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An integrated multicriteria decisionmaking methodology based on type2 fuzzy sets for selection among energy alternatives in Turkey
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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 multicriteria decisionmaking (MCDM) methodology based on type2 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 type2 fuzzy sets.Fuzzy Analytic Hierarchy Process (FAHP) based on interval type2 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 type2 fuzzy sets. The proposed integrated MCDM methodology based on interval type2 fuzzy sets is applied to obtain a road map of energy policies for Turkey.
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Melike
Erdogan
Department of Industrial Engineering, Yildiz Technical University, Yildiz, BESIKTAS, Istanbul, Turkey
Department of Industrial Engineering, Yildiz
Turkey
melike@yildiz.edu.tr


ihsan
Kaya
Department of Industrial Engineering, Yildiz Technical University, Yildiz, BESIKTAS, Istanbul, Turkey
Department of Industrial Engineering, Yildiz
Turkey
iekaya@yahoo.com
Energy
Multi criteria decision making
Interval type2 fuzzy sets
AHP
TOPSIS
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Approximation theorems for fuzzy set multifunctions in Vietoris topology. Physical implications of regularity
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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.
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A.
Gavrilut
Faculty of Mathematics, Alexandru Ioan Cuza" University of Iasi
Iasi, Romania
Faculty of Mathematics, Alexandru Ioan Cuza"
Romania
gavrilut@uaic.ro


M.
Agop
Department of Physics, Gheorghe Asachi Technical University of Iasi, Iasi,
Romania
Department of Physics, Gheorghe Asachi Technical
Romania
m.agop@yahoo.com
Vietoris topology
Regularity
Approximations
Fractal Theories
Nondifferentiable physics
Scale relativity theory
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Uniformities in fuzzy metric spaces
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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 quasiuniformities and $I$quasiuniformities is given and it is proved that the category of strongly stratified $I$quasiuniform spaces can be embedded in the category of Hutton quasiuniform spaces as a bicoreflective subcategory. Also it is shown that two kinds of Hutton quasiuniformities can generate the same $I$uniformity in fuzzy metric spaces.
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Yueli
Yue
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
Department of Mathematics, Ocean University
China
ylyue@ouc.edu.cn


Jinming
Fang
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
Department of Mathematics, Ocean University
China
jmfang@ouc.edu.cn
Fuzzy metric
$I$uniformity
Hutton quasiuniformity
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Application of parametric form for ranking of fuzzy numbers
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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.
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R.
Ezzati
Department of Mathematics, Karaj Branch, Islamic Azad University, 31485  413, Karaj, Iran
Department of Mathematics, Karaj Branch,
Iran
ezati@kiau.ac.ir


S.
Khezerloo
Department of Mathematics, Islamic Azad University  South Tehran, Branch, Tehran, Iran
Department of Mathematics, Islamic Azad University
Iran
s_khezerloo@azad.ac.ir


