ORIGINAL_ARTICLE
Cover vol. 12, no. 1, February 2015
http://ijfs.usb.ac.ir/article_2650_59e18134e188eee79afb2e07d9f951f0.pdf
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10.22111/ijfs.2015.2650
ORIGINAL_ARTICLE
An integrated multi-criteria decision-making methodology based on type-2 fuzzy sets for selection among energy alternatives in Turkey
Energy is a critical factor to obtain a sustainable development for countries and governments. Selection of the most appropriate energy alternative is a completely critical and a complex decision making problem. In this paper, an integrated multi-criteria decision-making (MCDM) methodology based on type-2 fuzzy sets is proposed for selection among energy alternatives. Then a roadmap has been created for Turkey.To overcome uncertainties in decision making process, the fuzzy set theory (FST) is suggested.For this aim, two of the most known MCDM methodologies are reconsidered by using type-2 fuzzy sets.Fuzzy Analytic Hierarchy Process (FAHP) based on interval type-2 fuzzy sets is constructed and is used to obtain the weights of the criteria affecting energy alternatives. To rank the energy alternatives, the other MCDM method that is Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is fuzzified by interval type-2 fuzzy sets. The proposed integrated MCDM methodology based on interval type-2 fuzzy sets is applied to obtain a road map of energy policies for Turkey.
http://ijfs.usb.ac.ir/article_1839_d23c7ca7b9fd0dade01c8ab6932814d4.pdf
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10.22111/ijfs.2015.1839
Energy
Multi criteria decision making
Interval type-2 fuzzy sets
AHP
TOPSIS
Melike
Erdogan
melike@yildiz.edu.tr
true
1
Department of Industrial Engineering, Yildiz Technical University, Yildiz, BESIKTAS, Istanbul, Turkey
Department of Industrial Engineering, Yildiz Technical University, Yildiz, BESIKTAS, Istanbul, Turkey
Department of Industrial Engineering, Yildiz Technical University, Yildiz, BESIKTAS, Istanbul, Turkey
LEAD_AUTHOR
ihsan
Kaya
iekaya@yahoo.com
true
2
Department of Industrial Engineering, Yildiz Technical University, Yildiz, BESIKTAS, Istanbul, Turkey
Department of Industrial Engineering, Yildiz Technical University, Yildiz, BESIKTAS, Istanbul, Turkey
Department of Industrial Engineering, Yildiz Technical University, Yildiz, BESIKTAS, Istanbul, Turkey
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ORIGINAL_ARTICLE
Approximation theorems for fuzzy set multifunctions in Vietoris topology. Physical implications of regularity
n this paper, we consider continuity properties(especially, regularity, also viewed as an approximation property) for $%mathcal{P}_{0}(X)$-valued set multifunctions ($X$ being a linear,topological space), in order to obtain Egoroff and Lusin type theorems forset multifunctions in the Vietoris hypertopology. Some mathematicalapplications are established and several physical implications of themathematical model of regularity are presented, which allows aclassification of the physical models.
http://ijfs.usb.ac.ir/article_1840_855de66e0a5045c0650164221c4a2935.pdf
2015-02-28T11:23:20
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27
42
10.22111/ijfs.2015.1840
Vietoris topology
regularity
Approximations
Fractal Theories
Non-differentiable physics
Scale
relativity theory
A.
Gavrilut
gavrilut@uaic.ro
true
1
Faculty of Mathematics, \Alexandru Ioan Cuza" University of Iasi
Iasi, Romania
Faculty of Mathematics, \Alexandru Ioan Cuza" University of Iasi
Iasi, Romania
Faculty of Mathematics, \Alexandru Ioan Cuza" University of Iasi
Iasi, Romania
LEAD_AUTHOR
M.
Agop
m.agop@yahoo.com
true
2
Department of Physics, Gheorghe Asachi Technical University of Iasi, Iasi,
Romania
Department of Physics, Gheorghe Asachi Technical University of Iasi, Iasi,
Romania
Department of Physics, Gheorghe Asachi Technical University of Iasi, Iasi,
Romania
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1
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ORIGINAL_ARTICLE
Uniformities in fuzzy metric spaces
The aim of this paper is to study induced (quasi-)uniformities in Kramosil and Michalek's fuzzy metric spaces. Firstly, $I$-uniformity in the sense of J. Guti'{e}rrez Garc'{i}a and $I$-neighborhood system in the sense of H"{o}hle and u{S}ostak are induced by the given fuzzy metric. It is shown that the fuzzy metric and the induced $I$-uniformity will generate the same $I$-neighborhood system. Secondly, the relationship between Hutton quasi-uniformities and $I$-quasi-uniformities is given and it is proved that the category of strongly stratified $I$-quasi-uniform spaces can be embedded in the category of Hutton quasi-uniform spaces as a bicoreflective subcategory. Also it is shown that two kinds of Hutton quasi-uniformities can generate the same $I$-uniformity in fuzzy metric spaces.
http://ijfs.usb.ac.ir/article_1841_934512989c8d6bed65891801d995c6a2.pdf
2015-02-28T11:23:20
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43
57
10.22111/ijfs.2015.1841
Fuzzy metric
$I$-uniformity
Hutton quasi-uniformity
Yueli
Yue
ylyue@ouc.edu.cn
true
1
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
LEAD_AUTHOR
Jinming
Fang
jmfang@ouc.edu.cn
true
2
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
AUTHOR
[1] J. Fang, Relationships between L-ordered convergence structures and strong L-topologies,
1
Fuzzy Sets and Systems, 161 (2010), 2923-2944.
