2016
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A PSObased Optimization of a fuzzybased MPPT controller for a photovoltaic pumping system used for irrigation of greenhouses
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The main asset of this paper is among the uses of fuzzy logic in the engineering sector and especially in the renewable energies as a large alternate of fossil energies, in this paper a PSObased optimization is used to find the optimal scaling parameters, of a fuzzy logicbased MPPT controller, that maximize the efficiency of a photovoltaic pumping system. The tuning of input and output parameters are of direct effect on the power that flows from the photovoltaic source to the load. In order to see concrete results, the PV system is used for irrigation of greenhouses in Laghouat, Algeria. The performances of the proposed PSObased fuzzy controller are compared with those obtained using fuzzy logic and P&O controllers under variations of meteorological conditions. The simulation results proved a good robustness performance of the proposed Fuzzy based PSO controller over the other regarding the gained solar energy and the daily pumped water.
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aboubakeur
Hadjaissa
LACoSERE Laboratory, Amar Telidji University, BP 37G,
Ghardaia Road, Laghouat (03000), Algeria
LACoSERE Laboratory, Amar Telidji University,
Algeria


Khaled
Ameur
LACoSERE Laboratory, Amar Telidji University, BP 37G, Ghardaia
Road, Laghouat (03000), Algeria
LACoSERE Laboratory, Amar Telidji University,
Algeria


Mohamed Salah
AitCheikh
LDCCP Laboratory, Ecole nationale polytchnique, 10
avenue H. Badi BP 182 Harrach Algiers, Algeria
LDCCP Laboratory, Ecole nationale polytchnique,
Algeria


Najib
Essounbouli
CReSTIC Laboratory, Reims University, 10026 Troyes CEDEX,
France
CReSTIC Laboratory, Reims University, 10026
France
PSObased optimization
Photovoltaic pumping system
MPPT controller
Fuzzy logic
Perturb and Observe (P&O)
[[1] M. A. Eltawil and Z. Zhao, MPPT techniques for photovoltaic applications, Renewable and##Sustainable Energy Reviews, 25 (2013), 793813.##[2] N. Gokmen, E. Karatepe, F. Ugranli and S. Silvestre, Voltage band based global MPPT##controller for photovoltaic systems, Solar Energy, 98 (2013), 322334.##[3] O. Guenounou, B. Dahhou and F.Chabour, Adaptive fuzzy controller based MPPT for pho##tovoltaic systems, Energy Conversion and Management, 78 (2014), 843850.##[4] A. M. Kassem, MPPT control design and performance improvements of a PV generator##powered DC motorpump system based on articial neural networksm, Electrical Power and##Energy Systems, 43 (2012), 90{98.##[5] L. K. Letting ,J. L. Munda and Y. Hamam, Optimization of a fuzzy logic controller for PV##grid inverter control using Sfunction based PSO, Solar Energy, 86 (2012), 16891700.##[6] T. Martire, C. Glaize, C. Joubert and B. Rouviere, A simplied but accurate prevision method##for along the sun PV pumping systems, Solar energy, 82 (2008), 10091020.##[7] E. Mehdizadeh, S. Sadinezhad and R. Tavakkolimoghaddam, Optimization of fuzzy clus##tering criteria by a hybrid PSO and fuzzy cmeans clustering algorithm, Iranian Journal of##Fuzzy Systems, 5(3) (2008), 114.##[8] P. Periasamy, N. K. Jain and I. P.Singh, A review on development of photovoltaic water##pumping system, Renewable and Sustainable Energy Reviews, 43 (2015), 918925.##[9] H. Rezk and A. M. Eltamaly, A comprehensive comparison of dierent MPPT techniques##for photovoltaic systems, Solar energy, 112 (2015), 111.##]
On minimal realization of IFlanguages: A categorical approach
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he purpose of this work is to introduce and study the concept of minimal deterministic automaton with IFoutputs which realizes the given IFlanguage. Among two methods for construction of such automaton presented here, one is based on MyhillNerode's theory while the other is based on derivatives of the given IFlanguage. Meanwhile, the categories of deterministic automata with IFoutputs and IFlanguages alongwith a functorial relationship between them are introduced
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Vijay K.
