,
I.R. Iran
Department of Mathematics, University of Birjand, Birjand,
I.R. Iran
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ORIGINAL_ARTICLE
Bisimulation for BL-general fuzzy automata
In this note, we define bisimulation for BL-general fuzzy automata and show that if there is a bisimulation between two BL-general fuzzy automata, then they have the same behavior.For a given BL-general fuzzy automata, we obtain the greatest bisimulation for the BL-general fuzzy automata. Thereafter, if we use the greatest bisimulation, then we obtain a quotient BL-general fuzzy automata and this quotient is minimal, furthermore there is a morphism from the first one to its quotient.Also, for two given BL-general fuzzy automata we present an algorithm, which determines bisimulation between them.Finally, we present some examples to clarify these new notions.
http://ijfs.usb.ac.ir/article_2594_42b1b8528d5cf9d63d89ed191424c188.pdf
2016-08-30T11:23:20
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50
10.22111/ijfs.2016.2594
BL-general fuzzy automata
Bisimulation
Reduction
General fuzzy automata
Quotient automata
M.
Shamsizadeh
true
1
Department of Mathematics, Graduate University of Advanced
Technology, Kerman, Iran
Department of Mathematics, Graduate University of Advanced
Technology, Kerman, Iran
Department of Mathematics, Graduate University of Advanced
Technology, Kerman, Iran
LEAD_AUTHOR
M. M.
Zahedi
zahedi_mm@ mail.uk.ac.ir
true
2
Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran
Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran
Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran
AUTHOR
K.
Abolpour
true
3
Department of Mathematics, Kazerun Branch, Islamic Azad University,
Kazerun, Iran
Department of Mathematics, Kazerun Branch, Islamic Azad University,
Kazerun, Iran
Department of Mathematics, Kazerun Branch, Islamic Azad University,
Kazerun, Iran
AUTHOR
[1] K. Abolpour and M. M. Zahedi, BL-general fuzzy automata and accept behavior, Journal
1
Applied Mathematics and Computing, 38 (2012), 103-118.
2
[2] K. Abolpour and M. M. Zahedi, Isomorphism between two BL-general fuzzy automata, Soft
3
Computing, 16 (2012), 729-736.
4
[3] C. Baier, B. Engelen and M. Majster Cederbaum, Deciding bisimilarity and similarity for
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probabilistic processes, Journal of Computer and System Sciences, 60 (2000), 187-231.
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393 (2008), 109-123.
8
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on Fuzzy Systems, 19 (2011), 540-552.
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[6] Y. Cao, H. Wang, S. X. Sun and G. Chen, A behavioral distance for fuzzy-transition systems,
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IEEE Transactions on Fuzzy Systems, 21 (2012), 735-747.
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[7] M. Ciric, J. Ignjatovic, M. Basic and I. Jancic, Nondeterministic automata: equivalence,
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bisimulations, and uniform relations, Information Sciences, 261 (2013), 185-218.
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ORIGINAL_ARTICLE
Characterizations of $L$-convex spaces
In this paper, the concepts of $L$-concave structures, concave $L$-interior operators and concave $L$-neighborhood systems are introduced. It is shown that the category of $L$-concave spaces and the category of concave $L$-interior spaces are isomorphic, and they are both isomorphic to the category of concave $L$-neighborhood systems whenever $L$ is a completely distributive lattice. Also, it is proved that these categories are all isomorphic to the category of $L$-convex spaces whenever $L$ is a completely distributive lattice with an order-reversing involution operator.
