University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
Cover vol. 12, no.2, April 2015
0
EN
10.22111/ijfs.2015.2648
http://ijfs.usb.ac.ir/article_2648.html
http://ijfs.usb.ac.ir/article_2648_7da56e08e1a4fb3a8299936955a993e7.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
A TS Fuzzy Model Derived from a Typical Multi-Layer Perceptron
1
21
EN
A.
Kalhor
System Engineering and Mechatronics Group, Faculty of New Sciences
and Technologies, University of Tehran, Tehran, Iran
akalhor@ut.ac.ir
B. N.
Aarabi
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
araabi@ut.ac.ir
C.
Lucas
Control and Intelligent Processing Center of Excellence, School of
Electrical and Computer Engineering, University of Tehran, Tehran, Iran
lucas@ut.ac.ir
B.
Tarvirdizadeh
System Engineering and Mechatronics Group, Faculty of New Sci-
ences and Technologies, University of Tehran, Tehran, Iran
bahram@ut.ac.ir
10.22111/ijfs.2015.1979
In this paper, we introduce a Takagi-Sugeno (TS) fuzzy model which is derived from a typical Multi-Layer Perceptron Neural Network (MLP NN). At first, it is shown that the considered MLP NN can be interpreted as a variety of TS fuzzy model. It is discussed that the utilized Membership Function (MF) in such TS fuzzy model, despite its flexible structure, has some major restrictions. After modifying the MF, we introduce a TS fuzzy model whose MFs are tunable near and far from focal points, separately. To identify such TS fuzzy model, an incremental learning algorithm, based on an efficient space partitioning technique, is proposed. Through an illustrative example, the methodology of the learning algorithm is explained. Next, through two case studies: approximation of a nonlinear function for a sun sensor and identification of a pH neutralization process, the superiority of the introduced TS fuzzy model in comparison to some other TS fuzzy models and MLP NN is shown.
Takagi-Sugeno fuzzy model,Multi layer perceptron,Tunable membership functions,Nonlinear function approximation,pH neutralization process
http://ijfs.usb.ac.ir/article_1979.html
http://ijfs.usb.ac.ir/article_1979_0f5c1f01dfef9d988a11fdcb9b404174.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
Modeling of Epistemic Uncertainty in Reliability Analysis of Structures Using a Robust Genetic Algorithm
23
40
EN
Mansour
Bagheri
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
mnsrbagheri@gmail.com
Mahmoud
Miri
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
mmiri@eng.usb.ac.ir
Naser
Shabakhty
Department of Civil Engineering, University of Sistan and Baluchestan, Zahedan, Iran
shabakhty@eng.usb.ac.ir
10.22111/ijfs.2015.1980
In this paper the fuzzy structural reliability index was determined through modeling epistemic uncertainty arising from ambiguity in statistical parameters of random variables. The First Order Reliability Method (FORM) has been used and a robust genetic algorithm in the alpha level optimization method has been proposed for the determination of the fuzzy reliability index. The sensitivity level of fuzzy response due to the introduced epistemic uncertainty was also measured using the modified criterion of Shannon entropy. By introducing bounds of uncertainty, the fuzzy response obtained from the proposed method presented more realistic estimation of the structure reliability compared to classic methods. This uncertainty interval is of special importance in concrete structures since the quality of production and implementation of concrete varies in different cross sections in reality. The proposed method is implementable in reliability problems in which most of random variables are fuzzy sets and in problems containing non-linear limit state functions and provides a precise acceptable response. The capabilities of the proposed method were demonstrated using different examples. The results indicated the accuracy of the proposed method and showed that classical methods like FORM cover only special case of the proposed method.
Fuzzy reliability index,Alpha level optimization method,Genetic Algorithm,First order reliability method
http://ijfs.usb.ac.ir/article_1980.html
http://ijfs.usb.ac.ir/article_1980_705e7461f624d40c8f31e42874bb83cb.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
EQ-logics with delta connective
41
61
EN
M.
Dyba
University of Ostrava, NSC IT4Innovations, 30. dubna 22, 702 00 Ostrava,
Czech Republic
martin.dyba@osu.cz
V.
Novak
University of Ostrava, NSC IT4Innovations, 30. dubna 22, 702 00 Ostrava,
Czech Republic
vilem.novak@osu.cz
10.22111/ijfs.2015.1981
In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binaryoperations of fuzzy equality and multiplication. EQ-algebra generalizesresiduated lattices, namely, every residuated lattice is an EQ-algebra but notvice-versa.In this paper, we introduce additional connective $logdelta$ in EQ-logics(analogous to Baaz delta connective in MTL-algebra based fuzzy logics) anddemonstrate that the resulting logic has again reasonable properties includingcompleteness. Introducing $Delta$ in EQ-logic makes it possible to prove alsogeneralized deduction theorem which otherwise does not hold in EQ-logics weakerthan MTL-logic.