Yadav
Department of Mathematics, National Institute of Technology,
Jamshedpur831014, Jharkhand, India
Department of Mathematics, National Institute
India


Vinay
Gautam
Department of Applied Mathematics, Indian School of Mines, Dhanbad
826004, Jharkhand, India
Department of Applied Mathematics, Indian
India
gautam.gautam181@gmail.com


S. P.
Tiwari
Department of Applied Mathematics, Indian School of Mines, Dhanbad
826004, Jharkhand, India
Department of Applied Mathematics, Indian
India
eterministic automaton
IFoutput
IFlanguage
Minimal realization
[[1] M. A. Arbib and E. G. Manes, Machines in a category: An expository introduction, SIAM##Review, 16 (1974), 285{302.##[2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87{96.##[3] K. T. Atanassov, More on Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 33 (1989), 37{45. ##[4] A. Choubey and K. M. Ravi, Minimization of deterministic nite automata with vague (nal)##states and intuitionistic fuzzy (nal) states, Iranian Journal of Fuzzy System, 10 (2013), 75{##[5] T. Y. Chen, H. P. Wang and J. C. Wang, Fuzzy automata based on Atanassov fuzzy sets##and applications on consumers, advertising involvement, African Journal of Business Man##agement, 6 (2012), 865{880.##[6] T. Y. Chen and C. C. Chou, Fuzzy automata with Atanassov's intuitionstic fuzzy sets and##their applications to product involvement, Journal of the Chinese Institute of Industrial En##gineers, 26 (2009), 245{254.##[7] D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade, Terminological diculties in##fuzzy set theory the case of intuitionistic fuzzy sets, Fuzzy Sets and Systems, 156 (2005),##[8] J. A. Goguen, Minimal realization of machines in closed categories, Bulletin of American##Mathematical Society, 78 (1972), 777{783.##[9] J. Ignjatovic, M. Ciric, S. Bogdanovic and T. Petkovic, MyhillNerode type theory for fuzzy##languages and automata, Fuzzy Sets and Systems, 161 (2010), 1288{1324.##[10] Y. B. Jun, Intuitionistic fuzzy nite state machines, Journal of Applied Mathematics and##Computing, 17 (2005), 109{120.##[11] Y. B. Jun, Quotient structures of intuitionistic fuzzy nite state machines, Information Sci##ences, 177 (2007), 4977{4986.##[12] Y. H. Kim, J. G. Kim and S. J. Cho, Products of Tgeneralized state machines and T##generalized transformation semigroups, Fuzzy Sets and Systems, 93 (1998), 87{97.##[13] H. V. Kumbhojkar and S. R. Chaudhri, On proper fuzzication of fuzzy nite state machines,##International Journal of Fuzzy Mathematics, 4 (2008), 1019{1027.##[14] E. T. Lee and L. A. Zadeh, Note on fuzzy languages, Information Sciences, 1 (1969), 421{434.##[15] F. Lin and H. Ying, Modeling and control of fuzzy discrete event systems, IEEE Transactions##on Systems, Man, and CyberneticsPart B, 32 (2002), 408{415.##[16] D. S. Malik, J. N. Mordeson and M. K. Sen, Submachines of fuzzy nite state machine,##Journal of Fuzzy Mathematics, 2 (1994), 781{792.##[17] D. S. Malik and J. N. Mordeson, Fuzzy automata and languages: theory and applications,##Chapman Hall, CRC Boca Raton, 2002.##[18] D. Qiu, Supervisory control of fuzzy discrete event systems: A formal approach, IEEE Trans##actions on Systems, Man, and CyberneticsPart B, 35 (2005), 72{88.##[19] D. Qiu and F. Liu, Fuzzy discrete event systems under fuzzy observability and a test##algorithm, IEEE Transactions on Fuzzy Systems, 17 (2009), 578{589.##[20] E. S. Santos, Maximin automata, Information and Control, 12 (1968), 367{377.##[21] A. K. Srivastava and S. P. Tiwari, IFtopologies and IFautomata, Soft Computing, 14 (2010),##[22] S. P. Tiwari and Anupam K. Singh, On bijective correspondence between IFpreorders and##saturated IFtopologies, International Journal of Machine Learning and Cybernetics, 4 (2013),##[23] S. P. Tiwari and Anupam K. Singh, IFpreorder, IFtopology and IFautomata, International##Journal of Machine Learning and Cybernetics, 6 (2015), 205{211.