http://ijfs.usb.ac.ir/article_2595_892a5985091b412961eb99fb84c5bfbe.pdf
2016-08-30T11:23:20
2019-02-16T11:23:20
51
61
10.22111/ijfs.2016.2595
$L$-convex structure
$L$-concave structure
Convex $L$-closure operator
Concave $L$-interior operator
Concave $L$-neighborhood system
Bin
Pang
pangbin1205@163.com
true
1
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
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
AUTHOR
Yi
Zhao
zhaoyisz420@sohu.com
true
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
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
LEAD_AUTHOR
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37
ORIGINAL_ARTICLE
Multiple Fuzzy Regression Model for Fuzzy Input-Output Data
A novel approach to the problem of regression modeling for fuzzy input-output data is introduced.In order to estimate the parameters of the model, a distance on the space of interval-valued quantities is employed.By minimizing the sum of squared errors, a class of regression models is derived based on the interval-valued data obtained from the $\alpha$-level sets of fuzzy input-output data.Then, by integrating the obtained parameters of the interval-valued regression models, the optimal values of parameters for the main fuzzy regression model are estimated.Numerical examples and comparison studies are given to clarify the proposed procedure, and to show the performance of the proposed procedure with respect to some common methods.
http://ijfs.usb.ac.ir/article_2596_c5d1e02ec07e74c58799b657496f0c39.pdf
2016-08-30T11:23:20
2019-02-16T11:23:20
63
78
10.22111/ijfs.2016.2596
Fuzzy regression
Interval-valued regression
Least squares method
$LR$-Fuzzy number
Multiple regression
Predictive ability
Jalal
Chachi
taheri.chachi@gmail.com
true
1
Department of Mathematics, Statistics and Computer Sciences, Sem-
nan University, Semnan, Semnan 35195-363, Iran
Department of Mathematics, Statistics and Computer Sciences, Sem-
nan University, Semnan, Semnan 35195-363, Iran
Department of Mathematics, Statistics and Computer Sciences, Sem-
nan University, Semnan, Semnan 35195-363, Iran
LEAD_AUTHOR
S. Mahmoud
Taheri
taher@cc.iut.ac.ir;sm_taheri@ut.ac.ir
true
2
Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, P.O. Box 11365-4563, Iran
Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, P.O. Box 11365-4563, Iran
Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, P.O. Box 11365-4563, Iran
AUTHOR
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1
Iranian Journal of Fuzzy Systms, 5(2) (2008), 1-19.
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[2] M. Are and S. M. Taheri, Least-squares regression based on Atanassov's intuitionistic fuzzy
3
inputs-outputs and Atanassov's intuitionistic fuzzy parameters, IEEE Trans. on Fuzzy Syst.,
4
23 (2015), 1142-1154.
5
[3] A. Bargiela, W. Pedrycz and T. Nakashima, Multiple regression with fuzzy data, Fuzzy Sets
6
Syst., 158 (2007), 2169-2188.
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[4] A. Bisserier, R. Boukezzoula and S. Galichet, A revisited approach to linear fuzzy regression
8
using trapezoidal fuzzy intervals, Inf. Sci., 180 (2010), 3653-3673.
9
[5] J. Chachi and M. Roozbeh, A fuzzy robust regression approach applied to bed-
10
load transport data, Communications in Statistics-Simulation and Computation, DOI:
11
10.1080/03610918.2015.1010002, 2015.
12
[6] J. Chachi and S. M. Taheri, A least-absolutes approach to multiple fuzzy regression, in: Proc.
13
58th ISI Congress, Dublin, Ireland, CPS077-01, 2011.
14
[7] J. Chachi and S. M. Taheri, A least-absolutes regression model for imprecise response based
15
on the generalized Hausdor-metric, J. Uncertain Syst., 7 (2013), 265-276.
16
[8] J. Chachi, S. M. Taheri and N. R. Arghami, A hybrid fuzzy regression model and its appli-
17
cation in hydrology engineering, Applied Soft Comput., 25 (2014), 149{158.
18
[9] J. Chachi, S. M. Taheri and H. Rezaei Pazhand, Suspended load estimation using L1-Fuzzy
19
regression, L2-Fuzzy regression and MARS-Fuzzy regression models, Hydrological Sciences
20
J., 61(8) (2016), 1489-1502.
21
[10] J. Chachi, S. M. Taheri and R. H. Rezaei Pazhand, An interval-based approach to fuzzy
22
regression for fuzzy input-output data, in: Proc. IEEE Int. Conf. Fuzzy Syst., Taipei, Taiwan,
23
(2011), 2859-2863.