2
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64 (1994), 395-399.
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and Systems, 90 (1997), 365-368.
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130 (2002), 399-404.
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[6] V. Gregori, A. Lopez-Crevillen, S. Morillas and A. Sapena, On convergence in fuzzy metric
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spaces, Topology and its Applications, 156 (2009), 3002-3006.
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concept of fuzzy L-unifom space, Chapter 3 in S. E. Rodabaugh, E. P. Klement, eds., Topological
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and Algebraic Structures in Fuzzy Sets: A Handbook of Recent Development in
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the Mathematics of Fuzzy Sets, Trends in Logic 20(2003), Kluwer Academic Publishers
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(Boston/Dordrecht/London).
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[8] J. Gutierrez Garca, A unied approach to the concept a fuzzy L-unifom space, Ph.D Thesis,
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[9] J. Gutierrez Garca and M. A. de Prada Vicente, Hutton [0, 1]-quasi-uniformities induced by
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fuzzy (quasi-)metric spaces, Fuzzy Sets and Systems, 157 (2006), 755-766.
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(1982), 289-323.
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(1982,) 63-69.
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Chapter 3 in U. Hohle and S. E. Rodabaugh, eds, Mathematics of Fuzzy Sets: Logic, Topology,
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and Measure Theory, The Handbooks of Fuzzy Sets Series, Volume 3 (1999), Kluwer Academic
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Publishers (Boston/Dordrecht/London).
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(1975), 336-344.
30
[15] K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. U.S.A., 28 (1942), 535-537.
31
[16] B. Schweizer and A. Sklar, Probabilistic metric spaces, North-Holland, NewYork, 1983.
32
[17] Y. Yue and F. G. Shi, On fuzzy pseudo-metric spaces, Fuzzy Sets and Systems, 161 (2010),
33
1105-1106.
34
[18] D. Zhang, An enriched category approach to many valued topology, Fuzzy Sets and Systems,
35
158 (2007), 349{366.
36
ORIGINAL_ARTICLE
Application of parametric form for ranking of fuzzy numbers
In this paper, we propose a new approach for ranking all fuzzynumbers based on revising the ranking method proposed by Ezzati et al. cite{Ezzati}.To this end, we present and investigate some properties of the proposed approach indetails. Finally, to illustrate the advantage of the proposed method, it is applied to several groups of fuzzy numbers and the results are compared with other related and familiar ones.
http://ijfs.usb.ac.ir/article_1842_27cb3eea8770ed442d2b473b328b2217.pdf
2015-02-28T11:23:20
2018-05-25T11:23:20
59
74
10.22111/ijfs.2015.1842
Ranking of fuzzy numbers
Parametric form of fuzzy number
Magnitude of fuzzy number
R.
Ezzati
ezati@kiau.ac.ir
true
1
Department of Mathematics, Karaj Branch, Islamic Azad University, 31485 - 413, Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University, 31485 - 413, Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University, 31485 - 413, Karaj, Iran
LEAD_AUTHOR
S.
Khezerloo
s_khezerloo@azad.ac.ir
true
2
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
S.
Ziari
sziari@iaufb.ac.ir
true
3
Department of Mathematics, Firoozkooh Branch,Islamic Azad University, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch,Islamic Azad University, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch,Islamic Azad University, Firoozkooh, Iran
AUTHOR
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1
Computers and Mathematics with Applications, {bf 57} (2009), 413-419.
2
bibitem{ABBAS}
3
S. Abbasbandy and B. Asady, {it Ranking of fuzzy numbers by sign
4
distance}, Information Sciences, {bf 176} (2006), 2405-2416.
5
bibitem{Asadi} B. Asady and A. Zendehnam, {it Ranking fuzzy numbers by distance minimizing},
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Applied Mathematical Modeling, {bf 31} (2007), 2589-2598.
7
bibitem{MatBrun} M. Brunelli and J. Mezeib, {it How different are ranking methods for fuzzy numbers?
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A numerical study}, International Journal of Approximate Reasoning, {bf 54} (2013), 627-639.
9
bibitem{ChenTang} C. C. Chen and H. C. Tang, {it Ranking of nonnormal p-norm
10
trapezoidal fuzzy numbers with integral value},
11
Computers and Mathematics with Applications, {bf 56} (2008), 2340-ï¿½2346.
12
bibitem{chu}
13
T. Chu and C. Tsao, {it Ranking fuzzy numbers with an area between the
14
centroid point and original points}, Computers and Mathematics with Application {bf 43} (2002),
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bibitem{cheng1}
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C. H. Cheng, {it A new approach for ranking fuzzy numbers by distance minimizing}, Fuzzy Sets and Systems, {bf 95}
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(1998), 307-317.