##[24] M. G. Thomason and P. N. Marinos, Deterministic acceptors of regular fuzzy languages,##IEEE Transactions Systems Man Cybernetics, 4 (1974), 228{230.##[25] W. G.Wee, On generalizations of adaptive algorithm and application of the fuzzy sets concept##to pattern classication, Ph. D. Thesis, Purdue University, Lafayette, IN 1967.##[26] L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338{353.##[27] L. A. Zadeh, Fuzzy languages and their relation to human and machine intelligence, Electrn.##Research Laboratory University California, Berkeley, CA,Technical Report 1971.##[28] X. Zhang and Y. Li, Intuitionistic fuzzy recognizers and intuitionistic fuzzy nite automata,##Soft Computing, 13 (2009), 611{616.##]
Power and Velocity Control of Wind Turbines by Adaptive Fuzzy Controller during Full Load Operation
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Research on wind turbine technologies have focused primarily on power cost reduction. Generally, this aim has been achieved by increasing power output while maintaining the structural load at a reasonable level. However, disturbances, such as wind speed, affect the performance of wind turbines, and as a result, the use of various types of controller becomes crucial.This paper deals with two adaptive fuzzy controllers at full load operation. The first controller uses the generated power, and the second one uses the angular velocity as feedback signals. These feedback signals act to control the load torque on the generator and blade pitch angle. Adaptive rules, derived from the fuzzy controller, are defined based on the differences between state variables of the power and angular velocity of the generator and their nominal values.The results, which are compared with verified results of reference controller, show that the proposed adaptive fuzzy controller in full load operation has a higher efficiency than that of reference ones, insensitive to fast wind speed variation that is considered as disturbance.
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Hamed
Habibi
PhD, Faculty of Science and Engineering, School of Civil and Me
chanical Engineering, Curtin University, Perth, Australia
PhD, Faculty of Science and Engineering,
Australia
hamed28160@gmail.com


Aghil
Yousefi Koma
Professor, Center of Advanced Systems and Technologies
(CAST), School of Mechanical Engineering, College of Engineering, University of
Tehran, Tehran, Iran
Professor, Center of Advanced Systems and
Australia
aykoma@ut.ac.ir


Ahmad
Sharifian
Computational Engineering and Science Research Centre (CESRC),
Faculty of Health, Engineering and Science, University of Southern Queensland, Toow
oomba, Australia
Computational Engineering and Science Research
Australia
Adaptive fuzzy controller
Control strategy
Full load region
Wind turbine model
[[1] A. G. Aissaoui, A. Tahour, N. Essounbouli, F. Nollet, M. Abid, and M. I. Chergui, A FuzzyPI##control to extract an optimal power from wind turbine, Energy Conversion and Management,##65(1) (2013), 688{696.##[2] R. Ata and Y. Kocyigit, An adaptive neurofuzzy inference system approach for prediction of##tip speed ratio in wind turbines, Expert Systems with Applications, 37(7) (2010), 5454{5460.##[3] K. Bedoud, M. Alirachedi, T. Bahi, and R. Lakel, Adaptive Fuzzy Gain Scheduling of PI##Controller for control of the Wind Energy Conversion Systems, Energy Procedia, 74(8)##(2015), 211225.##[4] F. D. Bianchi, H. De Battista and R. J. Mantz, Wind turbine control systems: principles,##modelling and gain scheduling design, Springer Science and Business Media, (2006).##[5] S. Bououden, M. Chadli, S. Filali, and A. El Hajjaji, Fuzzy model based multivariable pre##dictive control of a variable speed wind turbine: LMI approach, Renewable Energy, 37(1)##(2012), 434{439.