ORIGINAL_ARTICLE
Cover vol. 12, no.5, October 2015
http://ijfs.usb.ac.ir/article_2642_e38b90e7cce4505fe17c4f2f1a961d07.pdf
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ORIGINAL_ARTICLE
Functorial semantics of topological theories
Following the categorical approach to universal algebra through algebraic theories, proposed by F.~W.~Lawvere in his PhD thesis, this paper aims at introducing a similar setting for general topology. The cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. We introduce the quasicategory of catalg topological theories and consider its functorial relationships with the quasicategory of the categories of models, in order to provide convenient means for studying topological structures via the properties of their corresponding theories.
http://ijfs.usb.ac.ir/article_2110_e9eb0f65766fb9dfb4d98bd6fea53fbc.pdf
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10.22111/ijfs.2015.2110
Algebra
Algebraic theory
Comma category
Categorically-algebraic topology
Poslat topology
Powerset theory
Topological system
Topological theory
Variety
Sergey A.
Solovyov
sergejs.solovjovs@lumii.lv
true
1
Institute of Mathematics, Faculty of Mechanical Engineering,
Brno University of Technology, Technicka 2896/2, 616 69 Brno, Czech Republic
Institute of Mathematics, Faculty of Mechanical Engineering,
Brno University of Technology, Technicka 2896/2, 616 69 Brno, Czech Republic
Institute of Mathematics, Faculty of Mechanical Engineering,
Brno University of Technology, Technicka 2896/2, 616 69 Brno, Czech Republic
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ORIGINAL_ARTICLE
CVaR Reduced Fuzzy Variables and Their Second Order Moments
Based on credibilistic value-at-risk (CVaR) of regularfuzzy variable, we introduce a new CVaR reduction method fortype-2 fuzzy variables. The reduced fuzzy variables arecharacterized by parametric possibility distributions. We establishsome useful analytical expressions for mean values and secondorder moments of common reduced fuzzy variables. The convex properties of second order moments with respect to parameters are also discussed. Finally, we take second order moment as a new risk measure, and develop a mean-moment model to optimize fuzzy portfolio selection problems. According to the analytical formulas of second order moments, the mean-moment optimization model is equivalent to parametricquadratic convex programming problems, which can be solved by general-purpose optimization software. The solution results reported in the numerical experiments demonstrate the credibility of the proposed optimization method.
http://ijfs.usb.ac.ir/article_2111_ae9c29c1bd509c95fc8928b9778558da.pdf
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10.22111/ijfs.2015.2111
Credibilistic value-at-risk
Reduced fuzzy variable
Parametric possibility distribution
Second order moment
Xue-Jie
Bai
true
1
College of Management, Hebei University, Baoding 071002, Hebei, China and College of Science, Agricultural University of Hebei, Baoding 071001, Hebei, China
College of Management, Hebei University, Baoding 071002, Hebei, China and College of Science, Agricultural University of Hebei, Baoding 071001, Hebei, China
College of Management, Hebei University, Baoding 071002, Hebei, China and College of Science, Agricultural University of Hebei, Baoding 071001, Hebei, China
AUTHOR
Yan-Kui
Liu
true
2
College of Management, Hebei University, Baoding 071002, Hebei,
China
College of Management, Hebei University, Baoding 071002, Hebei,
China
College of Management, Hebei University, Baoding 071002, Hebei,
China
LEAD_AUTHOR
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ORIGINAL_ARTICLE
Linear matrix inequality approach for synchronization of chaotic fuzzy cellular neural networks with discrete and unbounded distributed delays based on\ sampled-data control
In this paper, linear matrix inequality (LMI) approach for synchronization of chaotic fuzzy cellular neural networks (FCNNs) with discrete and unbounded distributed delays based on sampled-data controlis investigated. Lyapunov-Krasovskii functional combining with the input delay approach as well as the free-weighting matrix approach are employed to derive several sufficient criteria in terms of LMIs ensuring the delayed FCNNs to be asymptotically synchronous. The restriction such as the time-varying delay required to be differentiable or even its time-derivative assumed to be smaller than one, are removed. Instead, the time-varying delay is only assumed to be bounded. Finally, numerical examples and its simulations are provided to demonstrate the effectiveness of the derived results.
http://ijfs.usb.ac.ir/article_2112_42c61297c52cf75dfbd00eb52c889040.pdf
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10.22111/ijfs.2015.2112
Chaos
Fuzzy cellular neural networks
Linear matrix inequality
Sampled-data control
Synchronization
P.