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[11] S. P. Chen and J. F. Dang, A variable spread fuzzy linear regression model with higher
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explanatory power and forecasting accuracy, Inf. Sci., 178 (2008), 3973-3988.
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gression model with LR fuzzy response, Comp. Stat. Data Anal., 51 (2006), 267-286.
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Comp. Stat. Data Anal., 42 (2003), 47-72.
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Fuzzy Set Syst., 130 (2002), 1-19.
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Sci., 180 (2010), 4737-4762.
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4154-4174.
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variable, Comp. Stat. Data Anal., 51 (2006), 287-313.
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exible spreads,
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98
ORIGINAL_ARTICLE
On impulsive fuzzy functional differential equations
In this paper, we prove the existence and uniqueness of solution to the impulsive fuzzy functional differential equations under generalized Hukuhara differentiability via the principle of contraction mappings. Some examples are provided to illustrate the result.
http://ijfs.usb.ac.ir/article_2597_14b4ee49034a4c88aca9d65fbe0dcb9b.pdf
2016-08-30T11:23:20
2019-02-16T11:23:20
79
94
10.22111/ijfs.2016.2597
Impulsive fuzzy functional differential equations
impulsive functional differential equations
impulsive differential equations
Ho
Vu
hovumath@gmail.com
true
1
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
AUTHOR
Ngo
VanHoa
true
2
Division of Computational Mathematics and Engineering, Institute
for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Division of Computational Mathematics and Engineering, Institute
for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Division of Computational Mathematics and Engineering, Institute
for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
LEAD_AUTHOR
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solving fuzzy linear dierential equations, Computing, 92 (2010), 181{197.
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tial equations with uncertainty, Soft Computing, 16 (2011), 297{302.
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dierentiability, Communications in Nonlinear Science and Numerical Simulation, 22 (2015),
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Mathematical Inequalities & Applications, 4 (2001), 239{246.
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[20] V. Lupulescu, On a class of fuzzy functional dierential equations, Fuzzy Sets and Systems,
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160 (2009), 1547{1562.
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sions, CRC Press, Singapore, 2003.
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generalized dierentiability, Nonlinear Analysis: Hybrid Systems, 3 (2009), 700{707.
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[23] J. J. Nieto and R. Rodrguez-Lopez, Periodic boundary value problem for non-Lipschitzian
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impulsive functional dierential equations, Journal of Mathematical Analysis and Applica-
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tions, 318 (2006), 593-610.
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[24] R. Rodrguez-Lopez, Periodic boundary value problems for impulsive fuzzy dierential equa-
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tions, Fuzzy Sets and Systems, 159 (2008), 1384{1409.
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Singapore, 1995.
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[26] P. V. Tri, N. V. Hoa and N. D. Phu, Sheaf fuzzy problems for functional dierential equations,
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Advance in Dierence Equation, 2014 2014:156
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Control Robot, 3 (2003), 851{859.
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[28] H. Vu, L. S. Dong and N. V. Hoa, Random fuzzy functional integro-dierential equations
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under generalized Hukuhara dierentiability , Journal of Intelligent & Fuzzy Systems, 27
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(2014), 1491-1506.
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type hukuhara derivative, Dierential Equations & Applications, 5 (2013), 501{518.
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tions, Advances in Dierence Equations, 2015 2015:373
64
ORIGINAL_ARTICLE
Stratified $(L,M)$-fuzzy Q-convergence spaces
This paper presents the concepts of $(L,M)$-fuzzy Q-convergence spaces and stratified $(L,M)$-fuzzy Q-convergence spaces. It is shown that the category of stratified $(L,M)$-fuzzy Q-convergence spaces is a bireflective subcategory of the category of $(L,M)$-fuzzy Q-convergence spaces, and the former is a Cartesian-closed topological category. Also, it is proved that the category of stratified $(L,M)$-fuzzy topological spaces can be embedded in the category of stratified $(L,M)$-fuzzy Q-convergence spaces as a reflective subcategory, and the former is isomorphic to the category of topological stratified $(L,M)$-fuzzy Q-convergence spaces.