##[6] S. Bououden, M. Chadli and H. R. Karimi, Robust Predictive Control of a variable speed wind##turbine using the LMI formalism, European Control Conference (ECC), France, (2014), 820{##[7] A. L. Elshafei and M. A. Azzouz, Adaptive fuzzy regulation of the DCbus capacitor voltage in##a wind energy conversion system (WECS), Expert Systems with Applications, 38(5) (2011),##5500{5506.##[8] T. Esbensen, B. Jensen, M. Niss, C. Sloth and J. Stoustrup, Joint power and speed control##of wind turbines, Aalborg University, Denmark, 2008.##[9] G. Feng, X. Daping and L. Yuegang, Pitchcontrol for largescale wind turbines based on##feed forward fuzzyPI, 7th World Congress on Intelligent Control and Automation (WCICA),##China, (2008), 2277{2282.##[10] S. Heier, Grid integration of wind energy conversion systems, Wiley, 1998.##[11] G. Hou, L. Hu and J. Zhang, Variable universe adaptive fuzzy PI control used in VSCF##wind power generator system, 8th World Congress on Intelligent Control and Automation##(WCICA), China, (2010), 48704874.##[12] X. JianJun, X. LiMei, Q. XiaoNing, J. ChunLei and W. JianRen, Study of variablepitch##wind turbine based on fuzzy control, 2nd International Conference on Future Computer and##Communication (ICFCC), China, (2010), V1235{V1239.##[13] K. E. Johnson, L. Y. Pao, M. J. Balas and L. J. Fingersh, Control of variablespeed wind##turbines: standard and adaptive techniques for maximizing energy capture, Control Systems,##26(3) (2006), 70{81.##[14] M. Mohandes, S. Rehman and S. M. Rahman, Estimation of wind speed prole using adaptive##neurofuzzy inference system (ANFIS), Applied Energy, 88(11) (2011), 4024{4032.##[15] Y. Qi and Q. Meng, The application of fuzzy PID control in pitch wind turbine, Energy##Procedia, 16(Part C) (2012), 1635{1641. ##[16] S. Shamshirband, D. Petkovi, . ojbai, V. Nikoli, N. B. Anuar, N. L. Mohd Shuib, et al.,##Adaptive neurofuzzy optimization of wind farm project net prot, Energy Conversion and##Management, 80(4) (2014), 229{237.##[17] S. Simani and P. Castaldi, Datadriven and adaptive control applications to a wind turbine##benchmark model, Control Engineering Practice, 21(12) (2013), 1678{1693.##[18] C. Sloth, T. Esbensen, M. Niss, J. Stoustrup and P. F. Odgaard, Robust LMIbased control##of wind turbines with parametric uncertainties, IEEE International Conference on Control##Applications (CCA) part of the IEEE MultiConference on Systems and Control (MSC),##Russia, (2009), 776{781.##[19] Y. Xiyun and L. Xinran, Integral variable structure fuzzy adaptive control for variable speed##wind power system, International Conference on Logistics Systems and Intelligent Manage##ment, China, (2010), 1247{1250.##]
Intuitionistic Fuzzy Information Measures with Application in Rating of Township Development
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Predominantly in the faltering atmosphere, the precise value of some factors is difficult to measure. Though, it can be easily approximated by intuitionistic fuzzy linguistic term in the reallife world problem. To deal with such situations, in this paper two information measures based on trigonometric function for intuitionistic fuzzy sets, which are a generalized version of the fuzzy information measures are introduced. Based on it new trigonometric similarity measure is developed. Mathematical illustration displays reasonability and effectiveness of the information measures for IFSs by comparing it with the existing information measures. Corresponding to information and similarity measures for IFSs, two new methods: (1) Intuitionistic Fuzzy Similarity Measure Weighted Average Operator (IFSMWAO) method for township development and (2) TOPSIS method for multiple criteria decision making (MCDM) (investment policies) problems have been developed. In the existing methods the authors have assumed the weight vectors, while in the proposed method it has been calculated using intuitionistic fuzzy information measure. This enhances the authenticity of the proposed method.