Balasubramaniam-pour
true
1
Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram - 624 302, Tamilnadu, India
Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram - 624 302, Tamilnadu, India
Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram - 624 302, Tamilnadu, India
LEAD_AUTHOR
K.
Ratnavelu
true
2
Institute of Mathematical Sciences, Faculty of Science, University
of Malaya - 50603, Kuala Lumpur, Malaysia
Institute of Mathematical Sciences, Faculty of Science, University
of Malaya - 50603, Kuala Lumpur, Malaysia
Institute of Mathematical Sciences, Faculty of Science, University
of Malaya - 50603, Kuala Lumpur, Malaysia
AUTHOR
M.
Kalpana
kalpana.nitt@gmail.com
true
3
Institute of Mathematical Sciences, Faculty of Science, University of
Malaya - 50603, Kuala Lumpur, Malaysia
Institute of Mathematical Sciences, Faculty of Science, University of
Malaya - 50603, Kuala Lumpur, Malaysia
Institute of Mathematical Sciences, Faculty of Science, University of
Malaya - 50603, Kuala Lumpur, Malaysia
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for synchronization control of fuzzy cellular neural networks with mixed time delays, Chinese
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[25] R. Sakthivel, R. Raja and S. Marshal Anthoni, Linear matrix inequality approach to stochastic
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41 (2009), 2387–2393.
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uncertain delayed state neural networks, Chaos Solitons Fractals, 39 (2009), 240–247.
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networks with stochastically hybrid coupling, Neurocomputing, 72 (2009), 3253–3262.
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895–908.
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delays and reaction-diffusion terms, Neurocomputing, 74 (2011), 509–515.
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88
ORIGINAL_ARTICLE
Hierarchical Functional Concepts for Knowledge Transfer among Reinforcement Learning Agents
This article introduces the notions of functional space and concept as a way of knowledge representation and abstraction for Reinforcement Learning agents. These definitions are used as a tool of knowledge transfer among agents. The agents are assumed to be heterogeneous; they have different state spaces but share a same dynamic, reward and action space. In other words, the agents are assumed to have different representations of an environment while having similar actions. The learning framework is $Q$-learning. Each dimension of the functional space is the normalized expected value of an action. An unsupervisedclustering approach is used to form the functional concepts as some fuzzy areas in the functional space. The functional concepts are abstracted further in a hierarchy using the clustering approach. The hierarchical concepts are employed for knowledge transfer among agents. Properties of the proposed approach are tested in a set of case studies. The results show that the approach is very effective in transfer learning among heterogeneous agents especially in the beginning episodes of the learning.
http://ijfs.usb.ac.ir/article_2113_282ba69af4a0a581fecc56675062be1d.pdf
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99
116
10.22111/ijfs.2015.2113
Reinforcement Learning
Transfer Learning
Heterogeneous Agents
Hierarchical Concepts
A.
Mousavi
true
1
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
LEAD_AUTHOR
M.
Nili Ahmadabadi
true
2
Control and Intelligent Processing Center of Excellence,
School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
and School of Cognitive Science, Institute for Research in Fundamental Sciences
(IPM), Tehran, Iran
Control and Intelligent Processing Center of Excellence,
School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
and School of Cognitive Science, Institute for Research in Fundamental Sciences
(IPM), Tehran, Iran
Control and Intelligent Processing Center of Excellence,
School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
and School of Cognitive Science, Institute for Research in Fundamental Sciences
(IPM), Tehran, Iran
AUTHOR
H.
Vosoughpour
true
3
Control and Intelligent Processing Center of Excellence, School
of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
Control and Intelligent Processing Center of Excellence, School
of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
Control and Intelligent Processing Center of Excellence, School
of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
AUTHOR
B. N.
Araabi
true
4
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran and School
of Cognitive Science, Institute for Research in Fundamental Sciences (IPM), Tehran,
Iran
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran and School
of Cognitive Science, Institute for Research in Fundamental Sciences (IPM), Tehran,
Iran
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran and School
of Cognitive Science, Institute for Research in Fundamental Sciences (IPM), Tehran,
Iran
AUTHOR
N.
Zaare
true
5
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
AUTHOR
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[2] T. Dietterich, Hierarchical reinforcement learning with the MAXQ value function decompo-
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sition, Journal of Articial Intelligent Research, 13 (2000), 227-303.
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[3] K. Driessens, J. Ramon and T. Croonenborghs, Transfer learning for reinforcement learn-
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ing through goal and policy parametrization, In ICML Workshop on Structural Knowledge
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Transfer for Machine Learning, (2006), 1-4.
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tems.com.ar/intsyst/index.htm, January (1997).
