University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
3
2015
06
01
Cover vol. 12, no.3, June 2015
0
EN
10.22111/ijfs.2015.2646
http://ijfs.usb.ac.ir/article_2646.html
http://ijfs.usb.ac.ir/article_2646_1c9f91d00aec73fbd39d7a287b238786.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
3
2015
06
30
Admissibility analysis for discrete-time singular systems with time-varying delays by adopting the state-space Takagi-Sugeno fuzzy model
1
16
EN
P.
Balasubramaniam -pour
Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram - 624 302, Tamilnadu, India
balugru@gmail.com
L.
Jarina Banu
Department of Mathematics, Gandhigram Rural Institute - Deemed
University, Gandhigram - 624 302, Tamilnadu, India
ljarina88@gmail.com
10.22111/ijfs.2015.2016
This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the lower and upper delay bounds. Finally, numerical examples are provided to substantiate the theoretical results.
Discrete-time Singular system,Takagi-Sugeno fuzzy systems,Stability,Lyapunov-Krasovskii functional,Linear Matrix Inequality (LMI)
http://ijfs.usb.ac.ir/article_2016.html
http://ijfs.usb.ac.ir/article_2016_669277d9b51e99a79677006ff39992f9.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
3
2015
06
30
Fuzzy Risk Analysis Based on Ranking of Fuzzy Numbers Via New Magnitude Method
17
29
EN
T.
Hajjari
Mathematics Department, Firoozkooh Branch of Islamic Azad University,
Firoozkooh, Iran
tayebehajjari@iaufb.ac.ir
10.22111/ijfs.2015.2017
Ranking fuzzy numbers plays a main role in many applied models inreal world and in particular decision-making procedures. In manyproposed methods by other researchers may exist some shortcoming.The most commonly used approaches for ranking fuzzy numbers isbased on defuzzification method. Many ranking fuzzy numberscannot discriminate between two symmetric fuzzy numbers withidentical core. In 2009, Abbasbandy and Hajjari proposed anapproach for ranking normal trapezoidal fuzzy numbers, whichcomputed the magnitude of fuzzy numbers namely ``Mag" method.Then Hajjari extended it for non-normal trapezoidal fuzzy numbersand also for all generalized fuzzy numbers. However, thesemethods have the weakness that we mentioned above. Moreover, theresult is not consistent with human intuition in this case.Therefore, we are going to present a new method to overcome thementioned weakness. In order to overcome the shortcoming, a newmagnitude approach for ranking trapezoidal fuzzy numbers based onminimum and maximum points and the value of fuzzy numbers isgiven. The new method is illustrated by some numerical examplesand in particular, the results of ranking by the proposed methodand some common and existing methods for ranking fuzzy numbers iscompared to verify the advantages of presented method.
Decision-Making,Magnitude,Fuzzy numbers,Ranking
http://ijfs.usb.ac.ir/article_2017.html
http://ijfs.usb.ac.ir/article_2017_2a119e1745d62f0454344e08d761a5e9.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
3
2015
06
30
Fixed Fuzzy Points of Fuzzy Mappings in Hausdorff Fuzzy Metric Spaces with Application
31
45
EN
Calogero
Vetro
Dipartimento di Matematica e Informatica, Universita degli Studi
di Palermo, Via Archirafi 34, 90123 Palermo, Italy
calogero.vetro@unipa.it
Mujahid
Abbas
Department of Mathematics and Applied Mathematics, University of
Pretoria, Lynnwood road, Pretoria 0002, South Africa, Department of Mathematics,
Syed Babar Ali School of Science and Engineering (SBASSE), Lahore University of
Management Sciences (LUMS), Lahore, 54792, Pakistan
mujahid.abbas@up.ac.za
Basit
Ali
Department of Mathematics, Syed Babar Ali School of Science and Engi-
neering (SBASSE), Lahore University of Management Sciences (LUMS), Lahore, 54792,
Pakistan
basit.aa@gmail.com
10.22111/ijfs.2015.2018
Recently, Phiangsungnoen et al. [J. Inequal. Appl. 2014:201 (2014)] studied fuzzy mappings in the framework of Hausdorff fuzzy metric spaces.Following this direction of research, we establish the existence of fixed fuzzy points of fuzzy mappings. An example is given to support the result proved herein; we also present a coincidence and common fuzzy point result. Finally, as an application of our results, we investigate the existence of solution for somerecurrence relations associated to the analysis of quicksort algorithms.