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Part 3, differentiation}, Fuzzy Sets and Systems, {bf 8} (1982), 225-233.
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Applied Mathematical Modelling, {bf 38}textbf{(5-6)} (2014), 1638-1646.
22
bibitem{Ezzati}
23
R. Ezzati, T. Allahviranloo, S. Khezerloo and M. Khezerloo, {it An approach for ranking of fuzzy numbers},
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Expert Systems with Applications, {bf 39} (2012), 690-695.
25
bibitem{SGG} S. G. Gal, {it Approximation theory in fuzzy setting}, In:
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G. A. Anastassiou, ed., Handbook of Analytic-Computational
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Methods in Applied Mathematics, Chapman Hall CRC Press, (2000), 617-666.
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R. Jain, {it Decision-making in the presence of fuzzy variable}, IEEE Trans. Syst. Man Cybren, {bf 6} (1976), 698-703.
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R. Jain, {it A procedure for multi-aspect decision making using fuzzy sets}, Int. J. Syst. Sci, {bf 8} (1977), 1-7.
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{it A new approach for ranking nonnormal p-norm trapezoidal fuzzy numbers},
35
Computers and Mathematics with Applications, {bf 61} (2011), 881-887.
36
bibitem{AmitKumar2} A. Kumar, P. Singh, P. Kaur and A. Kaur,
37
{it A new approach for ranking of L.R type generalized fuzzy numbers},
38
Expert Systems with Applications, {bf 38} (2011), 10906-10910.
39
bibitem{liwang}T. S. Liou and M. J. Wang, {it Ranking fuzzy numbers with integral value},
40
Fuzzy Sets and Systems, {bf 50} (1992), 247-255.
41
bibitem{liu}
42
X. Liu, {it Measuring the satisfaction of constraints in fuzzy
43
linear programming}, Fuzzy Sets and Systems, {bf 122} (2001), 263-275.
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bibitem{ma}
45
M. Ma, M. Friedman and A. Kandal, {it A new fuzzy arithmetic},
46
Fuzzy Sets and Systems, {bf 108} (1999), 83-90.
47
bibitem{mun}
48
B. Matarazzo and G. Munda, {it New approaches for the comparison of
49
L-R fuzzy numbers}, Fuzzy Sets and Systems, {bf 118} (2001), 407-418.
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bibitem{kerre1}
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X. Wang and E. E. Kerre, {it Reasonable properties for the ordering
52
of fuzzy quantities $(I)$}, Fuzzy Sets and Systems, {bf 118} (2001), 375-385.
53
bibitem{kerre2}
54
X. Wang and E. E. Kerre, {it Reasonable properties for the ordering
55
of fuzzy quantities $(I)$}, Fuzzy Sets and Systems, {bf 118} (2001), 387-405.
56
bibitem{Wang}
57
Y. J. Wang and S. H. Lee, {it The revised method of ranking fuzzy
58
numbers with an area between the centroid an original points},
59
Computers and mathematics with Applications, {bf 55} (2008). 2033-2042.
60
bibitem{Yao}
61
J. Yao and K. Wu, {it Ranking fuzzy numbers based on decomposition
62
principle and signed distance}, Fuzzy Sets and Systems, {bf 116} (2000), 275 - 288.
63
%bibitem{WZG}C. Wu, Z. Gong, {it On Henstock integral of fuzzy-number-valued functions I}, Fuzzy Sets and Systems, {bf 120} (2001), 523-532.
64
vspace{-.3cm}
65
ORIGINAL_ARTICLE
Coupled Coincidence and Common Fixed Point Theorems for Single-Valued and Fuzzy Mappings
In this paper, we study the existence of coupled coincidence andcoupled common fixed points for single-valued and fuzzy mappingsunder a contractive condition in metric space. Presented theoremsextend and improve the main results of Abbas and$acute{C}$iri$acute{c}$ {itshape et al.} [M. Abbas, L.$acute{C}$iri$acute{c}$, {itshape et al.}, Coupled coincidenceand common fixed point theorems for hybrid pair of mappings, FixedPoint Theory Appl. (4) (2012) doi:10.1186/1687-1812-2012-4].
http://ijfs.usb.ac.ir/article_1862_0c9a4b14e5a54b07a78dac040c0e304f.pdf
2015-02-28T11:23:20
2018-05-25T11:23:20
75
87
10.22111/ijfs.2015.1862
Fuzzy mapping
Coupled coincidence point
Coupled common fixed
point
Coupled fixed point
Li
Zhu
zflcz@aliyun.com
true
1
Department of Mathematics, Nanchang University, Nanchang 330031, P.
R. China And Department of Mathematics, Jiangxi Agricultural University, Nanchang
330045, P. R. China
Department of Mathematics, Nanchang University, Nanchang 330031, P.
R. China And Department of Mathematics, Jiangxi Agricultural University, Nanchang
330045, P. R. China
Department of Mathematics, Nanchang University, Nanchang 330031, P.