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Arunodaya Raj
Mishra
Department of Mathematics, ITM University, Gwalior474001,
M. P., India
Department of Mathematics, ITM University,
India
Intuitionistic fuzzy set
Intuitionistic fuzzy information
Similarity measure
Township development
TOPSIS
[[1] K. T. Atanassov and G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and##Systems, 31 (1989), 343{349.##[2] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87{96.##[3] K. T. Atanassov, Intuitionistic fuzzy sets, Springer PhysicaVerlag Heidelberg, Germany,##[4] P. Burillo and H. Bustince, Entropy on intuitionistic fuzzy sets and on intervalvalued fuzzy##sets, Fuzzy Sets and Systems, 78 (1996), 305{316.##[5] H. Bustince and P. Burillo, Vague sets are intuitionistic fuzzy sets, Fuzzy sets and systems,##79 (1996), 403{405.##[6] J. Chachi and S. M. Taheri, A unied approach to similarity measures between intuitionistic##fuzzy sets, International Journal of Intelligent Systems, 28 (2013), 669{685.##[7] T. Y. Chen and C. H. Li, Determining objective weights with intuitionistic fuzzy entropy##measures: A comparative analysis, Information Sciences, 180 (2010), 4207{4222.##[8] C. Cornelis, K. T. Atanassov and E. E. Kerre, Intuitionistic fuzzy sets and intervalvalued##fuzzy sets: a critical comparison, In: Proceedings of the 3rd Conference of the European##Society for Fuzzy Logic and Technology (EUSFLAT '03), Zittau, Germany, (2003), 159163.##[9] A. De Luca and S. Termini, A denition of nonprobabilistic entropy in the setting of fuzzy##set theory, Inform. Control, 20 (1972), 301{312.##[10] G. Deschrijver and E. E. Kerre, On the relationship between some extensions of fuzzy set##theory, Fuzzy Sets and Systems, 133 (2003), 227{235. ##[11] B. Farhadinia, A theoretical development on the entropy of intervalvalued fuzzy sets based##on the intuitionistic distance and its relationship with similarity measure, KnowledgeBased##Systems, 39 (2013), 79{84.##[12] W. L. Gau and D.J. Buehrer, Vague sets, IEEE Transactions on Systems, Man and Cyber##netics, 23 (1993), 610{614.##[13] P. Grzegorzewski and E. Mrowka, Some notes on (Atanassov's) intuitionistic fuzzy sets,##Fuzzy sets and systems, 156 (2005), 492{495.##[14] D. S. Hooda and A. R. Mishra, On trigonometric fuzzy information measures, ARPN Journal##of Science and Technology, 05 (2015), 145{152.##[15] C. Hung and L. H. Chen, A fuzzy TOPSIS decision making model with entropy under intu##itionistic fuzzy environment, In: Proceedings of the international multi conference of engi##neers and computer scientists (IMECS), 01 (2009), 01{04.##[16] W. L. Hung and M. S. Yang, Fuzzy entropy on intuitionistic fuzzy sets, International Journal##of Intelligent Systems, 21 (2006), 443{451.##[17] C. L. Hwang and K. S. Yoon, Multiple attribute decision making: Methods and applications,##Berlin: SpringerVerlag, 1981.##[18] Y. Jiang, Y. Tang, H. Liu and Z. Chen, Entropy on intuitionistic fuzzy soft sets and on##intervalvalued fuzzy soft sets, Information Sciences, 240 (2013), 95{114.##[19] D. Joshi and S. Kumar, Intuitionistic fuzzy entropy and distance measure based TOPSIS##method for multicriteria decision making, Egyptian informatics journal, 15 (2014), 97{104.##[20] A. Kauman, Fuzzy subsetsFundamental theoretical elements, Academic Press, New York,##[21] D. F. Li and C. T. Cheng, New similarity measure of intuitionistic fuzzy sets and application##to pattern recognitions, Pattern Recognition Letters, 23 (2002), 221{225.##[22] J. Li, D. Deng, H. Li and W. Zeng, The relationship between similarity measure and entropy##of intuitionistic fuzzy sets, Information Science, 188 (2012), 314{321.##[23] F. Li, Z. H. Lu and L. J. Cai, The entropy of vague sets based on fuzzy sets, J. Huazhong##Univ. Sci. Tech., 31 (2003), 24{25.##[24] Z. Z. Liang and P. F. Shi, Similarity measures on intuitionistic fuzzy sets, Pattern Recognition##Letters, 24 (2003), 2687{2693.##[25] L. Lin, X. H. Yuan and Z. Q. Xia, Multicriteria fuzzy decisionmaking methods based on##intuitionistic fuzzy sets, J. Comp Syst. Sci., 73 (2007), 84{88.##[26] H. W. Liu and G. J. Wang, Multicriteria decisionmaking methods based on intuitionistic##fuzzy sets, European Journal of Operational Research, 179 (2007), 220{233.##[27] P. D. Liu and Y. M. Wang, Multiple attribute group decision making methods based on##intuitionistic linguistic power generalized aggregation operators, Applied Soft Computing##Journal,17 (2014), 90{104.##[28] P. Liu, Some hamacher aggregation operators based on the intervalvalued intuitionistic fuzzy##numbers and their application to group decision making, IEEE Transactions on Fuzzy Sys##tems, 22 (2014), 83{97.