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[5] G. L. Klir, Uncertainty and information: foundations of generalized information theory,
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John Wiley, Hoboken, NJ (2005).
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[7] G. Konidaris, A. Barto, Autonomous shaping: Knowledge transfer in reinforcement learning,
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In Proceedings of the 23rd international conference on Machine learning, 2006, 489-496.
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[8] A. Lazaric, Knowledge Transfer in Reinforcement Learning, PhD thesis, Politecnico di Mi-
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lano, 2008.
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[9] L. Mihalkova, T. Huynh and R. Mooney, Mapping and revising Markov Logic Networks for
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transfer learning, In Proceedings of AAAI Conference on Articial Intelligence, (2007), 608-614.
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[10] H. Mobahi, M. Nili Ahmadabadi, and B. Nadjar Araabi, A biologically inspired method for
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conceptual imitation using reinforcement learning, Applied Articial Intelligence, 21 (2007),
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[11] R. A. Mollineda, F. J. Ferri and E. Vidal, A cluster-based merging strategy for nearest pro-
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totype classiers, In Proceedings of 15th International Conference on Pattern Recognition
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(ICPR'00), 2 (2000), 755-758.
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[12] G. L. Murphy, The big book of concepts, MIT Press, 2004.
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[13] S. Pan, J. Kwok and Q. Yang, Transfer learning via dimensionality reduction, In Proceedings
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of 23rd AAAI Conference on Articial Intelligence, (2008), 677-682.
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[14] V. Soni, S. Singh, Using hormomorphisms to transfer options across continuous reinforce-
26
ment learning domains, In Proceedings of 21st AAAI Conference on Articial Intelligence,
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(2006), 494-499.
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[15] R. S. Sutton, A. G. Barto, Reinforcement Learning: An Introduction, MIT Press, Cambridge,
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MA (1998).
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[16] F. Tanaka, M. Yamamura, Multitask reinforcement learning on the distribution of MDPs,
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Transactions of the Institute of Electrical Engineers of Japan, 123(5) (2003), 1004-1011.
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[17] M. Taylor, P. Stone, Transfer learning for reinforcement learning domains: a survey, Journal
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of Machine Learning Research, 10 (2009), 1633-1685.
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Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent
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systems, 1 (2008), 283-290.
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[19] M. Taylor, P. Stone, Representation Transfer for Reinforcement Learning, In Proceedings
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of AAAI Fall Symposium on Computational Approaches to Representation Change during
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Learning and Development, Arlington, Virginia, (2007), 78-85.
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[20] M. Taylor, P. Stone and Y. Liu, Value function for RL-based behavior transfer: A comparative
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study, In Proceedings of the AAAI-05 Conference on Articial Intelligence, (2005), 880-885.
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Edition, 2003.
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M., and Serrano, A., editors, Handbook of Research on Machine Learning Applications, IGI
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Bayesian approach, In Proceedings of the 24th International Conference on Machine Learning,
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53
analysis: an introduction, The Exprimental Analysis of Behavior, 3 (2002), 237-248.
54
ORIGINAL_ARTICLE
Non-Newtonian Fuzzy numbers and \related applications
Although there are many excellent ways presenting the principle of the classical calculus, the novel presentations probably leads most naturally to the development of the non-Newtonian calculus. The important point to note is that the non-Newtonian calculus is a self-contained system independent of any other system of calculus. Since this self-contained work is intended for a wide audience, including engineers, scientists and mathematicians. The main purpose of the present paper is to construct of fuzzy numbers with respect to the non-Newtonian calculus and is to give the necessary and sufficient conditions according to the generalization of the notion of fuzzy numbers by using the generating functions. Also we introduce the concept of non-Newtonian fuzzy distance and give some properties regarding convergence of sequences and series of fuzzy numbers with some illustrative examples.
http://ijfs.usb.ac.ir/article_2114_aafefe9d564507d2db1e4749261bbf48.pdf
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117
137
10.22111/ijfs.2015.2114
Non-Newtonian calculus
Fuzzy level sets
Trapezoidal fuzzy numbers
Convergence of fuzzy sequences and series
Ugur
Kadak
ugurkadak@gmail.com
true
1
Department of Mathematics, Bozok University, Yozgat, Turkey
Department of Mathematics, Bozok University, Yozgat, Turkey
Department of Mathematics, Bozok University, Yozgat, Turkey
LEAD_AUTHOR
[1] A. E. Bashirov, E. Kurpnar and A. Ozyapc, Multiplicative calculus and its applications, J.
1
Math. Anal. Appl., 337(1) (2008), 36-48.