R. China And Department of Mathematics, Jiangxi Agricultural University, Nanchang
330045, P. R. China
LEAD_AUTHOR
Chuanxi
Zhu
zhuchuanxi@sina.com
true
2
Department of Mathematics, Nanchang University, Nanchang 330031,
P. R. China
Department of Mathematics, Nanchang University, Nanchang 330031,
P. R. China
Department of Mathematics, Nanchang University, Nanchang 330031,
P. R. China
AUTHOR
Xianjiu
Huang
xjhuang99@163.com
true
3
Department of Mathematics, Nanchang University, Nanchang 330031,
P. R. China
Department of Mathematics, Nanchang University, Nanchang 330031,
P. R. China
Department of Mathematics, Nanchang University, Nanchang 330031,
P. R. China
AUTHOR
[1] M. Abbas, L. Ciric, B. Damjanovic and M. A. Khan, Coupled coincidence and common xed
1
point theorems for hybrid pair of mappings, Fixed Point Theory Appl., doi: 10.1186/1687-
2
1812-2012-4, 4 (2012).
3
[2] M. Abbas, B. Damjanovic and R. Lazovic, Fuzzy common xed point theorems for generalized
4
contractive mappings, Appl. Math. Lett., 23 (2010), 1326-1330.
5
[3] M. Abbas, A. R. Khan and T. Nazir, Coupled common xed point results in two generalized
6
metric spaces, Appl. Math. Comput., 217 (2011), 6328-6336.
7
[4] M. Abbas, M. A. Khan and S. Radenovic, Common coupled point theorems in cone metric
8
spaces for !-compatible mappings, Appl. Math. Comput., 217 (2010), 195-202.
9
[5] H. M. Abu-Donia, Common xed point theorems for fuzzy mappings in metric space under
10
'-contraction condition, Chaos Solitons Fractals, 34 (2007), 538-543.
11
[6] H. Aydi, B. Damjanovic, B. Samet and W. Shatanawi, Coupled xed point theorems for non-
12
linear contractions in partially ordered G-metric spaces, Math. Comput. Model., 54 (2011),
13
2443-2450.
14
[7] H. Aydi, M. Postolache and W. Shatanawi, Coupled xed point results for ( ; )-weakly
15
contractive mappings in ordered G-metric spaces, Comput. Math. Appl., 63 (2012), 298-309.
16
[8] A. Azam and I. Beg, Common xed points of fuzzy maps, Math. Comput. Model., 49 (2009),
17
1331-1336.
18
[9] I. Beg and A. R. Butt, Fixed point for set-valued mappings satisfying an implicit relation in
19
partially ordered metric spaces, Nonlinear Anal., 71 (2009), 3699-3704.
20
[10] T. G. Bhashkar and V. Lakshmikantham, Fixed point theorems in partially ordered metric
21
spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393.
22
[11] Y. J. Cho, B. E. Rhoades, R. Saadati, B. Samet and W. Shatanawi, Nonlinear coupled xed
23
point theorems in ordered generalized metric spaces with integral type, Fixed Point Theory
24
Appl., doi: 10.1186/1687-1812-2012-8, 8 (2012).
25
[12] B. S. Choudhury and A. Kundu, A coupled coincidence point result in partially ordered metric
26
spaces for compatible mappings, Nonlinear Anal., 73 (2010), 2524-2531.
27
[13] B. S. Choudhury and P. Maity, Coupled xed point results in generalized metric spaces, Math.
28
Comput. Model., 54 (2011), 73-79.
29
[14] B. S. Choudhury and N. Metiya, Multivalued and singlevalued xed point risults in partially
30
ordered metric spaces, Arab. J. Math. Sci., 17 (2011), 135-151.
31
[15] L. Ciric, M. Abbas and B. Damjanovic, Common fuzzy xed point theorems in ordered metric
32
spaces, Math. Comput. Model., 53 (2011), 1737-1741.
33
[16] B. Damjanovic, B. Samet and C. Vetro, Common xed point theorems for multi-valued maps,
34
Acta Math. Sci. Ser. B Engl. Ed., 32 (2012), 818-824.
35
[17] H. S. Ding, L. Li and S. Radenovic, Coupled coincidence point theorems for generalized
36
nonlinear contraction in partially ordered metric spaces, Fixed Point Theory Appl., doi:
37
10.1186/1687-1812-2012-96, 96 (2012).
38
[18] W. S. Du, On coincidence point and xed point theorems for nonlinear multivalued maps,
39
Topology Appl., 159 (2012), 49-56.
40
[19] V. D. Estruch and A. Vidal, A note on xed fuzzy points for fuzzy mappings, Rend. Istit.
41
Mat. Univ. Trieste, 32 (2001), 39-45.
42
[20] M. E. Gordji, M. Ramezani, Y. J. Cho and E. Akbartabar, Coupled commom xed point
43
theorems for mixed weakly monotone mappings in partially ordered metric spaces, Fixed
44
Point Theory Appl., doi: 10.1186/1687-1812-2012-95, 95 (2012).
45
[21] J. Harjani, B. Lopez and K. Sadarangani, Fixed point theorems for mixed monotone operators
46
and applications to integral equations, Nonlinear Anal., 74 (2011), 1749-1760.