##[29] A. R. Mishra, D. S. Hooda and D. Jain, Weighted trigonometric and hyperbolic fuzzy infor##mation measures and their applications in optimization principles, International Journal of##Computer and Mathematical Sciences, 03 (2014), 62{68.##[30] A. R. Mishra, D. Jain and D. S. Hooda, Exponential intuitionistic fuzzy information measure##with assessment of service quality, International journal of fuzzy systems, accepted.##[31] H. B. Mitchell, On the DengfengChuntian similarity measure and its application to pattern##recognition, Pattern Recognition Letters, 24 (2003), 3101{3104.##[32] E. Szmidt and J. Kacprzyk, A concept of similarity for intuitionistic fuzzy sets and its##application in group decision making, In: Proceedings of International Joint Conference on##Neural Networks & IEEE International Conference on Fuzzy Systems, Budapest, Hungary,##(2004), 25{29.##[33] E. Szmidt and J. Kacprzyk, A new concept of a similarity measure for intuitionistic fuzzy##sets and its use in group decision making, In: V. Torra, Y. Narukawa, S. Miyamoto (Eds.),##Modelling Decision for Articial Intelligence, LNAI 3558, Springer, (2005), 272{282. ##[34] E. Szmidt and J. Kacprzyk, Entropy for intuitionistic fuzzy sets, Fuzzy Sets and Systems,##118 (2001), 467{477.##[35] I. K. Vlachos and G. D. Sergiadis, Inner product based entropy in the intuitionistic fuzzy##setting, International Journal of Uncertainty, Fuzziness and KnowledgeBased Systems, 14##(2006), 351{366.##[36] I. K. Vlachos and G. D. Sergiadis, Intuitionistic fuzzy informationapplication to pattern##recognition, Pattern Recognition Letters, 28 (2007), 197{206.##[37] P.Z.Wang, Fuzzy sets and its applications, Shanghai Science and Technology Press, Shanghai,##[38] X. Z. Wang, B. D. Baets and E. E. Kerre, A comparative study of similarity measures, Fuzzy##Sets and Systems, 73 (1995), 259{268.##[39] C. P. Wei and Y. Zhang, Entropy measures for intervalvalued intuitionistic fuzzy sets and##their application in group decision making, Mathematical Problems in Engineering, 2015##(2015), 01{13.##[40] C. P. Wei, P. Wang and Y. Zhang, Entropy, similarity measure of intervalvalued intuition##istic fuzzy sets and their applications, Information Sciences, 181 (2011), 4273{4286.##[41] P. Wei, Z. H. Gao and T. T. Guo, An intuitionistic fuzzy entropy measure based on the##trigonometric function, Control and Decision, 27(2012), 571{574.##[42] G. Wei, X. Zhao and R. Lin, Some hesitant intervalvalued fuzzy aggregation operators##and their applications to multiple attribute decision making, KnowledgeBased Systems, 46##(2013), 43{53.##[43] M. M. Xia and Z. S. Xu, Entropy/cross entropybased group decision making under intu##itionistic fuzzy environment, Information Fusion, 13 (2012), 31{47.##[44] Z. S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Transactions on Fuzzy Systems,##15 (2007), 1179{1187.##[45] Z. S. Xu, On similarity measures of intervalvalued intuitionistic fuzzy sets and their appli##cation to pattern recognitions, Journal of Southeast University(English Edition), 23 (2007),##[46] R. R. Yager, On the measure of fuzziness and negation, part I: membership in unit interval,##International Journal of General Systems, 05 (1979), 221{229.##[47] J. Ye, Two eective measures of intuitionistic fuzzy entropy, Computing, 87 (2010), 55{62.##[48] Z. Yue, Extension of TOPSIS to determine weight of decision maker for group decision##making problems with uncertain information, Exp. Syst. Appl., 39 (2012), 6343{6350.##[49] L. A. Zadeh, Fuzzy sets, Information and Computation, 08 (1965), 338{353.##[50] W. Zeng and P. Guo, Normalized distance, similarity measure, inclusion measure and entropy##of intervalvalued fuzzy sets and their relationship, Information Sciences, 178 (2008), 1334{##[51] W. Zeng and H. Li, Inclusion measures, similarity measures, and the fuzziness of fuzzy sets##and their relations, International Journal of Intelligent Systems, 21 (2006), 639{653.##[52] W. Zeng and H. Li, Relationship between similarity measure and entropy of interval valued##fuzzy sets, Fuzzy Sets and Systems, 157 (2006), 1477{1484.##[53] H. Zhang, W. Zhang and C. Mei, Entropy of intervalvalued fuzzy sets based on distance and##its relationship with similarity measure, KnowledgeBased Systems, 22 (2009), 449{454.##[54] Q. S. Zhang and S. Y. Jiang, A note on information entropy measures for vague sets and its##applications, Information Sciences, 178 (2008), 4184{4191.##]
Solving fuzzy differential equations by using Picard method
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In this paper, The Picard method is proposed to solve the system of firstorder fuzzy differential equations $(FDEs)$ with fuzzy initial conditions under generalized $H$differentiability. Theexistence and uniqueness of the solution and convergence of theproposed method are proved in details. Finally, the method is illustrated by solving some examples.