S.
Ziari
Department of Mathematics, Firoozkooh Branch,Islamic Azad University, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch,Islam
Iran
sziari@iaufb.ac.ir
Ranking of fuzzy numbers
Parametric form of fuzzy number
Magnitude of fuzzy number
[bibitem{abb1} S. Abbasbandy and T. Hajjari, {it A new approach for ranking of trapezoidal fuzzy numbers},##Computers and Mathematics with Applications, {bf 57} (2009), 413419.##bibitem{ABBAS}##S. Abbasbandy and B. Asady, {it Ranking of fuzzy numbers by sign##distance}, Information Sciences, {bf 176} (2006), 24052416.##bibitem{Asadi} B. Asady and A. Zendehnam, {it Ranking fuzzy numbers by distance minimizing},##Applied Mathematical Modeling, {bf 31} (2007), 25892598.##bibitem{MatBrun} M. Brunelli and J. Mezeib, {it How different are ranking methods for fuzzy numbers?##A numerical study}, International Journal of Approximate Reasoning, {bf 54} (2013), 627639.##bibitem{ChenTang} C. C. Chen and H. C. Tang, {it Ranking of nonnormal pnorm##trapezoidal fuzzy numbers with integral value},##Computers and Mathematics with Applications, {bf 56} (2008), 2340ï¿½2346.##bibitem{chu}##T. Chu and C. Tsao, {it Ranking fuzzy numbers with an area between the##centroid point and original points}, Computers and Mathematics with Application {bf 43} (2002),##bibitem{cheng1}##C. H. Cheng, {it A new approach for ranking fuzzy numbers by distance minimizing}, Fuzzy Sets and Systems, {bf 95}##(1998), 307317.##bibitem{DUPR} D. Dubois and H. Prade, {it Towards fuzzy differential calculus:##Part 3, differentiation}, Fuzzy Sets and Systems, {bf 8} (1982), 225233.##bibitem{HD}H. Deng, {it Comparing and ranking fuzzy numbers using ideal solutions},##Applied Mathematical Modelling, {bf 38}textbf{(56)} (2014), 16381646.##bibitem{Ezzati}##R. Ezzati, T. Allahviranloo, S. Khezerloo and M. Khezerloo, {it An approach for ranking of fuzzy numbers},##Expert Systems with Applications, {bf 39} (2012), 690695.##bibitem{SGG} S. G. Gal, {it Approximation theory in fuzzy setting}, In:##G. A. Anastassiou, ed., Handbook of AnalyticComputational##Methods in Applied Mathematics, Chapman Hall CRC Press, (2000), 617666.## bibitem{voxman} R. Goetschel and W. Voxman, {it Elementary calculus}, Fuzzy Sets and Systems, {bf 18} (1986),## bibitem{jain1}##R. Jain, {it Decisionmaking in the presence of fuzzy variable}, IEEE Trans. Syst. Man Cybren, {bf 6} (1976), 698703.