Fuzzy metric space,Fuzzy mapping,Fixed fuzzy point,Quicksort algorithm
http://ijfs.usb.ac.ir/article_2018.html
http://ijfs.usb.ac.ir/article_2018_344dee53e41664d8f01d067965c0e8b6.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
3
2015
06
30
Some classes of statistically convergent sequences of fuzzy numbers generated by a modulus function
47
55
EN
U.
Cakan
Department of Mathematics, Nevsehir Hac Bektas Veli University, Nevsehir-
Turkey
umitcakan@gmail.com
Y.
Altin
Department of Mathematics, Firat University, Elazig-Turkey
yaltin23@yahoo.com
10.22111/ijfs.2015.2019
The purpose of this paper is to generalize the concepts of statisticalconvergence of sequences of fuzzy numbers defined by a modulus functionusing difference operator $Delta$ and give some inclusion relations.
Sequence of fuzzy numbers,Statistical convergence,Modulus function
http://ijfs.usb.ac.ir/article_2019.html
http://ijfs.usb.ac.ir/article_2019_acdb38af96e8a2b1a9eb92353d97a5e2.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
3
2015
06
30
Categorically-algebraic topology and its applications
57
94
EN
Sergey A.
Solovyov
Institute of Mathematics, Faculty of Mechanical Engineering,
Brno University of Technology, Technicka 2896/2, 616 69 Brno, Czech Republic and
Institute of Mathematics and Computer Science, University of Latvia, Raina bulvaris
29, LV-1459 Riga, Latvia
sergejs.solovjovs@lumii.lv
10.22111/ijfs.2015.2020
This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respective categories of topological structures are topological over their ground categories. The theory also extends the notion of topological system of S.~Vickers (and its numerous many-valued modifications of J.~T.~Denniston, A.~Melton and S.~E.~Rodabaugh), and shows that the categories of catalg topological structures are isomorphic to coreflective subcategories of the categories of catalg topological systems. This extension initiates a new approach to soft topology, induced by the concept of soft set of D.~Molodtsov, and currently pursued by various researchers.
Categorically-algebraic topology,Lattice-valued topology,Soft topology,Topological category,Topological system,Topological theory
http://ijfs.usb.ac.ir/article_2020.html
http://ijfs.usb.ac.ir/article_2020_3928dce38a41f1ffb43078cccd8ae550.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
3
2015
06
30
Convergence, Consistency and Stability in Fuzzy Differential Equations
95
112
EN
R.
Ezzati
Department of Mathematics, Karaj Branch, Islamic Azad University,
Karaj, Iran
ezati@kiau.ac.ir
K.
Maleknejad
Department of Mathematics, Karaj Branch, Islamic Azad University,
Karaj, Iran
maleknejad@iust.ac.ir
S.
Khezerloo
Department of Mathematics, Islamic Azad University - South Tehran
Branch, Tehran, Iran
s_khezerloo@azad.ac.ir
M.
Khezerloo
Department of Mathematics, Institute for Advanced Studies in Basic
Sciences(IASBS), P.O. BOX 45195-1159, Zanjan, Iran
khezerloo@iasbs.ac.ir
10.22111/ijfs.2015.2021
In this paper, we consider First-order fuzzy differential equations with initial value conditions. The convergence, consistency and stability of difference method for approximating the solution of fuzzy differential equations involving generalized H-differentiability, are studied. Then the local truncation error is defined and sufficient conditions for convergence, consistency and stability of difference method are provided and fuzzy stiff differential equation and one example are presented to illustrate the accuracy and capability of our proposed concepts.
Consistence,Stability,Local truncation error,Generalized differentiability,Fuzzy stiff differential equation
http://ijfs.usb.ac.ir/article_2021.html
http://ijfs.usb.ac.ir/article_2021_27827fb7f621d2c20415fb8f401902e5.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
3
2015
06
29
Interval Type-2 Fuzzy Rough Sets and Interval Type-2 Fuzzy Closure Spaces
113
125
EN
Shambhu
Sharan
School of Advanced Sciences, VIT University,Vellore-632014,Tamil
Nadu, India
shambhupuremaths@gmail.com
S. P.
Tiwari
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, India
sptiwarimaths@gmail.com
V. K.
Yadav
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, India
vijayyadav3254@gmail.com
10.22111/ijfs.2015.2022
The purpose of the present work is to establish a one-to-one correspondence between the family of interval type-2 fuzzy reflexive/tolerance approximation spaces and the family of interval type-2 fuzzy closure spaces.