EQ-algebra,EQ-logic,Equational logic,Delta connective,Generalized deduction theorem
http://ijfs.usb.ac.ir/article_1981.html
http://ijfs.usb.ac.ir/article_1981_f9c205b6a230d24728542018f1b3f176.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
Bifuzzy core of fuzzy automata
63
73
EN
S. P.
Tiwari
Department of Applied Mathematics, Indian School of Mines, Dhanbad
826004, India
sptiwarimaths@gmail.com
Anupam K.
Singh
Department of Applied Mathematics, Indian School of Mines,
Dhanbad-826004, India
anupam09.bhu@gmail.com
Shambhu
Sharan
Department of Mathematics, School of Applied Sciences, KIIT Uni-
versity, Bhubaneswar-751024, India
ssharanfma@kiit.ac.in
Vijay K.
Yadav
Department of Applied Mathematics, Indian School of Mines, Dhanbad
826004, India
10.22111/ijfs.2015.1982
The purpose of the present work is to introduce the concept of bifuzzy core of a fuzzy automaton, which induces a bifuzzy topology on the state-set of this fuzzy automaton. This is shown that this bifuzzy topology can be used to characterize the concepts such as bifuzzy family of submachines, bifuzzy separable family and bifuzzy retrievable family of a fuzzy automaton.
Fuzzy automata,Bifuzzy source,Bifuzzy successor,Bifuzzy core,Bifuzzy topology
http://ijfs.usb.ac.ir/article_1982.html
http://ijfs.usb.ac.ir/article_1982_23e6f3744366279e9ec0ca3d46e6e982.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
Existence and uniqueness of the solution of nonlinear fuzzy Volterra integral equations
75
86
EN
T.
Allahviranloo
Department of mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
tofigh@allahviranloo.com
P.
Salehi
Department of mathematics, Hamedan Branch, Islamic Azad University,
Hamedan, Iran
parhamsalehi@rocketmail.com
M.
Nejatiyan
Department of mathematics, Science and Research Branch, Islamic
Azad University, Tehran, Iran
maryamnejatiyan@yahoo.com
10.22111/ijfs.2015.1983
In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.
Fuzzy numbers,Fuzzy Volterra integral equations,Existence and uniqueness
http://ijfs.usb.ac.ir/article_1983.html
http://ijfs.usb.ac.ir/article_1983_4e17db286a759c153db5a9aa92c5c1e3.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
Existence and uniqueness of the solution of fuzzy-valued integral equations of mixed type
87
94
EN
R.
Ezzati
Department of Mathematics, Karaj Branch, Islamic Azad University,
Karaj, Iran
ezati@kiau.ac.ir
F.
Mokhtarnejad
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
fa_mokhtar@yahoo.com
10.22111/ijfs.2015.1984
In this paper, existence theorems for the fuzzy Volterra-Fredholm integral equations of mixed type (FVFIEMT) involving fuzzy number valued mappings have been investigated. Then, by using Banach's contraction principle, sufficient conditions for the existence of a unique solution of FVFIEMT are given. Finally, illustrative examples are presented to validate the obtained results.
Fuzzy Volterra-Fredholm integral equation,Two-dimensional integral equation,Fuzzy integral equations of mixed type,Fuzzy valued function
http://ijfs.usb.ac.ir/article_1984.html
http://ijfs.usb.ac.ir/article_1984_9ce4534f838ac7a99de3ae4a02061f23.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
Fuzzy resolvent equation with $H(cdot,cdot)$-$phi$-$eta$-accretive operator in Banach spaces
95
106
EN
Rais
Ahmad
Department of Mathematics, Aligarh Muslim University, Aligarh
202002, India
raisain_123@rediffmail.com
Mohd
Dilshad
Department of Mathematics, Aligarh Muslim University, Aligarh
202002, India
mdilshaad@gmail.com
10.22111/ijfs.2015.1985
In this paper, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and $H(cdot,cdot)$-$phi$-$eta$-accretive operator in realĀ uniformly smooth Banach spaces. It is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. This equivalence is used to define an iterative algorithm for solving fuzzy resolvent equation. Some examples are given.
