ORIGINAL_ARTICLE
Cover vol. 12, no.3, June 2015
http://ijfs.usb.ac.ir/article_2646_1c9f91d00aec73fbd39d7a287b238786.pdf
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10.22111/ijfs.2015.2646
ORIGINAL_ARTICLE
Admissibility analysis for discrete-time singular systems with time-varying delays by adopting the state-space Takagi-Sugeno fuzzy model
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.
http://ijfs.usb.ac.ir/article_2016_669277d9b51e99a79677006ff39992f9.pdf
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10.22111/ijfs.2015.2016
Discrete-time Singular system
Takagi-Sugeno fuzzy systems
Stability
Lyapunov-Krasovskii functional
Linear Matrix Inequality (LMI)
P.
Balasubramaniam -pour
balugru@gmail.com
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
L.
Jarina Banu
ljarina88@gmail.com
true
2
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
AUTHOR
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1
via delay partitioning approach, Fuzzy Sets Syst., 185(1) (2011), 83-94.
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systems in biomedical robotics, Int. J. Inf. Syst. Sci., 6(2) (2010), 128-141.
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criterion for a class of nonlinear singular systems, Nonlinear Anal. B: Real World Appl.,
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12(2) (2011), 1152-1162.
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[7] M. Fang, Delay-dependent stabililty analysis for discrete singular systems with time-varying
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delays, Acta Automat. Sinica, 36(5) (2010), 751-755.
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Signal Process., 92(12) (2012), 3010-3025.
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(2005), 155-165.
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varying delay and linear fractional uncertainty, Int. J. Autom. Comput., 9(1) (2012), 8-15.
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systems with mixed time delays, Asian J. Control, 14(1) (2012), 1411-1421.
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[13] J. Li, H. Su, Z. Wu and J. Chu, Less conservative robust stability criteria for uncertain
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discrete stochastic singular systems with time-varying delay, Int. J. Syst. Sci., 44(3) (2013),
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63
ORIGINAL_ARTICLE
Fuzzy Risk Analysis Based on Ranking of Fuzzy Numbers Via New Magnitude Method
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.
http://ijfs.usb.ac.ir/article_2017_2a119e1745d62f0454344e08d761a5e9.pdf
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10.22111/ijfs.2015.2017
Decision-Making
Magnitude
Fuzzy numbers
Ranking
T.
Hajjari
tayebehajjari@iaufb.ac.ir
true
1
Mathematics Department, Firoozkooh Branch of Islamic Azad University,
Firoozkooh, Iran
Mathematics Department, Firoozkooh Branch of Islamic Azad University,
Firoozkooh, Iran
Mathematics Department, Firoozkooh Branch of Islamic Azad University,
Firoozkooh, Iran
LEAD_AUTHOR
[1] S. Abbasbandy and B. Asady, Ranking of fuzzy numbers by sign distance, Inform. Sci., 176
1
(2006), 2405-2416.
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3
Comput. Math. Appl., 57 (2009), 413-419.
4
[3] S. Abbasbandy and T. Hajjari, An improvement on centroid point method for ranking of
5
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sets, Automatica, 13 (1977), 47-58.
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and Systems, 15 (1985), 1-19.
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(1981), 163-171.
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fuzzy numbers, Applied Intelligence, 26 (2007), 1-11.
24
[13] S. M. Chen and J. H. Chen, Fuzzy risk analysis based on ranking generalized fuzzy numbers
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with dierent heights and dierent spreads, Expert Systs with Applications, 36 (2009), 6833-
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[14] S. J Chen and C. L. Hwang, Fuzzy multiple attribute decision making, Spinger-Verlag, Berlin,
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[15] S. M. Chen and K. Sanguansat, Analysing fuzzy risk based on a new fuzzy ranking generalized
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fuzzy numbers with dierent heights and dierent spreads, Expert Systs with Applications,
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38 (2011), 2163-2171.
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orginal point, Comput. Math. Appl., 43 (2002), 11-117.
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[20] L. Q. Dat, F. Y. Vincent and S. Y chou, An improved ranking method for fuzzy numbers
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based on the centroid-index, International Fuzzy Systems, 14 (3) (2012), 413-419.
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integral value, J. Math. Stat. Allied Fields, 1(2) (2007), 2070-2077.
