University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
5
2015
10
01
Cover vol. 12, no.5, October 2015
0
EN
10.22111/ijfs.2015.2642
http://ijfs.usb.ac.ir/article_2642.html
http://ijfs.usb.ac.ir/article_2642_e38b90e7cce4505fe17c4f2f1a961d07.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
5
2015
10
30
Functorial semantics of topological theories
1
43
EN
Sergey A.
Solovyov
Institute of Mathematics, Faculty of Mechanical Engineering,
Brno University of Technology, Technicka 2896/2, 616 69 Brno, Czech Republic
sergejs.solovjovs@lumii.lv
10.22111/ijfs.2015.2110
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.
Algebra,Algebraic theory,Comma category,Categorically-algebraic topology,Poslat topology,Powerset theory,Topological system,Topological theory,Variety
http://ijfs.usb.ac.ir/article_2110.html
http://ijfs.usb.ac.ir/article_2110_e9eb0f65766fb9dfb4d98bd6fea53fbc.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
5
2015
10
30
CVaR Reduced Fuzzy Variables and Their Second Order Moments
45
75
EN
Xue-Jie
Bai
College of Management, Hebei University, Baoding 071002, Hebei, China and College of Science, Agricultural University of Hebei, Baoding 071001, Hebei, China
Yan-Kui
Liu
College of Management, Hebei University, Baoding 071002, Hebei,
China
10.22111/ijfs.2015.2111
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.
Credibilistic value-at-risk,Reduced fuzzy variable,Parametric possibility distribution,Second order moment
http://ijfs.usb.ac.ir/article_2111.html
http://ijfs.usb.ac.ir/article_2111_ae9c29c1bd509c95fc8928b9778558da.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
5
2015
10
30
Linear matrix inequality approach for synchronization of chaotic fuzzy cellular neural networks with discrete and unbounded distributed delays based on sampled-data control
77
98
EN
P.
Balasubramaniam-pour
Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram - 624 302, Tamilnadu, India
K.
Ratnavelu
Institute of Mathematical Sciences, Faculty of Science, University
of Malaya - 50603, Kuala Lumpur, Malaysia
M.
Kalpana
Institute of Mathematical Sciences, Faculty of Science, University of
Malaya - 50603, Kuala Lumpur, Malaysia
kalpana.nitt@gmail.com
10.22111/ijfs.2015.2112
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.
Chaos,Fuzzy cellular neural networks,Linear matrix inequality,Sampled-data control,Synchronization
http://ijfs.usb.ac.ir/article_2112.html
http://ijfs.usb.ac.ir/article_2112_42c61297c52cf75dfbd00eb52c889040.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
5
2015
10
30
Hierarchical Functional Concepts for Knowledge Transfer among Reinforcement Learning Agents
99
116
EN
A.
Mousavi
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
M.
Nili Ahmadabadi
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
H.
Vosoughpour
Control and Intelligent Processing Center of Excellence, School
of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
B. N.
Araabi
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
N.
Zaare
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
10.22111/ijfs.2015.2113
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.
Reinforcement Learning,Transfer Learning,Heterogeneous Agents,Hierarchical Concepts
http://ijfs.usb.ac.ir/article_2113.html
http://ijfs.usb.ac.ir/article_2113_282ba69af4a0a581fecc56675062be1d.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
5
2015
10
30
Non-Newtonian Fuzzy numbers and related applications
117
137
EN
Ugur
Kadak
Department of Mathematics, Bozok University, Yozgat, Turkey
ugurkadak@gmail.com
10.22111/ijfs.2015.2114
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.
Non-Newtonian calculus,Fuzzy level sets,Trapezoidal fuzzy numbers,Convergence of fuzzy sequences and series
http://ijfs.usb.ac.ir/article_2114.html
http://ijfs.usb.ac.ir/article_2114_aafefe9d564507d2db1e4749261bbf48.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
5
2015
10
30
Order intervals in the metric space of fuzzy numbers
139
147
EN
S.
Aytar
Faculty of Arts and Sciences, Department of Mathematics, Suleyman
Demirel University, Isparta, Turkey
10.22111/ijfs.2015.2115
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.
Fuzzy number,Order interval of fuzzy numbers,Decision making
http://ijfs.usb.ac.ir/article_2115.html
http://ijfs.usb.ac.ir/article_2115_28bfba3b526dd2943ba3639b4db69957.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
5
2015
10
30
A note on soft topological spaces
149
155
EN
Fu-Gui
Shi
School of Mathematics and Statistics, Beijing Institute of Technology,
5 South Zhongguancun Street, Haidian District, 100081 Beijing, P.R. China
fugushi@bit.edu.cn
Bin
Pang
School of Mathematics and Statistics, Beijing Institute of Technology, 5
South Zhongguancun Street, Haidian District, 100081 Beijing, P. R. China
pangbin1205@163.com
10.22111/ijfs.2015.2116
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.
Soft set,Soft topology
http://ijfs.usb.ac.ir/article_2116.html
http://ijfs.usb.ac.ir/article_2116_72c56938f64cab0a8312fcbb598fa53d.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
5
2015
10
29
Persian-translation vol. 12, no.5, October 2015
159
165
EN
10.22111/ijfs.2015.2643
http://ijfs.usb.ac.ir/article_2643.html
http://ijfs.usb.ac.ir/article_2643_0921b835f0d81e0b0abec67977f149f7.pdf