47
[22] S. Heilpern, Fuzzy mappings and fuzzy xed point theorems, J. Math. Anal. Appl., 83 (1981),
48
[23] S. H. Hong, Fixed points of multivalued operators in ordered metric spaces with applications,
49
Nonlinear Anal., 72 (2010), 3929-3942.
50
[24] N. Hussain and A. Alotaibi, Coupled coincidences for multi-valued contractions in partially
51
ordered metric spaces, Fixed Point Theory Appl., doi: 10.1186/1687-1812-2011-82, 82 (2011).
52
[25] M. Imdad and L. Khan, Fixed point theorems for a family of hybrid pairs of mappings in
53
metrically convex spaces, Fixed Point Theory Appl., 3 (2005), 281-294.
54
[26] T. Kamran, Common xed points theorems for fuzzy mappings, Chaos Solitons Fractals, 38
55
(2008), 1378-1382.
56
[27] H. Kaneko and S. Sessa, Fixed point theorems for compatible multi-valued and single-valued
57
mappings, Int. J. Math. Math. Sci., 12 (1989), 257-262.
58
[28] E. Karapinar, Coupled xed point theorems for nonlinear contractions in cone metric spaces,
59
Comput. Math. Appl., 59 (2010), 3656-3668.
60
[29] F. Khojasteh and V. Rakocevic, Some new common xed point results for generalized con-
61
tractive multi-valued non-self-mappings, Appl. Math. Lett., 25 (2012), 287-293.
62
[30] V. Lakshmikantham and L. Ciric, Coupled xed point theorems for nonlinear contractions in
63
partially ordered metric space, Nonlinear Anal., 70 (2009), 4341-4349.
64
[31] B. S. Lee, G. M. Lee, S. J. Cho and D. S. Kim, A common xed point theorem for a pair of
65
fuzzy mappings, Fuzzy Sets and Systems, 98 (1998), 133-136.
66
[32] Y. C. Liu, J. Wu and Z. X. Li, Common xed points of single-valued and multivalued maps,
67
Int. J. Math. Math. Sci., 19 (2005), 3045-3055.
68
[33] N. V. Luong and N. X. Thuan, Coupled xed points in partially ordered metric spaces and
69
application, Nonlinear Anal., 74 (2011), 983-992.
70
[34] N. V. Luong and N. X. Thuan, Coupled xed point theorems in partially ordered G-metric
71
spaces, Math. Comput. Model., 55 (2012), 1601-1609.
72
[35] J. T. Markin, A xed point theorem for set-valued mappings, Bull. Am. Math. Soc., 74 (1968),
73
[36] S. B. Nadler, Multivalued contraction mappings, Pacic J. Math., 30 (1969), 475-488.
74
[37] F. Sabetghadam, H. P. Masiha and A. H. Sanatpour, Some coupled xed point theorems in
75
cone metric spaces, Fixed Point Theory Appl., doi: 10.1155/2009/125426. Article ID 125426,
76
[38] B. Samet, Coupled xed point theorems for a generalized Meir-Keeler contraction in partially
77
ordered metric spaces, Nonlinear Anal., 72 (2010), 4508-4517.
78
[39] S. Sedghi, I. Altun and N. Shobe, A xed point theorem for multi-maps satisfying an implicit
79
relation on metric spaces, Appl. Anal. Discrete Math., 2 (2008), 189-196.
80
[40] W. Shatanawi, B. Samet and M. Abbas, Coupled xed point theorems for mixed monotone
81
mappings in ordered partial metric spaces, Math. Comput. Model., 55 (2012), 680-687.
82
[41] S. L. Singh and S. N. Mishra, Fixed point theorems for single-valued and multi-valued maps,
83
Nonlinear Anal., 74 (2011), 2243-2248.
84
[42] W. Sintunavarat and P. Kumam, Common xed point theorem for hybrid generalized mulit-
85
valued contraction mappings, Appl. Math. Lett., 25 (2012), 52-57.
86
ORIGINAL_ARTICLE
Minimal solution of fuzzy linear systems
In this paper, we use parametric form of fuzzy number and we converta fuzzy linear system to two linear system in crisp case. Conditions for the existence of a minimal solution to $mtimes n$ fuzzy linear equation systems are derived and a numerical procedure for calculating the minimal solution is designed. Numerical examples are presented to illustrate the proposed method.
http://ijfs.usb.ac.ir/article_1863_1b8410b23769ca1ff9adc789b590ebb0.pdf
2015-02-28T11:23:20
2018-05-25T11:23:20
89
99
10.22111/ijfs.2015.1863
Fuzzy linear system
Pseudo-inverse
Minimal solution
M.
Otadi
mahmoodotadi@yahoo.com
true
1
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer-
sity, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer-
sity, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer-
sity, Firoozkooh, Iran
LEAD_AUTHOR
M.
Mosleh
mosleh@iaufb.ac.ir
true
2
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer-
sity, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer-
sity, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer-
sity, Firoozkooh, Iran
AUTHOR
[1] S. Abbasbandy and M. Alavi, A new method for solving symmetric fuzzy linear systems,
1
Mathematics Scientic Journal, Islamic Azad University of Arak, 1 (2005), 55-62.