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71
81


S. S.
Behzadi
Department of Mathematics, Islamic Azad University, Qazvin Branch
Qazvin Iran
Department of Mathematics, Islamic Azad University
Iran


T.
Allahviranloo
Department of Mathematics, Islamic Azad University, Science and
Research Branch, Tehran Iran
Department of Mathematics, Islamic Azad University
Iran
First order fuzzy differential equations
Fuzzy number
Fuzzyvalued function
$h$difference
Generalized differentiability
Picard method
[[1] S. Abbasbandy and T. Allahviranloo, Numerical solutions of fuzzy dierential equations by##Taylor method, J. Comput. Meth. Appl. Math., 2 (2002), 113124.##[2] S. Abbasbandy, T. Allahviranloo, O. LopezPouso and J. J. Nieto, Numerical methods for##fuzzy dierential inclusions, Comput. Math. Appl., 48 (2004), 16331641.##[3] S. Abbasbandy, J. J. Nieto and M. Alavi, Tuning of reachable set in one dimensional fuzzy##dierential inclusions, Chaos Soliton and Fractals., 26 (2005), 13371345.##[4] T. Allahviranloo, N. Ahmady and E. Ahmady, Numerical solution of fuzzy dierential equa##tions by predictorcorrector method, Inform. Sci., 177 (2007), 16331647.##[5] B. Bede, Note on Numerical solutions of fuzzy dierential equations by predictorcorrector##method, Inform. Sci., 178 (2008), 19171922.##[6] B. Bede and S. G. Gal, Generalizations of the dierentiability of fuzzy number valued func##tions with applications to fuzzy dierential equation, Fuzzy Set.Syst., 151 (2005), 581599.##[7] B. Bede, J. Imre, C. Rudas and L. Attila, First order linear fuzzy dierential equations under##generalized dierentiability, Inform. Sci., 177 (2007), 36273635.##[8] J. J. Buckley and T. Feuring, Fuzzy dierential equations, Fuzzy Set. Syst., 110 (2000),##[9] J.J. Buckley, T. Feuring and Y. Hayashi, Linear systems of rst order ordinary dierential##equations: fuzzy initial conditions, Soft Comput., 6 (2002), 415421.##[10] J. J. Buckley and L. J. Jowers, Simulating Continuous Fuzzy Systems, SpringerVerlag, Berlin##Heidelberg, 2006.##[11] Y. ChalcoCano and H. RomnFlores,On new solutions of fuzzy dierential equations, Chaos##Soliton and Fractals., 45 (2006), 10161043.##[12] Y. ChalcoCano, RomnFlores, M. A. RojasMedar, O. Saavedra and M. JimnezGamero, The##extension principle and a decomposition of fuzzy sets, Inform. Sci., 177 (2007), 53945403.##[13] C. K. Chen and S. H. Ho,Solving partial dierential equations by twodimensional dierential##transform method, Appl. Math. Comput., 106 (1999), 171179.##[14] Y. J. Cho and H. Y. Lan, The existence of solutions for the nonlinear rst order fuzzy##dierential equations with discontinuous conditions, Dyn. Contin.Discrete., 14 (2007) , 873##[15] W. Congxin and S. Shiji,Exitance theorem to the Cauchy problem of fuzzy dierential equa##tions under compactancetype conditions, Inform. Sci., 108 (1993), 123134.##[16] P. Diamond, Timedependent dierential inclusions, cocycle attractors and fuzzy dierential##equations, IEEE Trans. Fuzzy Syst., 7 (1999), 734740.##[17] P. Diamond, Brief note on the variation of constants formula for fuzzy dierential equations,##Fuzzy Set. Syst., 129 (2002), 6571.##[18] Z. Ding, M. Ma and A. Kandel, Existence of solutions of fuzzy dierential equations with##parameters, Inform. Sci., 99 (1997), 205217.##[19] D. Dubois and H. Prade, Towards fuzzy dierential calculus: Part 3, dierentiation, Fuzzy##Set. Syst., 8 (1982), 225233.##[20] O. S. Fard, Z. Hadi, N. GhalEh and A. H. Borzabadi,A note on iterative method for solving##fuzzy initial value problems, J. Adv. Res. Sci. Comput., 1 (2009), 2233.