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and Applied Sciences., 5(1) (2011), 62-69.
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values, Appl. Soft Comput., 14 (2014), 603-608.
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99
ORIGINAL_ARTICLE
Fixed Fuzzy Points of Fuzzy Mappings in Hausdorff Fuzzy Metric Spaces with Application
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.
http://ijfs.usb.ac.ir/article_2018_344dee53e41664d8f01d067965c0e8b6.pdf
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10.22111/ijfs.2015.2018
Fuzzy metric space
Fuzzy mapping
Fixed fuzzy point
Quicksort algorithm
Calogero
Vetro
calogero.vetro@unipa.it
true
1
Dipartimento di Matematica e Informatica, Universita degli Studi
di Palermo, Via Archirafi 34, 90123 Palermo, Italy
Dipartimento di Matematica e Informatica, Universita degli Studi
di Palermo, Via Archirafi 34, 90123 Palermo, Italy
Dipartimento di Matematica e Informatica, Universita degli Studi
di Palermo, Via Archirafi 34, 90123 Palermo, Italy
LEAD_AUTHOR
Mujahid
Abbas
mujahid.abbas@up.ac.za
true
2
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
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
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
AUTHOR
Basit
Ali
basit.aa@gmail.com
true
3
Department of Mathematics, Syed Babar Ali School of Science and Engi-
neering (SBASSE), Lahore University of Management Sciences (LUMS), Lahore, 54792,
Pakistan
Department of Mathematics, Syed Babar Ali School of Science and Engi-
neering (SBASSE), Lahore University of Management Sciences (LUMS), Lahore, 54792,
Pakistan
Department of Mathematics, Syed Babar Ali School of Science and Engi-
neering (SBASSE), Lahore University of Management Sciences (LUMS), Lahore, 54792,
Pakistan
AUTHOR
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72
ORIGINAL_ARTICLE
Some classes of statistically convergent sequences of fuzzy numbers generated by a modulus function
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.
http://ijfs.usb.ac.ir/article_2019_acdb38af96e8a2b1a9eb92353d97a5e2.pdf
2015-06-30T11:23:20
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10.22111/ijfs.2015.2019
Sequence of fuzzy numbers
Statistical convergence
Modulus function
U.
Cakan
umitcakan@gmail.com
true
1
Department of Mathematics, Nevsehir Hac Bektas Veli University, Nevsehir-
Turkey
Department of Mathematics, Nevsehir Hac Bektas Veli University, Nevsehir-
Turkey
Department of Mathematics, Nevsehir Hac Bektas Veli University, Nevsehir-
Turkey
AUTHOR
Y.
Altin
yaltin23@yahoo.com
true
2
Department of Mathematics, Firat University, Elazig-Turkey
Department of Mathematics, Firat University, Elazig-Turkey
Department of Mathematics, Firat University, Elazig-Turkey
LEAD_AUTHOR
[1] H. Altnok, R. C olak and M. Et, -dierence sequence spaces of fuzzy numbers, Fuzzy Sets
1
and Systems, 160(21) (2009), 3128{3139.
2
[2] H. Altnok and R. C olak, Almost lacunary statistical and strongly almost lacunary conver-
3
gence of generalized dierence sequences of fuzzy numbers, J. Fuzzy Math., 17(4) (2009),
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5
Taiwanese Journal of Mathematics, 15(5) (2011), 2081-2093.
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37
ORIGINAL_ARTICLE
Categorically-algebraic topology and its applications
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.
http://ijfs.usb.ac.ir/article_2020_3928dce38a41f1ffb43078cccd8ae550.pdf
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10.22111/ijfs.2015.2020
Categorically-algebraic topology
Lattice-valued topology
Soft topology
Topological category
Topological system
Topological theory
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 and
Institute of Mathematics and Computer Science, University of Latvia, Raina bulvaris
29, LV-1459 Riga, Latvia
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
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
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ORIGINAL_ARTICLE
Convergence, Consistency and Stability in Fuzzy Differential Equations
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.
http://ijfs.usb.ac.ir/article_2021_27827fb7f621d2c20415fb8f401902e5.pdf
2015-06-30T11:23:20
2017-11-22T11:23:20
95
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10.22111/ijfs.2015.2021
Consistence
Stability
Local truncation error
Generalized differentiability
Fuzzy stiff differential equation
R.