2
[2] A. F. Cakmak and F. Basar, Some new results on sequence spaces with respect to non-
3
Newtonian calculus, J. Inequal. Appl., 2012(1) (2012), 228.
4
[3] M. Grossman and R. Katz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA, 1972.
5
[4] M. Grossman, Bigeometric Calculus, Archimedes Foundation, Rockport, Mass, USA, 1983.
6
[5] M. Grossman, The First Nonlinear System of Dierential and Integral Calculus, Mathco,
7
[6] U. Kadak and H. Efe, Matrix transformations between certain sequence spaces over the non-
8
Newtonian complex eld, Sci. World J., 2014 (2014).
9
[7] U. Kadak and M. Ozluk, Generalized Runge-Kutta method with respect to the non-Newtonian
10
calculus, Abstr. Appl. Anal., 2014 (2014).
11
[8] U. Kadak and F. Basar, On Fourier series of fuzzy-valued function, Sci. World J., 2014
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[9] M. Matloka, Sequences of fuzzy numbers, BUSEFAL, 28 (1986), 28-37.
13
[10] E. Msrl, and Y. Gurefe, Multiplicative Adams-Bashforth-Moulton methods, Numer. Algorithms,
14
57(4) (2011), 425-439.
15
[11] M. Stojakovic and Z. Stojakovic, Series of fuzzy sets, Fuzzy Sets Syst., 160(21) (2009),
16
3115{3127.
17
[12] M. Stojakovic and Z. Stojakovic, Addition and series of fuzzy sets, Fuzzy Sets Syst., 83(3)
18
(1996), 341{346.
19
[13] O. Talo and F. Basar, Determination of the duals of classical sets of sequences of fuzzy
20
numbers and related matrix transformations, Comput. Math. Appl., 58(4) (2009), 717-733.
21
[14] O. Talo and F. Basar, Quasilinearity of the classical sets of sequences of the fuzzy numbers
22
and some applications, Taiwanese J. Math., 14(5) (2010), 1799-1819.
23
[15] S. Tekin and F. Basar, Certain sequence spaces over the non-Newtonian complex eld, Abstr.
24
Appl. Anal., 2012 (2013).
25
[16] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338{353.
26
ORIGINAL_ARTICLE
Order intervals in the metric space\ of fuzzy numbers
In this paper, we introduce a function in order to measure the distancebetween two order intervals of fuzzy numbers, and show that this function isa metric. We investigate some properties of this metric, and finally presentan application. We think that this study could provide a more generalframework for researchers studying on interval analysis, fuzzy analysis andfuzzy decision making.
http://ijfs.usb.ac.ir/article_2115_28bfba3b526dd2943ba3639b4db69957.pdf
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139
147
10.22111/ijfs.2015.2115
Fuzzy number
Order interval of fuzzy numbers
Decision making
S.
Aytar
true
1
Faculty of Arts and Sciences, Department of Mathematics, Suleyman
Demirel University, Isparta, Turkey
Faculty of Arts and Sciences, Department of Mathematics, Suleyman
Demirel University, Isparta, Turkey
Faculty of Arts and Sciences, Department of Mathematics, Suleyman
Demirel University, Isparta, Turkey
LEAD_AUTHOR
[1] G. Bortolan and R. Degani, A review of some methods for ranking fuzzy subsets, Fuzzy Sets
1
and Systems, 15 (1985), 1-19.
2
[2] H. Bustince, Indicator of inclusion grade for interval-valued fuzzy sets: Application to ap-
3
proximate reasoning based on interval-valued fuzzy sets, Int. J. Approximate Reasoning, 23
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(2000), 137-209.
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[3] P. T. Chang and E. S. Lee, Fuzzy arithmetic and comparison of fuzzy numbers, In: M.
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Delgado, J. Kacprzyk (Eds.), Fuzzy Optimization, Physica-Verlag, Heidelberg, (1994), 69-82.
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[4] P. Diamond and P. Kloeden, Metric Spaces of Fuzzy Sets: Theory and Applications, World
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Scientic, Singapore, 1994.
9
[5] J-x. Fang and H. Huang, On the level convergence of a sequence of fuzzy numbers, Fuzzy
10
Sets and Systems, 147 (2004), 417-435.
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[6] P. Grzegorzewski, Metrics and orders in space of fuzzy numbers, Fuzzy Sets and Systems, 97
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(1998), 83-94.
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6 (1995), 47-53.
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[11] Q. Zhu and E. S. Lee, Comparison and ranking of fuzzy numbers, in: J. Kacprzyk, M. Fedrizzi
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(Eds.), Fuzzy Regression Analysis, Omnitech Press, Warsaw, (1992), 21-44.