2
[2] S. Abbasbandy, E. Babolian and M. Alavi, Numerical method for solving linear Fredholm
3
fuzzy integral equations of the second kind, Chaos, Solitons & Fractals, 31(1) (2007), 138-
4
[3] S. Abbasbandy, A. Jafarian and R. Ezzati, Conjugate gradient method for fuzzy symmetric
5
positive denite system of linear equations, Appl. Math. Comput., 171(2) (2005), 1184-1191.
6
[4] S. Abbasbandy, R. Ezzati and A. Jafarian, LU decomposition method for solving fuzzy system
7
of linear equations, Appl. Math. Comput., 172(1) (2006), 633-643.
8
[5] S. Abbasbandy, J. J. Nieto and M. Alavi, Tuning of reachable set in one dimensional fuzzy
9
dierential inclusions, Chaos, Solitons & Fractals, 26(5) (2005), 1337-1341.
10
[6] S. Abbasbandy, M. Otadi and M. Mosleh, Minimal solution of general dual fuzzy linear
11
systems, Chaos, Solitons & Fractals, 37(4) (2008), 1113-1124.
12
[7] T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Appl. Math. Com-
13
put., 155(2) (2004), 493-502.
14
[8] T. Allahviranloo, Successive over relaxation iterative method for fuzzy system of linear equa-
15
tions, Appl. Math. Comput., 162(1) (2005), 189-196.
16
[9] T. Allahviranloo, The Adomian decomposition method for fuzzy system of linear equations,
17
Appl. Math. Comput., 163(2) (2005), 553-563.
18
[10] S. E. Amrahov and I. N. Askerzade, Strong solutions of the fuzzy linear systems, Computer
19
Modeling in Engineering & Sciences, 76 (2011), 207-216.
20
[11] B. Asady, S. Abbasbandy and M. Alavi, Fuzzy general linear systems, Appl. Math. Comput.,
21
169(1) (2005), 34-40.
22
[12] S. Barnet, Matrix methods and applications, Clarendon Press, Oxford, 1990.
23
[13] W. Cong-Xin and M. Ming, Embedding problem of fuzzy number space, Fuzzy Sets and
24
Systems, 44(1) (1991), 33-38.
25
[14] D. Dubois and H. Prade, Operations on fuzzy numbers, J. Systems Sci., 9(6) (1978), 613-626.
26
[15] R. Ezzati, Solving fuzzy linear systems, Soft Computing, 15(1) (2011), 193-197.
27
[16] M. Friedman, M. Ming and A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems, 96(2)
28
(1998), 201-209.
29
[17] M. Friedman, M. Ming and A. Kandel, Duality in fuzzy linear systems, Fuzzy Sets and
30
Systems, 109(1) (2000), 55-58.
31
[18] N. Gasilov, A. G. Fatullayev and S. E. Amrahov, Solution of non-square fuzzy linear systems,
32
Journal of Multiple-Valued Logic and Soft Computing, 20(1) (2013), 221-237.
33
[19] O. Kaleva, Fuzzy dierential equations, Fuzzy Sets and Systems, 24(3) (1987), 301-317.
34
[20] A. Kaufmann and M. M. Gupta, Introduction to Fuzzy Arithmetic, Van Nostrand Reinhold,
35
New York, 1985.
36
[21] G. J. Klir, U. S. Clair and B. Yuan, Fuzzy set theory: foundations and applications, Prentice-
37
Hall Inc., 1997.
38
[22] D. Kincaid and W. Cheney, Numerical analysis, Mathematics of scientic computing. Second
39
Edition. Brooks/Cole Publishing Co., Pacic Grove, CA, 1996.
40
[23] M. Ming, M. Friedman and A. Kandel, A new fuzzy arithmetic, Fuzzy Sets and Systems,
41
108(1) (1999), 83-90.
42
[24] M. Otadi, New solution of fuzzy linear matrix equations, Theory of Approximation and
43
Applications, 9(1) (2013), 55-66.
44
[25] M. Otadi and M. Mosleh, Simulation and evaluation of dual fully fuzzy linear systems by
45
fuzzy neural network, Applied Mathematical Modelling, 35(10) (2011), 5026-5039.
46
[26] M. Otadi and M. Mosleh, Solving fully fuzzy matrix equations, Applied Mathematical Mod-
47
elling, 36(12) (2012), 61146121.
48
[27] M. Otadi and M. Mosleh, Minimal solution of non-square fuzzy linear systems, Journal of
49
Fuzzy Set Valued Analysis, Article ID jfsva-00105, doi: 10.5899/2012/jfsva-00105, 2012.
50
[28] M. Otadi, M. Mosleh and S. Abbasbandy, Numerical solution of fully fuzzy linear systems
51
by fuzzy neural network, Soft Comput, 15 (2011), 15131522.
52
[29] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22(5) (2004),
53
1039-1046.
54
[30] K. Wang, G. Chen and Y. Wei, Perturbation analysis for a class of fuzzy linear systems, J.
55
of Comput. Appl. Math., 224(1) (2009), 54-65.