Ezzati
ezati@kiau.ac.ir
true
1
Department of Mathematics, Karaj Branch, Islamic Azad University,
Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University,
Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University,
Karaj, Iran
LEAD_AUTHOR
K.
Maleknejad
maleknejad@iust.ac.ir
true
2
Department of Mathematics, Karaj Branch, Islamic Azad University,
Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University,
Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University,
Karaj, Iran
AUTHOR
S.
Khezerloo
s_khezerloo@azad.ac.ir
true
3
Department of Mathematics, Islamic Azad University - South Tehran
Branch, Tehran, Iran
Department of Mathematics, Islamic Azad University - South Tehran
Branch, Tehran, Iran
Department of Mathematics, Islamic Azad University - South Tehran
Branch, Tehran, Iran
AUTHOR
M.
Khezerloo
khezerloo@iasbs.ac.ir
true
4
Department of Mathematics, Institute for Advanced Studies in Basic
Sciences(IASBS), P.O. BOX 45195-1159, Zanjan, Iran
Department of Mathematics, Institute for Advanced Studies in Basic
Sciences(IASBS), P.O. BOX 45195-1159, Zanjan, Iran
Department of Mathematics, Institute for Advanced Studies in Basic
Sciences(IASBS), P.O. BOX 45195-1159, Zanjan, Iran
AUTHOR
[1] S. Abbasbandy and T. Allahviranloo, Numerical solutions of fuzzy dierential equations by
1
Taylor method, Journal of Computational Methods in Applied Mathematics, 2 (2002), 113{
2
[2] T. Allahviranloo, N. A. Kiani and M. Barkhordari, Toward the existence and uniquness
3
of solution of second- order fuzzy dierential equations, Information Sciences, 179 (2009),
4
1207{1215.
5
[3] T. Allahviranloo and M. Barkhordari, Fuzzy laplace transforms, Soft Computing, 14 (2010),
6
[4] B. Bede and SG. Gal, Almost periodic fuzzy-number valued functions, Fuzzy Sets and Sys-
7
tems, 147 (2004), 385{403.
8
[5] B. Bede and SG. Gal, Generalizations of dierentiablity of fuzzy number valued function with
9
application to fuzzy dierential equations, Fuzzy Sets and Systems, 151 (2005), 581-599.
10
[6] B. Bede, Imre J. Rudas c and Attila L., First order linear fuzzy dierential equations under
11
generalized dierentiability, Information Sciences, 177 (2007), 3627-3635.
12
[7] Y. Chalco-Cano and H. Roman-Flores, On new solutions of fuzzy dierential equations,
13
Chaos, solitons and Fractals (2006), 1016-1043.
14
[8] S. L. Chang and L. A. Zadeh, On fuzzy mapping and control, IEEE Trans, Systems Man
15
Cybernet., 2 (1972), 30-34.
16
[9] D. Dubois and H. Prade, Towards fuzzy dierential calculus: Part 3, dierentiation, Fuzzy
17
Sets and Systems, 8 (1982), 225-233.
18
[10] S. G. Gal, Approximation theory in fuzzy setting, in: G.A. Anastassiou (Ed.), Handbook of
19
Analytic-Computational Methods in Applied Mathematics, Chapman Hall CRC Press, (2000),
20
[11] R. Goetschel and W. Voxman, Elementary fuzzy calculus, Fuzzy sets and Systems, 18 (1986),
21
[12] O. Kaleva, Fuzzy dierential equations, Fuzzy Sets and Systems, 24 (1987), 301-317.
22
[13] O. Kaleva, The Cuachy problem for fuzzy dierential equations, Fuzzy Sets and Systems, 35
23
(1990), 389-396.
24
[14] M. Ma, M. Friedman and A. Kandel, Numerical solutions of fuzzy dierential equations,
25
Fuzzy Sets and Systems, 105 (1999), 133-138.
26
[15] M. L. Puri and D. A. Ralescu, Dierentials of fuzzy functions, J. math. Analysis. Appl., 91
27
(1983), 552-558.
28
[16] S. Salahshour and T. Allahviranloo, Applications of fuzzy Laplace transforms, Soft comput-
29
ing, 17 (2013), 145-158.