##bibitem{jain2}##R. Jain, {it A procedure for multiaspect decision making using fuzzy sets}, Int. J. Syst. Sci, {bf 8} (1977), 17.##bibitem{AmitKumar1} A. Kumar, P. Singh, A. Kaur and P. Kaur,##{it A new approach for ranking nonnormal pnorm trapezoidal fuzzy numbers},## Computers and Mathematics with Applications, {bf 61} (2011), 881887.##bibitem{AmitKumar2} A. Kumar, P. Singh, P. Kaur and A. Kaur,##{it A new approach for ranking of L.R type generalized fuzzy numbers},##Expert Systems with Applications, {bf 38} (2011), 1090610910.##bibitem{liwang}T. S. Liou and M. J. Wang, {it Ranking fuzzy numbers with integral value},##Fuzzy Sets and Systems, {bf 50} (1992), 247255.##bibitem{liu}##X. Liu, {it Measuring the satisfaction of constraints in fuzzy##linear programming}, Fuzzy Sets and Systems, {bf 122} (2001), 263275.## bibitem{ma}##M. Ma, M. Friedman and A. Kandal, {it A new fuzzy arithmetic},##Fuzzy Sets and Systems, {bf 108} (1999), 8390.## bibitem{mun}##B. Matarazzo and G. Munda, {it New approaches for the comparison of##LR fuzzy numbers}, Fuzzy Sets and Systems, {bf 118} (2001), 407418.##bibitem{kerre1}##X. Wang and E. E. Kerre, {it Reasonable properties for the ordering##of fuzzy quantities $(I)$}, Fuzzy Sets and Systems, {bf 118} (2001), 375385.##bibitem{kerre2}##X. Wang and E. E. Kerre, {it Reasonable properties for the ordering##of fuzzy quantities $(I)$}, Fuzzy Sets and Systems, {bf 118} (2001), 387405.##bibitem{Wang}##Y. J. Wang and S. H. Lee, {it The revised method of ranking fuzzy##numbers with an area between the centroid an original points},##Computers and mathematics with Applications, {bf 55} (2008). 20332042.##bibitem{Yao}##J. Yao and K. Wu, {it Ranking fuzzy numbers based on decomposition##principle and signed distance}, Fuzzy Sets and Systems, {bf 116} (2000), 275  288.##%bibitem{WZG}C. Wu, Z. Gong, {it On Henstock integral of fuzzynumbervalued functions I}, Fuzzy Sets and Systems, {bf 120} (2001), 523532.##vspace{.3cm}##]
Coupled Coincidence and Common Fixed Point Theorems for SingleValued and Fuzzy Mappings
2
2
In this paper, we study the existence of coupled coincidence andcoupled common fixed points for singlevalued 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:10.1186/1687181220124].
1