Interval type-2 fuzzy set,Interval type-2
fuzzy rough set,Interval type-2 fuzzy reflexive approximation
space,Interval type-2 fuzzy tolerance approximation space,Interval type-2 fuzzy closure space,Interval type-2 fuzzy
topology
http://ijfs.usb.ac.ir/article_2022.html
http://ijfs.usb.ac.ir/article_2022_3ededbfe97b2d5a0693ea6c5302fba77.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
3
2015
06
30
Boundedness of linear order-homomorphisms in $L$-topological vector spaces
127
135
EN
Hua-Peng
Zhang
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
huapengzhang@163.com
Jin-Xuan
Fang
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
jxfang@njnu.edu.cn
10.22111/ijfs.2015.2023
A new definition of boundedness of linear order-homomorphisms (LOH)in $L$-topological vector spaces is proposed. The new definition iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprinciple in $L$-topological vector spaces is established in thesense of a new definition of uniform boundedness for a family ofLOHs.
$L$-topological vector space,Linear order-homomorphism,Bounde-\dness
http://ijfs.usb.ac.ir/article_2023.html
http://ijfs.usb.ac.ir/article_2023_6994345f4f77c7f78c179cfc9a2c1c83.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
3
2015
06
30
Distinct Fuzzy Subgroups of a Dihedral Group of Order $2pqrs$ for Distinct Primes $p, , q, , r$ and $s$
137
149
EN
Babington
Makamba
Department of Mathematics, University of Fort Hare, Alice
5700 , Eastern Cape , South Africa
bmakamba@ufh.ac.za
Odilo
Ndiweni
Department of Mathematics, University of Fort Hare, Alice 5700 ,
Eastern Cape , South Africa
ondiweni@ufh.ac.za
10.22111/ijfs.2015.2024
In this paper we classify fuzzy subgroups of the dihedral group $D_{pqrs}$ for distinct primes $p$, $q$, $r$ and $s$. This follows similar work we have done on distinct fuzzy subgroups of some dihedral groups.We present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equivalence and isomorphism. Some results presented here hold for any dihedral group of order $2n$ where $n$ is a product of any number of distinct primes.
Dihedral group,Equivalence,Isomorphism,Fuzzy subgroup,Maximal chain,Keychain,Distinguishing factor
http://ijfs.usb.ac.ir/article_2024.html
http://ijfs.usb.ac.ir/article_2024_a19538744d9dc0e80b3a8fe6a94fe7a9.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
3
2015
06
30
Solvable $L$-subgroup of an $L$-group
151
166
EN
Iffat
Jahan
Department of Mathematics, Ramjas College,, University of Delhi,,
Delhi-110007, India
ij.umar@yahoo.com
Naseem
Ajmal
Department of Mathematics, Zakir Husain Delhi College,, J.N.Marg,
University of Delhi, Delhi-110006, India
nasajmal@yahoo.com
10.22111/ijfs.2015.2025
In this paper, we study the notion of solvable $L$-subgroup of an $L$-group and provide its level subset characterization and this justifies the suitability of this extension. Throughout this work, we have used normality of an $L$-subgroup of an $L$-group in the sense of Wu rather than Liu.
$L$-algebra,$L$-subgroup,Normal $L$-subgroup,Solvable $L$-subgroup,Derived series,Solvable series
http://ijfs.usb.ac.ir/article_2025.html
http://ijfs.usb.ac.ir/article_2025_54e716181d9591e118bc01071c130667.pdf
University of Sistan and Baluchestan
Iranian Journal of Fuzzy Systems
1735-0654
12
3
2015
06
29
Persian-translation vol. 12, no.3, June 2015
169
178
EN
10.22111/ijfs.2015.2647
http://ijfs.usb.ac.ir/article_2647.html
http://ijfs.usb.ac.ir/article_2647_57c7fc92eea1f99ca53467fa3f4fe555.pdf