30
[17] S. Salahshour and T. Allahviranloo, A new method for solving fuzzy rst order dierential
31
equations, IPMU, 2012.
32
[18] S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets and Systems, 24 (1987), 319-330.
33
[19] C. Wu and Z. Gong, On Henstock integral of fuzzy-number-valued functions I, Fuzzy Sets
34
and Systems, 120 (2001), 523-532.
35
ORIGINAL_ARTICLE
Interval Type-2 Fuzzy Rough Sets and Interval Type-2 Fuzzy Closure Spaces
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.
http://ijfs.usb.ac.ir/article_2022_3ededbfe97b2d5a0693ea6c5302fba77.pdf
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125
10.22111/ijfs.2015.2022
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
Shambhu
Sharan
shambhupuremaths@gmail.com
true
1
School of Advanced Sciences, VIT University,Vellore-632014,Tamil
Nadu, India
School of Advanced Sciences, VIT University,Vellore-632014,Tamil
Nadu, India
School of Advanced Sciences, VIT University,Vellore-632014,Tamil
Nadu, India
LEAD_AUTHOR
S. P.
Tiwari
sptiwarimaths@gmail.com
true
2
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, India
AUTHOR
V. K.
Yadav
vijayyadav3254@gmail.com
true
3
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, India
Department of Applied Mathematics, Indian School of Mines, Dhanbad-
826004, India
AUTHOR
[1] D. Dubois and H. Prade, Rough fuzzy set and fuzzy rough set, Internation Journal of General
1
Systems, 17(2-3) (1990), 191-209.
2
[2] J. Elorza and P. Burillo, On the relation between fuzzy peorders and fuzzy consequence oper-
3
ators, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 7(3)
4
(1999), 219-234.
5
[3] J. Elorza and P. Burillo, Connecting fuzzy preorders, fuzzy consequence operators and fuzzy
6
closure and co-closure systems, Fuzzy Sets and Systems, 139(3) (2003), 601-613.
7
[4] J. Elorza, R. Fuentes-Gonzalez, J. Bragard and P. Burillo, On the relation between fuzzy
8
closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and
9
fuzzy closure and co-closure systems, Fuzzy Sets and Systems, 218 (2013), 73-89.
10
[5] J. Fang and P. Chen, One-to-one correspondence between fuzzifying topologies and fuzzy
11
preorders, Fuzzy Sets and Systems, 158(16) (2007), 1814-1822.
12
[6] J. Hao and Q. Li, The relationship between L-fuzzy rough set and L-topology, Fuzzy Sets and
13
Systems, 178(1) (2011), 74-83.
14
[7] M. Kondo, On the structure of generalized rough sets, Information Sciences, 176(5) (2006),
15
[8] H. Lai and D. Zhang, Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems, 157(14)
16
(2006), 1865-1885.
17
[9] Q. Liang and J. M. Mendel, Interval type-2 fuzzy logic systems: Theory and design, IEEE
18
Transactions on Fuzzy Systems, 8(5) (2000), 535-550.
19
[10] A. S. Mashhour and M. H. Ghanim, Fuzzy closure spaces, Journal of Mathematical Analysis
20
and Applications, 106(1) (1985), 154-170.
21
[11] J. M. Mendel and R. I. John, Type-2 fuzzy sets made simple, IEEE Transactions on Fuzzy
22
Systems, 10(2) (2002), 117-127.
23
[12] J. M. Mendel, R. I. John and F. Liu, Interval type-2 fuzzy logic systems made simple, IEEE
24
Transactions on Fuzzy Systems, 14(6) (2006), 808-821.
25
[13] M. Mizumoto and K. Tanaka, Some properties of fuzzy sets of type-2, Information and Con-
26
trol, 31(4) (1976), 312-340.
27
[14] Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences, 11
28
(1982), 341{356.
29
[15] K. Qin and Z. Pei, On the topological properties of fuzzy rough sets, Fuzzy sets and Systems,
30
151 (2005), 601-613.
31
[16] E. Sanchez, Eigen fuzzy sets and fuzzy relations, Journal of Mathematical Analysis and
32
Applications, 81(2) (1981), 399-421.