75
87


Li
Zhu
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,
China
zflcz@aliyun.com


Chuanxi
Zhu
Department of Mathematics, Nanchang University, Nanchang 330031,
P. R. China
Department of Mathematics, Nanchang University,
China
zhuchuanxi@sina.com


Xianjiu
Huang
Department of Mathematics, Nanchang University, Nanchang 330031,
P. R. China
Department of Mathematics, Nanchang University,
China
xjhuang99@163.com
Fuzzy mapping
Coupled coincidence point
Coupled common fixed point
Coupled fixed point
[[1] M. Abbas, L. Ciric, B. Damjanovic and M. A. Khan, Coupled coincidence and common xed##point theorems for hybrid pair of mappings, Fixed Point Theory Appl., doi: 10.1186/1687##181220124, 4 (2012).##[2] M. Abbas, B. Damjanovic and R. Lazovic, Fuzzy common xed point theorems for generalized##contractive mappings, Appl. Math. Lett., 23 (2010), 13261330.##[3] M. Abbas, A. R. Khan and T. Nazir, Coupled common xed point results in two generalized##metric spaces, Appl. Math. Comput., 217 (2011), 63286336.##[4] M. Abbas, M. A. Khan and S. Radenovic, Common coupled point theorems in cone metric##spaces for !compatible mappings, Appl. Math. Comput., 217 (2010), 195202.##[5] H. M. AbuDonia, Common xed point theorems for fuzzy mappings in metric space under##'contraction condition, Chaos Solitons Fractals, 34 (2007), 538543.##[6] H. Aydi, B. Damjanovic, B. Samet and W. Shatanawi, Coupled xed point theorems for non##linear contractions in partially ordered Gmetric spaces, Math. Comput. Model., 54 (2011),##24432450.##[7] H. Aydi, M. Postolache and W. Shatanawi, Coupled xed point results for ( ; )weakly##contractive mappings in ordered Gmetric spaces, Comput. Math. Appl., 63 (2012), 298309.##[8] A. Azam and I. Beg, Common xed points of fuzzy maps, Math. Comput. Model., 49 (2009),##13311336. ##[9] I. Beg and A. R. Butt, Fixed point for setvalued mappings satisfying an implicit relation in##partially ordered metric spaces, Nonlinear Anal., 71 (2009), 36993704.##[10] T. G. Bhashkar and V. Lakshmikantham, Fixed point theorems in partially ordered metric##spaces and applications, Nonlinear Anal., 65 (2006), 13791393.##[11] Y. J. Cho, B. E. Rhoades, R. Saadati, B. Samet and W. Shatanawi, Nonlinear coupled xed##point theorems in ordered generalized metric spaces with integral type, Fixed Point Theory##Appl., doi: 10.1186/1687181220128, 8 (2012).##[12] B. S. Choudhury and A. Kundu, A coupled coincidence point result in partially ordered metric##spaces for compatible mappings, Nonlinear Anal., 73 (2010), 25242531.##[13] B. S. Choudhury and P. Maity, Coupled xed point results in generalized metric spaces, Math.##Comput. Model., 54 (2011), 7379.##[14] B. S. Choudhury and N. Metiya, Multivalued and singlevalued xed point risults in partially##ordered metric spaces, Arab. J. Math. Sci., 17 (2011), 135151.##[15] L. Ciric, M. Abbas and B. Damjanovic, Common fuzzy xed point theorems in ordered metric##spaces, Math. Comput. Model., 53 (2011), 17371741.##[16] B. Damjanovic, B. Samet and C. Vetro, Common xed point theorems for multivalued maps,##Acta Math. Sci. Ser. B Engl. Ed., 32 (2012), 818824.##[17] H. S. Ding, L. Li and S. Radenovic, Coupled coincidence point theorems for generalized##nonlinear contraction in partially ordered metric spaces, Fixed Point Theory Appl., doi:##10.1186/16871812201296, 96 (2012).##[18] W. S. Du, On coincidence point and xed point theorems for nonlinear multivalued maps,##Topology Appl., 159 (2012), 4956.##[19] V. D. Estruch and A. Vidal, A note on xed fuzzy points for fuzzy mappings, Rend. Istit.##Mat. Univ. Trieste, 32 (2001), 3945.