21
ORIGINAL_ARTICLE
A note on soft topological spaces
This paper demonstrates the redundancies concerning the increasing popular ``soft set" approaches to general topologies. It is shown that there is a complement preserving isomorphism (preserving arbitrary $widetilde{bigcup}$ and arbitrary $widetilde{bigcap}$) between the lattice ($mathcal{ST}_E(X,E),widetilde{subset}$) of all soft sets on $X$ with the whole parameter set $E$ as domains and the powerset lattice ($mathcal{P}(Xtimes E),subseteq$) of all subsets of $Xtimes E$. It therefore follows that soft topologies are redundant and unnecessarily complicated in theoretical sense.
http://ijfs.usb.ac.ir/article_2116_72c56938f64cab0a8312fcbb598fa53d.pdf
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149
155
10.22111/ijfs.2015.2116
Soft set
Soft topology
Fu-Gui
Shi
fugushi@bit.edu.cn
true
1
School of Mathematics and Statistics, Beijing Institute of Technology,
5 South Zhongguancun Street, Haidian District, 100081 Beijing, P.R. China
School of Mathematics and Statistics, Beijing Institute of Technology,
5 South Zhongguancun Street, Haidian District, 100081 Beijing, P.R. China
School of Mathematics and Statistics, Beijing Institute of Technology,
5 South Zhongguancun Street, Haidian District, 100081 Beijing, P.R. China
LEAD_AUTHOR
Bin
Pang
pangbin1205@163.com
true
2
School of Mathematics and Statistics, Beijing Institute of Technology, 5
South Zhongguancun Street, Haidian District, 100081 Beijing, P. R. China
School of Mathematics and Statistics, Beijing Institute of Technology, 5
South Zhongguancun Street, Haidian District, 100081 Beijing, P. R. China
School of Mathematics and Statistics, Beijing Institute of Technology, 5
South Zhongguancun Street, Haidian District, 100081 Beijing, P. R. China
AUTHOR
[1] U. Acar, F. Koyuncu and B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59 (2010),
1
3458{3463.
2
[2] H. Aktas and N. C agan, Soft sets and soft groups, Inf. Sci., 177 (2007), 2726{2735.
3
[3] N. C agan, S. Karatas and S. Enginoglu, Soft topology, Comput. Math. Appl., 62 (2011),
4
[4] N. C agan and S. Enginoglu, Soft set theory and uni-int decision making, Eur. J. Oper. Res.,
5
207 (2010), 848{855.
6
[5] B. Chen, Soft semi-open sets and related properties in soft topological spaces, Appl. Math.
7
Inform. Sci., 7 (2013), 287{294.
8
[6] F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Comput. Math. Appl., 56 (2008), 2621{2628.
9
[7] J. Gutierrez Garcia and S. E. Rodabaugh, Order-theoretic, topological, categorical redundan-
10
cies of interval-valued sets, grey sets, vague sets, interval-valued intuitionistic sets, intu-
11
itionistic fuzzy sets and topologies, Fuzzy Sets Syst., 156 (2005), 445{484.
12
[8] S. Hussain and B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl.,
13
62 (2011), 4058{4067.
14
[9] Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl., 56 (2008), 1408{1413.
15
[10] Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras,
16
Inf. Sci., 178 (2008), 2466{2475.
17
[11] P. K. Maji, R. Biswas and R. Roy, An application of soft sets in a decision making problem,
18
Comput. Math. Appl., 44 (2002), 1077{1083.
19
[12] P. K. Maji, R. Biswas and R. Roy, Soft set thoery, Comput. Math. Appl., 45 (2003), 555{562.
20
[13] W. K. Min, A note on soft topological spaces, Comput. Math. Appl., 62 (2011), 3524{3528.
21
[14] D. Molodtsov, Soft set theory rst results, Comput. Math. Appl., 37 (1999), 19{31.
22
[15] B. V. S. T. Sai and S. Kumar, On soft semi-open sets and soft semi-topology, Int. J. Math.
23
Arch., 4(4) (2013), 114-117.
24
[16] M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl., 61 (2011), 1786{
25
[17] F. G. Shi and B. Pang, Redundancy of fuzzy soft topological spaces, J. Intell. Fuzzy Syst., 27
26
(2014), 1757{1760.
27
ORIGINAL_ARTICLE
Persian-translation vol. 12, no.5, October 2015
http://ijfs.usb.ac.ir/article_2643_0921b835f0d81e0b0abec67977f149f7.pdf
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159
165
10.22111/ijfs.2015.2643