33
[17] Y. H. She and G. J. Wang, An axiomatic approach of fuzzy rough sets based on residuated
34
lattices, Computers and Mathematics with Applications, 58(1) (2009), 189-201.
35
[18] R. Srivastava, A. K. Srivastava and A. Choubey, Fuzzy closure spaces, Journal of fuzzy
36
Mathematics, 2 (1994), 525-534.
37
[19] S. P. Tiwari and A. K. Srivastava, Fuzzy rough sets, fuzzy preorders and fuzzy topologies,
38
Fuzzy sets and Systems, 210 (2013), 63-68.
39
[20] H. Y. Wu, Y. Y. Wu and J. P. Luo, An interval type-2 fuzzy rough set model for attribute
40
reduction, IEEE Transactions on Fuzzy Systems, 17(2) (2009), 301-315.
41
[21] Y. Y. Yao, Constructive and algebraic methods of the theory of rough sets, Information
42
Sciences, 109(1-4) (1998), 21-47.
43
[22] D. S. Yeung, D. Chen, E. C. C. Tsang, J. W. T. Lee and W. Xizhao, On the generalization
44
of fuzzy rough sets, IEEE Transactions on Fuzzy Systems, 13(3) (2005), 343-361.
45
[23] L. A. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338-353.
46
[24] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning,
47
Information Sciences, 8(3) (1975), 199-249.
48
[25] Z. Zhang, On characterization of generalized interval type-2 fuzzy rough sets, Information
49
Sciences, 219 (2013), 124-150.
50
ORIGINAL_ARTICLE
Boundedness of linear order-homomorphisms in $L$-topological vector spaces
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.
http://ijfs.usb.ac.ir/article_2023_6994345f4f77c7f78c179cfc9a2c1c83.pdf
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127
135
10.22111/ijfs.2015.2023
$L$-topological vector space
Linear order-homomorphism
Bounde-dness
Hua-Peng
Zhang
huapengzhang@163.com
true
1
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
LEAD_AUTHOR
Jin-Xuan
Fang
jxfang@njnu.edu.cn
true
2
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
AUTHOR
[1] D. Dubois and H. Prade, Fuzzy sets and systems: theory and applications, Academic Press,
1
New York, 1980.
2
[2] M. A. Erceg, Functions, equivalence relations, quotient spaces and subsets in fuzzy set theory,
3
Fuzzy Sets and Systems, 3 (1980), 75{92.
4
[3] J. X. Fang, Fuzzy linear order-homomorphism and its structures, J. Fuzzy Math., 4(1) (1996),
5
[4] J. X. Fang, The continuity of fuzzy linear order-homomorphism, J. Fuzzy Math., 5(4) (1997),
6
[5] J. X. Fang and C. H. Yan, L-fuzzy topological vector spaces, J. Fuzzy Math., 5(1) (1997),
7
[6] J. X. Fang and H. Zhang, Boundedness and continuity of fuzzy linear order-homomorphisms
8
on I-topological vector spaces, Iranian Journal of Fuzzy Systems, 11(1) (2014), 147{157.
9
[7] M. He, Bi-induced mappings on L-fuzzy sets, Kexue Tongbao, (in Chinese), 31 (1986), 475.
10
[8] U. Hohle and S. E. Rodabaugh (Eds.), Mathematics of fuzzy sets: logic, topology and measure
11
theory, the handbooks of fuzzy sets series, vol. 3, Kluwer Academic Publishers, Dordrecht,
12
[9] A. K. Katsaras, Fuzzy topological vector spaces I, Fuzzy Sets and Systems, 6 (1981), 85{95.
13
[10] Y. M. Liu, Structures of fuzzy order homomorphisms, Fuzzy Sets and Systems, 21 (1987),
14
[11] Y. M. Liu and M. K. Luo, Fuzzy topology, World Scientic Publishing, Singapore, 1997.
15
[12] S. E. Rodabaugh, Point-set lattice-theoretic topology, Fuzzy Sets and Systems, 40 (1991),
16
[13] S. E. Rodabaugh, Powerset operator based foundation for point-set lattice-theoretic
17
(POSLAT) fuzzy set theories and topologies, Quaestiones Math., 20 (1997), 463{530.
18
[14] G. J. Wang, Order-homomorphisms on fuzzes, Fuzzy Sets and Systems, 12 (1984), 281{288.