##[20] M. E. Gordji, M. Ramezani, Y. J. Cho and E. Akbartabar, Coupled commom xed point##theorems for mixed weakly monotone mappings in partially ordered metric spaces, Fixed##Point Theory Appl., doi: 10.1186/16871812201295, 95 (2012).##[21] J. Harjani, B. Lopez and K. Sadarangani, Fixed point theorems for mixed monotone operators##and applications to integral equations, Nonlinear Anal., 74 (2011), 17491760.##[22] S. Heilpern, Fuzzy mappings and fuzzy xed point theorems, J. Math. Anal. Appl., 83 (1981),##[23] S. H. Hong, Fixed points of multivalued operators in ordered metric spaces with applications,##Nonlinear Anal., 72 (2010), 39293942.##[24] N. Hussain and A. Alotaibi, Coupled coincidences for multivalued contractions in partially##ordered metric spaces, Fixed Point Theory Appl., doi: 10.1186/16871812201182, 82 (2011).##[25] M. Imdad and L. Khan, Fixed point theorems for a family of hybrid pairs of mappings in##metrically convex spaces, Fixed Point Theory Appl., 3 (2005), 281294.##[26] T. Kamran, Common xed points theorems for fuzzy mappings, Chaos Solitons Fractals, 38##(2008), 13781382.##[27] H. Kaneko and S. Sessa, Fixed point theorems for compatible multivalued and singlevalued##mappings, Int. J. Math. Math. Sci., 12 (1989), 257262.##[28] E. Karapinar, Coupled xed point theorems for nonlinear contractions in cone metric spaces,##Comput. Math. Appl., 59 (2010), 36563668.##[29] F. Khojasteh and V. Rakocevic, Some new common xed point results for generalized con##tractive multivalued nonselfmappings, Appl. Math. Lett., 25 (2012), 287293.##[30] V. Lakshmikantham and L. Ciric, Coupled xed point theorems for nonlinear contractions in##partially ordered metric space, Nonlinear Anal., 70 (2009), 43414349.##[31] B. S. Lee, G. M. Lee, S. J. Cho and D. S. Kim, A common xed point theorem for a pair of##fuzzy mappings, Fuzzy Sets and Systems, 98 (1998), 133136.##[32] Y. C. Liu, J. Wu and Z. X. Li, Common xed points of singlevalued and multivalued maps,##Int. J. Math. Math. Sci., 19 (2005), 30453055.##[33] N. V. Luong and N. X. Thuan, Coupled xed points in partially ordered metric spaces and##application, Nonlinear Anal., 74 (2011), 983992. ##[34] N. V. Luong and N. X. Thuan, Coupled xed point theorems in partially ordered Gmetric##spaces, Math. Comput. Model., 55 (2012), 16011609.##[35] J. T. Markin, A xed point theorem for setvalued mappings, Bull. Am. Math. Soc., 74 (1968),##[36] S. B. Nadler, Multivalued contraction mappings, Pacic J. Math., 30 (1969), 475488.##[37] F. Sabetghadam, H. P. Masiha and A. H. Sanatpour, Some coupled xed point theorems in##cone metric spaces, Fixed Point Theory Appl., doi: 10.1155/2009/125426. Article ID 125426,##[38] B. Samet, Coupled xed point theorems for a generalized MeirKeeler contraction in partially##ordered metric spaces, Nonlinear Anal., 72 (2010), 45084517.##[39] S. Sedghi, I. Altun and N. Shobe, A xed point theorem for multimaps satisfying an implicit##relation on metric spaces, Appl. Anal. Discrete Math., 2 (2008), 189196.##[40] W. Shatanawi, B. Samet and M. Abbas, Coupled xed point theorems for mixed monotone##mappings in ordered partial metric spaces, Math. Comput. Model., 55 (2012), 680687.##[41] S. L. Singh and S. N. Mishra, Fixed point theorems for singlevalued and multivalued maps,##Nonlinear Anal., 74 (2011), 22432248.##[42] W. Sintunavarat and P. Kumam, Common xed point theorem for hybrid generalized mulit##valued contraction mappings, Appl. Math. Lett., 25 (2012), 5257.##]
Minimal solution of fuzzy linear systems
2
2
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.
1