http://ijfs.usb.ac.ir/article_2598_1c939cd4dac89ee78894504a9620668f.pdf
2016-08-30T11:23:20
2019-02-16T11:23:20
95
111
10.22111/ijfs.2016.2598
(Stratified) $(L
M)$-fuzzy topology
M)$-fuzzy Q-convergence structure
Topological category
Cartesian-closedness
Bin
Pang
pangbin1205@163.com
true
1
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
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
AUTHOR
Yi
Zhao
zhaoyisz420@sohu.com
true
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
Shenzhen Graduate School, Harbin Institute of Technology, 518055 Shen-
zhen, P.R. China
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[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, Wiley, New
1
York, 1990.
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[2] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182{190.
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[3] J. M. Fang, Categories isomorphic to L-FTOP, Fuzzy Sets Syst., 157 (2006), 820{831.
4
[4] J. M. Fang, Stratied L-ordered convergence structures, Fuzzy Sets Syst., 161 (2010), 2130{
5
[5] J. M. Fang, Relationships between L-ordered convergence structures and strong L-topologies,
6
Fuzzy Sets Syst., 161 (2010), 2923{2944.
7
[6] M. Guloglu and D. Coker, Convergence in I-fuzzy topological spaces, Fuzzy Sets Syst., 151
8
(2005), 615{623.
9
[7] U. Hohle and A. P. Sostak, Axiomatic foudations of xed-basis fuzzy topology, In: U. Hohle,
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S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory,
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[9] G. Jager, Subcategories of lattice-valued convergence spaces, Fuzzy Sets Syst., 156 (2005),
14
[10] G. Jager, Pretopological and topological lattice-valued convergence spaces, Fuzzy Sets Syst.,
15
158 (2007), 424{435.
16
[11] G. Jager, Lattice-valued convergence spaces and regularity, Fuzzy Sets Syst., 159 (2008),
17
2488{2502.
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[12] G. Jager, Fischer's diagonal condition for lattice-valued convergence spaces, Quaest. Math.,
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31 (2008), 11{25.
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[13] G. Jager, Stratied LMN-convergence tower spaces, Fuzzy Sets Syst., 282 (2016), 62{73.
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[14] T. Kubiak, On fuzzy topologies, Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, 1985.
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[15] L. Q. Li and Q. Jin, On adjunctions between Lim, SL-Top, and SL-Lim, Fuzzy Sets Syst.,
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182 (2011), 66{78.
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axioms, Fuzzy Sets Syst., 204 (2012), 40{52.
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[18] K. C. Min, Fuzzy limit spaces, Fuzzy Sets Syst., 32 (1989), 343{357.
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[19] B. Pang and J.M. Fang, L-fuzzy Q-convergence structures, Fuzzy Sets Syst., 182 (2011),
29
[20] B. Pang, Futher study on L-fuzzy Q-convergence structures, Iranian Journal of Fuzzy Systems,
30
10(5) (2013), 147{164.
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[21] B. Pang, On (L;M)-fuzzy convergence spaces, Fuzzy Sets Syst., 238 (2014), 46{70.
32
[22] B. Pang and F. G. Shi, Degrees of compactness of (L;M)-fuzzy convergence spaces and its
33
applications, Fuzzy Sets Syst., 251 (2014), 1{22.
34
[23] B. Pang, Enriched (L;M)-fuzzy convergence spaces, J. Intell. Fuzzy Syst., 27 (2014), 93{103.
35
[24] G. Preuss, Foundations of topology{an approach to convenient topology, Kluwer Academic
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Publisher, Dordrecht, Boston, London, 2002.
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(1985), 89{103.
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123 (2001), 169{176.
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[27] W. Yao, On many-valued stratied L-fuzzy convergence spaces, Fuzzy Sets Syst., 159 (2008),
42
2503{2519.