Fuzzy variational-like inclusion,Fuzzy resolvent equation,$H(cdot,cdot)$-$phi$-$eta$-accretive operator,Algorithm,Fixed point
http://ijfs.usb.ac.ir/article_1985.html
http://ijfs.usb.ac.ir/article_1985_86f566343f7b89986c214aecb2f7d718.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
Classifying fuzzy normal subgroups of finite groups
107
115
EN
Marius
Tarnauceanu
Faculty of Mathematics, "Al.I. Cuza" University, Iasi, Romania
tarnauc@uaic.ro
10.22111/ijfs.2015.1986
In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.
Fuzzy normal subgroups,Chains of normal
subgroups,Maximal chains of normal subgroups,Symmetric groups,Dihedral groups
http://ijfs.usb.ac.ir/article_1986.html
http://ijfs.usb.ac.ir/article_1986_41edad298512bef030d02e273bcb6a1c.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
Numerical solutions of nonlinear fuzzy Fredholm integro-differential equations of the second kind
117
127
EN
M.
Mosleh
Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran
mosleh@iaufb.ac.ir
M.
Otadi
Department of Mathematics, Firoozkooh Branch, Islamic Azad University,
Firoozkooh, Iran
mahmoodotadi@yahoo.com
10.22111/ijfs.2015.1987
In this paper, we use parametric form of fuzzy number, then aniterative approach for obtaining approximate solution for a classof nonlinear fuzzy Fredholmintegro-differential equation of the second kindis proposed. This paper presents a method based on Newton-Cotesmethods with positive coefficient. Then we obtain approximatesolution of the nonlinear fuzzy integro-differential equations by an iterativeapproach.
Nonlinear fuzzy integro-differential equations,Newton-Cotes methods
http://ijfs.usb.ac.ir/article_1987.html
http://ijfs.usb.ac.ir/article_1987_0cf46298a686ec0a96c8d069d42f41f9.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
Generated $textbf{textit{L}}$-subgroup of an $textbf{textit{L}}$-group
129
136
EN
Naseem
Ajmal
Department of Mathematics, Zakir Husain Delhi College,, J.N.Marg,
University of Delhi, Delhi-110006, India
nasajmal@yahoo.com
Iffat
Jahan
Department of Mathematics, Ramjas College,, University of Delhi,,
Delhi-110007, India
ij.umar@yahoo.com
10.22111/ijfs.2015.1988
In this paper, we extend the construction of a fuzzy subgroup generated by a fuzzy subset to $L$-setting. This construction is illustrated by an example. We also prove that for an $L$-subset of a group, the subgroup generated by its level subset is the level subset of the subgroup generated by that $L$-subset provided the given $L$-subset possesses sup-property.
$L$-algebra,$L$-subgroup,Normal $L$-subgroup,Generated $L$-subgroup
http://ijfs.usb.ac.ir/article_1988.html
http://ijfs.usb.ac.ir/article_1988_1a3e3cd32dc886edfac691c6b2b2e9e0.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
A New Approach to Caristi's Fixed Point Theorem on Non-Archimedean Fuzzy Metric Spaces
137
143
EN
S.
Sedghi
Department of Mathematics, Qaemshahr Branch, Islamic Azad University,
Qaemshahr, Iran
sedghi.gh@qaemshahriau.ac.ir
N.
Shobkolaei
Department of Mathematics, Babol Branch, Islamic Azad University,
Babol, Iran
nabi_shobe@yahoo.comg
I.
Altun
Department of Mathematics, Faculty of Science and Arts, Kirikkale Uni-
versity, 71450 Yahsihan, Kirikkale, Turkey
ishakaltun@yahoo.com
10.22111/ijfs.2015.1989
In the present paper, we give a new approach to Caristi's fixed pointtheorem on non-Archimedean fuzzy metric spaces. For this we define anordinary metric $d$ using the non-Archimedean fuzzy metric $M$ on a nonemptyset $X$ and we establish some relationship between $(X,d)$ and $(X,M,ast )$%. Hence, we prove our result by considering the original Caristi's fixedpoint theorem.
Fixed point,Caristi map,Fuzzy metric space
http://ijfs.usb.ac.ir/article_1989.html
http://ijfs.usb.ac.ir/article_1989_f8d6aae87a58b7c8804d05459ea70ac5.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
2
2015
04
29
Persian-translation vol. 12, no.2, April 2015
147
157
EN
10.22111/ijfs.2015.2649
http://ijfs.usb.ac.ir/article_2649.html
http://ijfs.usb.ac.ir/article_2649_c4b7501bfa4858c0dbecc382a6043f85.pdf