89
99


M.
Otadi
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer
sity, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch,
Iran
mahmoodotadi@yahoo.com


M.
Mosleh
Department of Mathematics, Firoozkooh Branch, Islamic Azad Univer
sity, Firoozkooh, Iran
Department of Mathematics, Firoozkooh Branch,
Iran
mosleh@iaufb.ac.ir
Fuzzy linear system
Pseudoinverse
Minimal solution
[[1] S. Abbasbandy and M. Alavi, A new method for solving symmetric fuzzy linear systems,##Mathematics Scientic Journal, Islamic Azad University of Arak, 1 (2005), 5562.##[2] S. Abbasbandy, E. Babolian and M. Alavi, Numerical method for solving linear Fredholm##fuzzy integral equations of the second kind, Chaos, Solitons & Fractals, 31(1) (2007), 138##[3] S. Abbasbandy, A. Jafarian and R. Ezzati, Conjugate gradient method for fuzzy symmetric##positive denite system of linear equations, Appl. Math. Comput., 171(2) (2005), 11841191.##[4] S. Abbasbandy, R. Ezzati and A. Jafarian, LU decomposition method for solving fuzzy system##of linear equations, Appl. Math. Comput., 172(1) (2006), 633643.##[5] S. Abbasbandy, J. J. Nieto and M. Alavi, Tuning of reachable set in one dimensional fuzzy##dierential inclusions, Chaos, Solitons & Fractals, 26(5) (2005), 13371341.##[6] S. Abbasbandy, M. Otadi and M. Mosleh, Minimal solution of general dual fuzzy linear##systems, Chaos, Solitons & Fractals, 37(4) (2008), 11131124.##[7] T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Appl. Math. Com##put., 155(2) (2004), 493502.##[8] T. Allahviranloo, Successive over relaxation iterative method for fuzzy system of linear equa##tions, Appl. Math. Comput., 162(1) (2005), 189196.##[9] T. Allahviranloo, The Adomian decomposition method for fuzzy system of linear equations,##Appl. Math. Comput., 163(2) (2005), 553563. ##[10] S. E. Amrahov and I. N. Askerzade, Strong solutions of the fuzzy linear systems, Computer##Modeling in Engineering & Sciences, 76 (2011), 207216.##[11] B. Asady, S. Abbasbandy and M. Alavi, Fuzzy general linear systems, Appl. Math. Comput.,##169(1) (2005), 3440.##[12] S. Barnet, Matrix methods and applications, Clarendon Press, Oxford, 1990.##[13] W. CongXin and M. Ming, Embedding problem of fuzzy number space, Fuzzy Sets and##Systems, 44(1) (1991), 3338.##[14] D. Dubois and H. Prade, Operations on fuzzy numbers, J. Systems Sci., 9(6) (1978), 613626.##[15] R. Ezzati, Solving fuzzy linear systems, Soft Computing, 15(1) (2011), 193197.##[16] M. Friedman, M. Ming and A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems, 96(2)##(1998), 201209.##[17] M. Friedman, M. Ming and A. Kandel, Duality in fuzzy linear systems, Fuzzy Sets and##Systems, 109(1) (2000), 5558.##[18] N. Gasilov, A. G. Fatullayev and S. E. Amrahov, Solution of nonsquare fuzzy linear systems,##Journal of MultipleValued Logic and Soft Computing, 20(1) (2013), 221237.##[19] O. Kaleva, Fuzzy dierential equations, Fuzzy Sets and Systems, 24(3) (1987), 301317.##[20] A. Kaufmann and M. M. Gupta, Introduction to Fuzzy Arithmetic, Van Nostrand Reinhold,##New York, 1985.##[21] G. J. Klir, U. S. Clair and B. Yuan, Fuzzy set theory: foundations and applications, Prentice##Hall Inc., 1997.##[22] D. Kincaid and W. Cheney, Numerical analysis, Mathematics of scientic computing. Second##Edition. Brooks/Cole Publishing Co., Pacic Grove, CA, 1996.##[23] M. Ming, M. Friedman and A. Kandel, A new fuzzy arithmetic, Fuzzy Sets and Systems,##108(1) (1999), 8390.##[24] M. Otadi, New solution of fuzzy linear matrix equations, Theory of Approximation and##Applications, 9(1) (2013), 5566.##[25] M. Otadi and M. Mosleh, Simulation and evaluation of dual fully fuzzy linear systems by##fuzzy neural network, Applied Mathematical Modelling, 35(10) (2011), 50265039.##[26] M. Otadi and M. Mosleh, Solving fully fuzzy matrix equations, Applied Mathematical Mod##elling, 36(12) (2012), 61146121.##[27] M. Otadi and M. Mosleh, Minimal solution of nonsquare fuzzy linear systems, Journal of##Fuzzy Set Valued Analysis, Article ID jfsva00105, doi: 10.5899/2012/jfsva00105, 2012.##[28] M. Otadi, M. Mosleh and S. Abbasbandy, Numerical solution of fully fuzzy linear systems##by fuzzy neural network, Soft Comput, 15 (2011), 15131522.##[29] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22(5) (2004),##10391046.##[30] K. Wang, G. Chen and Y. Wei, Perturbation analysis for a class of fuzzy linear systems, J.##of Comput. Appl. Math., 224(1) (2009), 5465.##[31] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning,##Information Sciences, 8(3) (1975), 199249.##]
On upper and lower almost weakly continuous fuzzy multifunctions
2
2
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
1