19
[15] G. J. Wang, Theory of L-fuzzy topological spaces, Shaanxi Normal University Press, Xi'an,
20
(in Chinese), 1988 .
21
[16] C. H. Yan, Initial L-fuzzy topologies determined by the family of L-fuzzy linear order-
22
homomorphisms, Fuzzy Sets and Systems, 116 (2000), 409{413.
23
[17] C. H. Yan, Generalization of inductive topologies to L-topological vector spaces, Fuzzy Sets
24
and Systems, 131 (2002), 347{352.
25
[18] C. H. Yan and J. X. Fang, The uniform boundedness principle in L-topological vector spaces,
26
Fuzzy Sets and Systems, 136 (2003), 121{126.
27
ORIGINAL_ARTICLE
Distinct Fuzzy Subgroups of a Dihedral Group of Order $2pqrs$ for Distinct Primes $p, , q, , r$ and $s$
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.
http://ijfs.usb.ac.ir/article_2024_a19538744d9dc0e80b3a8fe6a94fe7a9.pdf
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137
149
10.22111/ijfs.2015.2024
Dihedral group
Equivalence
Isomorphism
Fuzzy subgroup
Maximal chain
Keychain
Distinguishing factor
Babington
Makamba
bmakamba@ufh.ac.za
true
1
Department of Mathematics, University of Fort Hare, Alice
5700 , Eastern Cape , South Africa
Department of Mathematics, University of Fort Hare, Alice
5700 , Eastern Cape , South Africa
Department of Mathematics, University of Fort Hare, Alice
5700 , Eastern Cape , South Africa
LEAD_AUTHOR
Odilo
Ndiweni
ondiweni@ufh.ac.za
true
2
Department of Mathematics, University of Fort Hare, Alice 5700 ,
Eastern Cape , South Africa
Department of Mathematics, University of Fort Hare, Alice 5700 ,
Eastern Cape , South Africa
Department of Mathematics, University of Fort Hare, Alice 5700 ,
Eastern Cape , South Africa
AUTHOR
[1] S. Branimir and A. Tepavcevic, A note on a natural equivalence relation on fuzzy power set,
1
Fuzzy Sets and Systems, 148(2) (2004), 201{210.
2
[2] C. Degang, J. Jiashang, W. Congxin and E. C. C. Tsang, Some notes on equivalent fuzzy
3
sets and fuzzy subgroups, Fuzzy Sets and systems, 152(2) (2005), 403{409.
4
[3] V. Murali and B. B. Makamba, On an equivalence of fuzzy subgroups I, Fuzzy Sets and
5
Systems 123(2) (2001), 259{264.
6
[4] O. Ndiweni and B. B. Makamba, Classication of fuzzy subgroups of a dihedral group of
7
order 2pqr for distinct primes p, q and r, International Jounal of Mathematical Sciences and
8
Engineering Applications, 6(4) (2012) , 159{174.
9
[5] M. Pruszyriska and M. Dudzicz, On isomorphism between nite chains, Journal of Formalised
10
Mathematics, 12(1) (2003) , 1{2.
11
[6] S. Ray, Isomorphic fuzzy groups, Fuzzy Sets and Systems, 50(2) (1992) , 201{207.
12
[7] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971) , 512{517.
13
[8] M. Tarnauceanu and L. Bentea, On the number of subgroups of nite abelian groups, Fuzzy
14
Sets and Systems, 159(10) (2008) , 1084{1096.
15
[9] A. C. Volf, Counting fuzzy subgroups and chains of subgroups, Fuzzy Systems and Articial
16
Intelligence, 10(3) (2004) , 191{200.