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[28] W. Yao, On L-fuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 6(1) (2009),
44
[29] W. Yao, Moore-Smith convergence in (L;M)-fuzzy topology, Fuzzy Sets Syst., 190 (2012),
45
ORIGINAL_ARTICLE
Fuzzy Topology Generated by Fuzzy Norm
In the current paper, consider the fuzzy normed linear space $(X,N)$ which is defined by Bag and Samanta. First, we construct a new fuzzy topology on this space and show that these spaces are Hausdorff locally convex fuzzy topological vector space. Some necessary and sufficient conditions are established to illustrate that the presented fuzzy topology is equivalent to two previously studied fuzzy topologies.
http://ijfs.usb.ac.ir/article_2599_80e905324f5d0d9df4942f664b21aabb.pdf
2016-08-30T11:23:20
2019-02-16T11:23:20
113
123
10.22111/ijfs.2016.2599
Fuzzy norm
Fuzzy topology
locally convex topological vector space
M.
Saheli
true
1
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
LEAD_AUTHOR
[1] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math.,
1
11(3) (2003), 687-705.
2
[2] T. Bag and S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151
3
(2005), 513-547.
4
[3] S. C. Cheng and J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces,
5
Bull. Cal. Math. Soc., 86 (1994), 429-436.
6
[4] N. F. Das and P. Das, Fuzzy topology generated by fuzzy norm, Fuzzy Sets and Systems, 107
7
(1999), 349-354.
8
[5] J. X. Fang, On I-topology generated by fuzzy norm, Fuzzy Sets and Systems, 157 (2006),
9
2739-2750.
10
[6] C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48 (1992),
11
[7] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),
12
[8] I. Karmosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11
13
(1975), 326-334.
14
[9] A. K. Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems, 12 (1984), 143-
15
[10] M. Saheli, On fuzzy topology and fuzzy norm, Annals of Fuzzy Mathematics and Informatics,
16
10(4) (2015), 639647.
17
[11] J. Xiao and X. Zhu, Fuzzy normed space of operators and its completeness, Fuzzy Sets and
18
Systems, 133 (2003) 389-399.
19
[12] G. H. Xu and J. X. Fang, A new I-vector topology generated by a fuzzy norm, Fuzzy Sets and
20
Systems, 158 (2007), 2375-2385.
21
ORIGINAL_ARTICLE
Extended Fuzzy $BCK$-subalgebras
This paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study considers a type of fuzzy hyper $BCK$-ideals in this hyperstructure and describes the relationship between hyper $BCK$-ideals and fuzzy hyper $BCK$-ideals. In fact, it tries to introduce a strongly regular relation on hyper $BCK$-algebras. Moreover, by using the fuzzy hyper $BCK$-ideals, it defines a congruence relation on (weak commutative) hyper $BCK$-algebras that under some conditions is strongly regular and the quotient of any hyper $BCK$-algebra via this relation is a $($hyper $BCK$-algebra$)$ $BCK$-algebra.
http://ijfs.usb.ac.ir/article_2600_ec5ab1057962c6beff342819cbfc8af5.pdf
2016-08-30T11:23:20
2019-02-16T11:23:20
125
144
10.22111/ijfs.2016.2600
Extended fuzzy $BCK$-subalgebra
(Strongly) Fuzzy hyper $BCK$-ideal
Fundamental relation $beta^*$
Jianming
Zhan
zhanjianming@ hotmail.com
true
1
Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China
Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China
Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China
AUTHOR
Mohammad
Hamidi
m.hamidi20@gmail.com
true
2
Department of Mathematics, Payame Noor University, Tehran,
Iran
Department of Mathematics, Payame Noor University, Tehran,
Iran
Department of Mathematics, Payame Noor University, Tehran,
Iran
AUTHOR
Arsham
Borumand Saeid
arsham@iauk.ac.ir
true
3
Department of Pure Mathematics, Faculty of Mathematics
and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Pure Mathematics, Faculty of Mathematics
and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Pure Mathematics, Faculty of Mathematics
and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
LEAD_AUTHOR
[1] M. Bakhshi, M. M. Zahdi and R. A. Borzooei, Fuzzy (positive, weak) implicative hyper BCK-
1
ideals, Iranian Journal of Fuzzy Systems, 1(2) (2004), 63-79.