56
[31] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning,
57
Information Sciences, 8(3) (1975), 199-249.
58
ORIGINAL_ARTICLE
On upper and lower almost weakly continuous fuzzy multifunctions
The aim of this paper is to introduce the concepts of fuzzy upper and fuzzy lower almost continuous, weakly continuous and almost weakly continuous multifunctions. Several characterizations and properties of these multifunctions along with their mutual relationships are established in $L$-fuzzy topological spaces
http://ijfs.usb.ac.ir/article_1864_eefebf9043466cbd4a7fffd52e7d586e.pdf
2015-02-28T11:23:20
2018-05-25T11:23:20
101
114
10.22111/ijfs.2015.1864
$L$-fuzzy topology
Fuzzy multifunction
Fuzzy upper and lower almost continuous
Weakly continuous
Almost weakly continuous
Composition
Union
S. E.
Abbas
sabbas73@yahoo.com
true
1
Department of Mathematics, Faculty of Science, Jazan University, Saudi
Arabia
Department of Mathematics, Faculty of Science, Jazan University, Saudi
Arabia
Department of Mathematics, Faculty of Science, Jazan University, Saudi
Arabia
AUTHOR
M. A.
Hebeshi
mhebeshi@yahoo.com
true
2
Department of Mathematics, Faculty of Science, Sohag University,
Egypt
Department of Mathematics, Faculty of Science, Sohag University,
Egypt
Department of Mathematics, Faculty of Science, Sohag University,
Egypt
AUTHOR
I. M.
Taha
imtaha2010@yahoo.com
true
3
Department of Mathematics, Faculty of Science, Sohag University,
Egypt
Department of Mathematics, Faculty of Science, Sohag University,
Egypt
Department of Mathematics, Faculty of Science, Sohag University,
Egypt
LEAD_AUTHOR
[1] S. E. Abbas, M. A. Hebeshi and I. M. Taha, On fuzzy upper and lower semi-continuous
1
multifunctions, Journal of Fuzzy Mathematics, 22(4) (2014).
2
[2] K. M. A. Al-hamadi and S. B. Nimse, On fuzzy -continuous multifunctions, Miskolc Mathematical
3
Notes, 11(2) (2010), 105-112.
4
[3] M. Alimohammady, E. Ekici, S. Jafari and M. Roohi, On fuzzy upper and lower contra-
5
continuous multifunctions, Iranian Journal of Fuzzy Systems, 8(3) (2011), 149-158.
6
[4] H. Aygun and S. E. Abbas, Some good extensions of compactness in Sostak's L-fuzzy topology,
7
Hacettepe Journal of Mathematics and Statistics, 36(2) (2007), 115-125.
8
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topology, Indian J. Pure Appl. Math., 34(2) (2003), 311-333.
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47
ORIGINAL_ARTICLE
Fuzzy Vector Equilibrium Problem
In the present paper, we introduce and study a fuzzy vector equilibrium problem and prove some existence results with and without convexity assumptions by using some particular forms of results of textit{Kim} and textit{Lee} [W.K. Kim and K.H. Lee, Generalized fuzzy games and fuzzy equilibria, Fuzzy Sets and Systems, 122 (2001), 293-301] and textit{Tarafdar} [E. Tarafdar, Fixed point theorems in $H$-spaces and equilibrium points of abstract economies, J. Aust. Math. Soc.(Series A), 53(1992), 252-260]. An example is also constructed in support of fuzzy vector equilibrium problem.
http://ijfs.usb.ac.ir/article_1865_534c7c77c8a3bbb244c81ad089b2ba68.pdf
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115
122
10.22111/ijfs.2015.1865
Equilibrium
Upper semicontinuity
Fuzzy mapping
$H$-space
Mijanur
Rahaman
mrahman96@yahoo.com
true
1
Department of Mathematics, Aligarh Muslim University, Aligarh-
202002, India
Department of Mathematics, Aligarh Muslim University, Aligarh-
202002, India
Department of Mathematics, Aligarh Muslim University, Aligarh-
202002, India
LEAD_AUTHOR
Rais
Ahmad
raisain_123@rediffmail.com
true
2
Department of Mathematics, Aligarh Muslim University, Aligarh-202002,
India
Department of Mathematics, Aligarh Muslim University, Aligarh-202002,
India
Department of Mathematics, Aligarh Muslim University, Aligarh-202002,
India
AUTHOR
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1
Mazukiewicz theorem and minimax inequalities, Journal of Mathematical Analysis and Ap-
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plications, 132 (1988), 484-490.
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the new existence theorems, Journal of Mathematical Economics, 3(3) (1976), 313-316.
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6
and qualitative fuzzy games, Fuzzy Sets and Systems, 125(3) (2002), 389-399.
7
[4] B. S. Choudhury and S. Kundu, A viscosity type iteration by weak contraction for approx-
8
imating solutions of generalized equilibrium problem, Journal of Nonlinear Science and Ap-
9
plications, Special issue, 5(3) (2012), 243-251.
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of Mathematical Analysis and Applications, 305(1) (2005), 29-42.