101
114


S. E.
Abbas
Department of Mathematics, Faculty of Science, Jazan University, Saudi
Arabia
Department of Mathematics, Faculty of Science,
Saudi Arabia
sabbas73@yahoo.com


M. A.
Hebeshi
Department of Mathematics, Faculty of Science, Sohag University,
Egypt
Department of Mathematics, Faculty of Science,
Egypt
mhebeshi@yahoo.com


I. M.
Taha
Department of Mathematics, Faculty of Science, Sohag University,
Egypt
Department of Mathematics, Faculty of Science,
Egypt
imtaha2010@yahoo.com
$L$fuzzy topology
Fuzzy multifunction
Fuzzy upper and lower almost continuous
Weakly continuous
Almost weakly continuous
Composition
Union
[[1] S. E. Abbas, M. A. Hebeshi and I. M. Taha, On fuzzy upper and lower semicontinuous##multifunctions, Journal of Fuzzy Mathematics, 22(4) (2014).##[2] K. M. A. Alhamadi and S. B. Nimse, On fuzzy continuous multifunctions, Miskolc Mathematical##Notes, 11(2) (2010), 105112.##[3] M. Alimohammady, E. Ekici, S. Jafari and M. Roohi, On fuzzy upper and lower contra##continuous multifunctions, Iranian Journal of Fuzzy Systems, 8(3) (2011), 149158.##[4] H. Aygun and S. E. Abbas, Some good extensions of compactness in Sostak's Lfuzzy topology,##Hacettepe Journal of Mathematics and Statistics, 36(2) (2007), 115125.##[5] C. Berge, Topological spaces, including a treatment of multivalued functions, vector spaces##and convexity, Oliver, Boyd London, 1963.##[6] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182190.##[7] K. C. Chattopadhyay and S. K. Samanta, Fuzzy topology: fuzzy closure operator, fuzzy##compactness and fuzzy connectedness, Fuzzy Sets and Systems, 54(2) (1993), 207212.##[8] J. A. Goguen, The Fuzzy Tychono theorem, J. Math. Anal. Appl., 43 (1993), 734742.##[9] U. Hohle, Upper semicontinuous fuzzy sets and applications, J. Math. Anall. Appl., 78 (1980),##[10] U. Hohle and A. P. Sostak, A general theory of fuzzy topological spaces, Fuzzy Sets and##Systems, 73 (1995), 131149.##[11] U. Hohle and A. P. Sostak, Axiomatic Foundations of FixedBasis fuzzy topology, The Handbooks##of Fuzzy sets series, Volume 3, Kluwer Academic Publishers, Dordrecht (Chapter 3),##[12] Y. C. Kim, A. A. Ramadan and S. E. Abbas, Weaker forms of continuity in Sostaks fuzzy##topology, Indian J. Pure Appl. Math., 34(2) (2003), 311333.##[13] Y. C. Kim, Initial Lfuzzy closure spaces, Fuzzy Sets and Systems, 133 (2003), 277297.##[14] T. Kubiak, On fuzzy topologies, Ph. D. Thesis, A. Mickiewicz, Poznan, 1985. ##[15] T. Kubiak and A. P. Sostak, Lower setvalued fuzzy topologies, Quaestions Math., 20(3)##(1997), 423429.##[16] Y. Liu and M. Luo, Fuzzy topology, World Scientic Publishing, Singapore, 1997.##[17] R. A. Mahmoud, An application of continuous fuzzy multifunctions, Chaos, Solitons and##Fractals, 17 (2003), 833841.##[18] M. N. Mukherjee and S. Malakar, On almost continuous and weakly continuous fuzzy multi##functions, Fuzzy Sets and Systems, 41 (1991), 113125.##[19] T. Noiri and V. Popa, Almost weakly continuous multifunctions, Demonstratio Mathematica,##VI(2) (1993), 363480.##[20] N. S. Papageorgiou, Fuzzy topology and fuzzy multifunctions, J. Math. Anal. Appl., 109##(1985), 397425.##[21] V. Popa, On characterizations of irresolute multimapping, J. Univ. Kuwait (Sci), 15 (1988),##[22] V. Popa, Irresolute multifunctions, Internat. J. Math. and Math. Sci., 13(2) (1990), 275280.##[23] A. A. Ramadan, S. E. Abbas and Y. C. Kim, Fuzzy irresolute mappings in smooth fuzzy##topological spaces, 9(4) (2001), 865877.##[24] A. P. Sostak, On a fuzzy topological structure, Suppl. Rend. Circ. Matem. Palerms ser II, 11##(1985), 89103.##[25] A. P. Sostak Two decades of fuzzy topology: basic ideas, notion and results, Russian Math.##Surveys, 44(6) (1989), 125186.##[26] A. P. Sostak, Basic structures of fuzzy topology, J. Math. Sci., 78(6) (1996), 662701.##[27] E. Tsiporkova, B. De Baets and E. Kerre, A fuzzy inclusion based approach to upper inverse##images under fuzzy multivalued mappings, Fuzzy Sets and Systems, 85 (1997), 93108.##[28] E. Tsiporkova, B. De Baets and E. Kerre, Continuity of fuzzy multivalued mappings, Fuzzy##Sets and Systems, 94 (1998), 335348.##]
Fuzzy Vector Equilibrium Problem
2
2
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), 293301] 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), 252260]. An example is also constructed in support of fuzzy vector equilibrium problem.
1