2
[2] R. A. Borzooei, R. Ameri and M. Hamidi, Fundamental relation on hyper BCK-algebras, An.
3
Univ. oradea, fasc. Mat., 21(1) (2014), 123{136.
4
[3] G. R. Biyogmam, O. A. Heubo-Kwegna and J. B. Nganou, Super implicative hyper BCK-
5
algebras, Int. J. Pure Appl. Math., 76(2) (2012), 267-275.
6
[4] J. Chvalina, S. Hoskova-Mayerova and A. D. Nezhad, General actions of hyperstructures and
7
some applications, An. St. Univ. Ovidius Constanta, 21(1) (2013), 59{82.
8
[5] P. Corsini, Prolegomena of hypergroup theory, Second Edition, Aviani Editor, 1993.
9
[6] P. Corsini and V. Leoreanu, Applications of Hyperstructure Theory, Klwer Academic Pub-
10
lishers, 2002.
11
[7] J. Dongho, Category of fuzzy hyper BCK-algebras, arXiv:1101.2471.
12
[8] P. F. He and X. L. Xin, Fuzzy hyperlattices, Comput. Math. Appl., 62 (2011), 4682{4690.
13
[9] S. Hoskova, Topological hypergroupoids, Comput. Math. Appl., 64 (2012), 2845{2849.
14
[10] Y. Imai and K. Iseki, On axiom systems of propositional calculi, XIV, Proc. Japan Acad.
15
Ser. A Math. Sci., 42 (1966), 19{22.
16
[11] Y. B. Jun, M. M. Zahedi, X. L. Xin and R. A. Borzooei, On hyper BCK-algebras, Ital. J.
17
Pure Appl. Math., 10 (2000), 127{136.
18
[12] Y. B. Jun and X. L. Xin, Fuzzy hyper BCK-ideals of hyper BCK-algebras, Sci. Math. Jpn.,
19
53(2) (2001), 353{360.
20
[13] Y. B. Jun, M. S. Kang and S. Z. Song, Several types of bipolar fuzzy hyper BCK-ideals in
21
hyper BCK-algebras, Honam Math. J., 34(2) (2012), 145{159.
22
[14] V. Leoreanu-Fotea, Fuzzy hypermodules, Comput. Math. Appl., 57 (2009), 466{475.
23
[15] F. Marty, Sur une Generalization de la notion de groupe, 8th Congres Math. Scandinaves,
24
Stockholm., (1934), 45{49.
25
[16] J. Meng and Y. B. Jun, BCK-algebra, Kyung Moonsa, Seoul, 1994.
26
[17] H. T. Nguyen and E. A. Walker, A First Course in Fuzzy Logic, (Third Edition), Chapman
27
and Hall/CRC. Boca Raton, 2005.
28
[18] M. K. Sen, R. Ameri and G. Chowdhury, Fuzzy hypersemigroups, Soft Comput., 12 (2008),
29
[19] X. Xie, Fuzzy ideals extensions in semigroups, Kyungpook Math. J., 42(1) (2002), 39{49.
30
[20] X. L. Xin and P. Wang, States and measures on hyper BCK-algebras, J. Appl. Math., (2014),
31
[21] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338{353.
32
[22] J. Zhan, Fuzzy regular relations on hyperquasigroups, J. Math. Res. Exposition, Nov., 30(6)
33
(2010), 1083{1090.
34
ORIGINAL_ARTICLE
Persian Translation of Abstracts
http://ijfs.usb.ac.ir/article_2623_142703c45c95558598fdf7e2eb9c6fb3.pdf
2016-08-01T11:23:20
2019-02-16T11:23:20
145
158
10.22111/ijfs.2016.2623