17
ORIGINAL_ARTICLE
Solvable $L$-subgroup of an $L$-group
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.
http://ijfs.usb.ac.ir/article_2025_54e716181d9591e118bc01071c130667.pdf
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151
166
10.22111/ijfs.2015.2025
$L$-algebra
$L$-subgroup
Normal $L$-subgroup
Solvable $L$-subgroup
Derived series
Solvable series
Iffat
Jahan
ij.umar@yahoo.com
true
1
Department of Mathematics, Ramjas College,, University of Delhi,,
Delhi-110007, India
Department of Mathematics, Ramjas College,, University of Delhi,,
Delhi-110007, India
Department of Mathematics, Ramjas College,, University of Delhi,,
Delhi-110007, India
LEAD_AUTHOR
Naseem
Ajmal
nasajmal@yahoo.com
true
2
Department of Mathematics, Zakir Husain Delhi College,, J.N.Marg,
University of Delhi, Delhi-110006, India
Department of Mathematics, Zakir Husain Delhi College,, J.N.Marg,
University of Delhi, Delhi-110006, India
Department of Mathematics, Zakir Husain Delhi College,, J.N.Marg,
University of Delhi, Delhi-110006, India
AUTHOR
[1] N. Ajmal, Fuzzy groups with sup property, Inform. Sci., 93 (1996), 247-264.
1
[2] N. Ajmal and I. Jahan , A study of normal fuzzy subgroups and characteristic fuzzy subgroups
2
of a fuzzy group, Fuzzy Information and Engineering, 2 (2012), 123-143.
3
[3] N. Ajmal and I. Jahan, Nilpotency and theory of L-subgroups of an L-group, Fuzzy Informa-
4
tion and Engineering, 6 (2014), 1-17.
5
[4] N. Ajmal and A. Jain, Some constructions of the join of fuzzy subgroups and certain lattices
6
of fuzzy subgroups with sup property, Inform. Sci., 179 (2009), 4070-4082.
7
[5] N. Ajmal and I. Jahan,Generated L-subgroup of an L-group, Iranian Journal of Fuzzy Sys-
8
tems, 12(2) (2015), 129-136.
9
[6] J. A. Goguen, Lfuzzy sets, J. Math. Anal. Appl., 18 (1967), 145-174.
10
[7] K. C. Gupta and B. K. Sarma, nilpotent fuzzy groups, Fuzzy Sets and Systems, 101 (1999),
11
[8] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982),
12
[9] D. S. Malik, J. N. Mordeson and P. S. Nair, Fuzzy normal subgroups in fuzzy subgroups, J.
13
Korean Math. Soc., 29 (1992), 1-8.
14
[10] L. Martinez, L Fuzzy subgroups of fuzzy groups and fuzzy ideals of fuzzy rings, J. Fuzzy
15
Math., 3 (1995), 833-849.
16
[11] J. N. Mordeson, K. R. Bhutani and A. Rosenfeld, Fuzzy group theory, Springer, 2005.
17
[12] J. N. Mordeson and D. S. Malik, Fuzzy commutative algebra, World Scientic, 1998.
18
[13] N. P. Mukherjee and P. Bhattacharya, Fuzzy groups: some group-theoretic analogs, Inform.
19
Science, 39 (1986), 247-268.
20
[14] A. S. Prajapati and N. Ajmal, Maximal ideals of L-subrings, J. Fuzzy Math., 15 (1999),
21
[15] A. S. Prajapati and N. Ajmal,Maximal ideals of L{subrings. II, J. Fuzzy Math., 15 (2007),
22
[16] M. G. Ranitovic and A. Tepavcevic, General form of lattice-valued fuzzy sets under the
23
cutworthy approach, Fuzzy Sets and Systems, 158 (2007), 1213-1216.
24
[17] S. Ray, Solvable fuzzy groups, Inform. Science 75 (1993) 47-61.
25
[18] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
26
[19] B. K. Sarma, Solvable fuzzy groups, Fuzzy Sets and Systems, 106 (1999), 463-467.
27
[20] B. Seselja, D. Stojic and A. Tepavcevic, On existence of P-valued fuzzy sets with a given
28
collection of cuts, Fuzzy Sets and Systems, 161 (2010), 763-768.
29
[21] B. Seselja and A. Tepavcevic,Completion of ordered structures by cuts of fuzzy sets: an
30
overview, Fuzzy Sets and Systems, 136 (2003), 1-19.
31
[22] W. Wu, Normal fuzzy subgroups, Fuzzy Math., 1 (1981), 21-30.
32
ORIGINAL_ARTICLE
Persian-translation vol. 12, no.3, June 2015
http://ijfs.usb.ac.ir/article_2647_57c7fc92eea1f99ca53467fa3f4fe555.pdf
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178
10.22111/ijfs.2015.2647