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Mathematical Society, 68(2) (2009), 295-302.
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[8] W. K. Kim and K. H. Lee, Generalized fuzzy games and fuzzy equilibria, Fuzzy Sets and
17
Systems, 122 (2001), 293-301.
18
[9] W. K. Kim and K. H. Lee, Fuzzy xed point and existence of equilibria of fuzzy games, The
19
Journal of Fuzzy Mathematics, 6 (1998), 193-202.
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and multi-leader-follower games, Computational Management Science, 2(1) (2005), 21-56.
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[11] E. Tarafdar, Fixed point theorems in H-spaces and equilibrium points of abstract economies,
23
Journal of the Australian Mathematical Society (Series A), 53 (1992), 252-260.
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Theory, 20(3) (1992), 247-254.
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35
drecht, 1988.
36
ORIGINAL_ARTICLE
Generalized Weakly Contractions in Partially Ordered Fuzzy Metric Spaces
In this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and coincidence point theorems on partially ordered fuzzy metric spaces are proved. Also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.
http://ijfs.usb.ac.ir/article_1866_7f6476dc4b3ff67400972d3c18b7a46c.pdf
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123
129
10.22111/ijfs.2015.1866
Partially ordered fuzzy metric space
Generalized weakly contraction
Fixed point theorem
Common fixed point theorem
S. M.
Vaezpour
vaez@aut.ac.ir
true
1
Department of Mathematics and Computer Science, Amirkabir Uni-
versity of Technology, 424 Hafez Avenue, Tehran 15914, Iran
Department of Mathematics and Computer Science, Amirkabir Uni-
versity of Technology, 424 Hafez Avenue, Tehran 15914, Iran
Department of Mathematics and Computer Science, Amirkabir Uni-
versity of Technology, 424 Hafez Avenue, Tehran 15914, Iran
LEAD_AUTHOR
S.
Vaezzadeh
sarah_vaezzadeh@yahoo.com
true
2
Department of Mathematics and Computer Science,, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran
Department of Mathematics and Computer Science,, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran
Department of Mathematics and Computer Science,, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran
AUTHOR
[1] M. A. Ahmed, Fixed point theorems in fuzzy metric spaces, Journal of the Egyptian Mathe-
1
matical Society, (in press).
2
[2] Y. J. Cho, Fixed points in fuzzy metric spaces. J Fuzzy Math, 39 (1997), 949-962.
3
[3] Y. J. Cho, S. Sedghi, N. Shobe, Generalized xed point theorems for compatible mappings
4
with some types in fuzzy metric spaces. J Fuzzy Math, 39 (2009), 2233-2244.
5
[4] L. B. Ciric, D. Mihet and R. Saadati, Monotone generalized contractions in partially ordered
6
probabilistic metric spaces, Topol. Appl., 156 (2009), 2838-2844.
7
[5] M. Goudarzi and S. M. Vaezpour,On the denition of fuzzy Hilbert spaces and its application,
8
J. Nonlinear Sci. Appl., 2(1) (2009) 46-59.
9
[6] O. Hadzic and E. Pap, Fixed Point Theory in PM Spaces, Kluwer Academic Publ., 2001.
10
[7] Y. Liu and Z. Li, Coincidence point theorems in probabilistic and fuzzy metric spaces, 158
11
(2007), 58-70.
12
[8] D. Mihe t, A generalization of a contraction principle in probabilistic metric spaces (II),
13
Int. J. Math. Math. Sci, 5 (2005), 729-736.
14
[9] S. N. Mishra, N. Sharma and S. L. Singh, Common xed points of maps on fuzzy metric
15
spaces, International Journal of Mathematics and Mathematical Sciences, 17 (1994), 253-
16
[10] S. H. Nasseri, Fuzzy nonlinear optimization, Nonlinear Anal, 1 (2008), 236-240.
17
[11] H. K. Nashine and B. Samet, Fixed point results for mappings satisfying ( ; ') weakly
18
contractive condition in partially ordered metric spaces, Nonlinear Anal, 74 (2011), 2201-
19
[12] D. O'Regan and R. Saadati, Nonlinear contraction theorems in probabilistic spaces. Appl.
20
Math. Comput, 195 (2008), 86-93.
21
[13] B. Singh and M. S. Chauhan, Common xed points of compatible maps in fuzzy metric spaces,
22
Fuzzy Sets and Systems, 115 (2000), 471-475.
23
[14] B. Singh and S. Jain, Semi-compatibility, compatibility and xed point theorems in Fuzzy
24
metric space, Journal of Chungecheong Math. Soc., 18(1) (2005), 1-22.
25
[15] B. Schweizer and A. Sklar, Probabilistic Metric Spaces, Elsevier North Holand, New York,
26
[16] P. V. Subrahmanyam, A Common xed point theorem in fuzzy metric spaces, Information
27
Sciences, 83 (1995), 109-112
28
ORIGINAL_ARTICLE
Persian-translation vol. 12, no. 1, February 2015
http://ijfs.usb.ac.ir/article_2651_15ce1ae24f3cd06bf99f720897fdd3a3.pdf
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141
10.22111/ijfs.2015.2651