115
122


Mijanur
Rahaman
Department of Mathematics, Aligarh Muslim University, Aligarh
202002, India
Department of Mathematics, Aligarh Muslim
India
mrahman96@yahoo.com


Rais
Ahmad
Department of Mathematics, Aligarh Muslim University, Aligarh202002,
India
Department of Mathematics, Aligarh Muslim
India
raisain_123@rediffmail.com
Equilibrium
Upper semicontinuity
Fuzzy mapping
$H$space
[[1] C. Bardaro and R. Cappitelli, Some further generalizations of the KnasterKuratowski##Mazukiewicz theorem and minimax inequalities, Journal of Mathematical Analysis and Ap##plications, 132 (1988), 484490.##[2] A. Borglin and H. Keiding, Existence of equilibrium actions and of equilibrium: A note on##the new existence theorems, Journal of Mathematical Economics, 3(3) (1976), 313316.##[3] S. S. Chang and K. K. Tan, Equilibria and maximal elements of abstract fuzzy economies##and qualitative fuzzy games, Fuzzy Sets and Systems, 125(3) (2002), 389399.##[4] B. S. Choudhury and S. Kundu, A viscosity type iteration by weak contraction for approx##imating solutions of generalized equilibrium problem, Journal of Nonlinear Science and Ap##plications, Special issue, 5(3) (2012), 243251.##[5] G. Debreu, A social equilibrium existence theorem, Proc. National Academy of Sciences,##U.S.A., 38 (1952), 886893.##[6] X. P. Ding, Maximal element theorems in product FCspaces and generalized games, Journal##of Mathematical Analysis and Applications, 305(1) (2005), 2942.##[7] A. Khaliq and S. Krishnan, Vector quasiequilibrium problems, Bulletin of the Australian##Mathematical Society, 68(2) (2009), 295302.##[8] W. K. Kim and K. H. Lee, Generalized fuzzy games and fuzzy equilibria, Fuzzy Sets and##Systems, 122 (2001), 293301.##[9] W. K. Kim and K. H. Lee, Fuzzy xed point and existence of equilibria of fuzzy games, The##Journal of Fuzzy Mathematics, 6 (1998), 193202.##[10] J. S. Pang and M. Fukushima, Quasivariational inequalities, generalized Nash equilibria,##and multileaderfollower games, Computational Management Science, 2(1) (2005), 2156.##[11] E. Tarafdar, Fixed point theorems in Hspaces and equilibrium points of abstract economies,##Journal of the Australian Mathematical Society (Series A), 53 (1992), 252260. ##[12] G. Tian, On the existence of equilibria in generalized games,International Journal of Game##Theory, 20(3) (1992), 247254.##[13] G. Tian, Equilibrium in abstract economies with a noncompact innite dimensional strategy##space, an innite number of agents and without ordered preferences, Economics Letters, 33##(1990), 203206.##[14] U. Witthayarat, Y. J. Cho and P. Kumam, Approximation algorithm for xed points of##nonlinear operators and solutions of mixed equilibrium problems and variational inclusion##problems with applications, Journal of Nonlinear Science and Applications, Special issue, 5(6)##(2012), 475494.##[15] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##[16] H. J. Zimmermann, Fuzzy set theory and its applications, Kluwer Academic Publishers, Dor##drecht, 1988.##]
Generalized Weakly Contractions in Partially Ordered Fuzzy Metric Spaces
2
2
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.
1

123
129


S. M.
Vaezpour
Department of Mathematics and Computer Science, Amirkabir Uni
versity of Technology, 424 Hafez Avenue, Tehran 15914, Iran
Department of Mathematics and Computer Science,
Iran
vaez@aut.ac.ir


S.
Vaezzadeh
Department of Mathematics and Computer Science,, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran
Department of Mathematics and Computer Science,,
Iran
sarah_vaezzadeh@yahoo.com
Partially ordered fuzzy metric space
Generalized weakly contraction
Fixed point theorem
Common fixed point theorem
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