##[21] O. S. Fard, A numerical scheme for fuzzy cauchy problems, J. Uncertain Syst., 3 (2009),##[22] O. S. Fard, An iterative scheme for the solution of generalized system of linear fuzzy dier##ential equations, World Appl. Sci. J., 7 (2009), 15971604.##[23] O. S. Fard and A. V. Kamyad, Modied kstep method for solving fuzzy initial value problems,##Iranian Journal of Fuzzy Systems, 8(1) (2011), 4963.##[24] O. S. Fard, T. A. Bidgoli and A. H. Borzabadi, Approximateanalytical approach to nonlinear##FDEs under generalized dierentiability, J. Adv. Res. Dyn. Control Syst., 2 (2010), 5674.##[25] W. Fei,Existence and uniqueness of solution for fuzzy random dierential equations with##nonLipschitz coecients, Inform. Sci., 177 (2007), 3294337.##[26] M. J. Jang and C. L. Chen, Y.C. Liy,On solving the initialvalue problems using the dier##ential transformation method, Appl. Math. Comput., 115 (2000), 145 160.##[27] L. J. Jowers, J. J. Buckley and K. D. Reilly, Simulating continuous fuzzy systems, Inform.##Sci., 177 (2007), 436448.##[28] O. Kaleva, Fuzzy dierential equations, Fuzzy Set. Syst., 24 (1987), 301317.##[29] O. Kaleva, The Cauchy problem for fuzzy dierential equations, Fuzzy Set. Syst., 35 (1990),##[30] O. Kaleva, A note on fuzzy dierential equations, Nonlinear Anal.,64 (2006) 895900.##[31] R. R. Lopez, Comparison results for fuzzy dierential equations, Inform. Sci., 178 (2008),##17561779.##[32] M. Ma, M. Friedman and A. Kandel, Numerical solutions of fuzzy dierential equations,##Fuzzy Set. Syst., 105 (1999), 133138.##[33] M. T. Mizukoshi, L. C. Barros, Y. ChalcoCano, H. RomnFlores and R. C. Bassanezi, Fuzzy##dierential equations and the extension principle, Inform. Sci., 177(2007) , 36273635.##[34] M. Oberguggenberger and S. Pittschmann,Dierential equations with fuzzy parameters,##Math. Mod. Syst., 5 (1999), 181202.##[35] G. Papaschinopoulos, G. Stefanidou and P. Efraimidi, Existence uniqueness and asymptotic##behavior of the solutions of a fuzzy dierential equation with piecewise constant argument,##Inform. Sci., 177 (2007), 38553870.##[36] M. L. Puri and D. A. Ralescu, Dierentials of fuzzy functions, J. Math. Anal. Appl., 91##(1983), 552558.##[37] M. L. Puri and D. Ralescu, Fuzzy random variables, J. Math. Anal. Appl., 114 (1986),##[38] H. J. Zimmermann, Fuzzy sets theory and its applications, Kluwer Academic Press, Dor##drecht, 1991.##]
A Quadratic Programming Method for Ranking Alternatives Based on Multiplicative and Fuzzy Preference Relations
2
2
This paper proposes a quadratic programming method (QPM) for ranking alternatives based on multiplicative preference relations (MPRs) and fuzzy preference relations (FPRs). The proposed QPM can be used for deriving a ranking from either a MPR or a FPR, or a group of MPRs, or a group of FPRs, or their mixtures. The proposed approach is tested and examined with two numerical examples, and comparative analyses with the existing methods are provided to show the effectiveness and advantages of the QPM.
1

83
94


Yejun
Xu
State Key Laboratory of HydrologyWater Resources and Hydraulic
Engineering, Hohai University, No.1 Xikang Road, Nanjing, 210098, Jiangsu,China and
Business School, Hohai University, Jiangning Campus, No.8 Focheng West Road, Jiangning, Nanjing,
State Key Laboratory of HydrologyWater Resources
China
xuyejohn@163.com


Qianqian
Wang
State Key Laboratory of HydrologyWater Resources and Hydraulic
Engineering, Hohai University, No.1 Xikang Road, Nanjing, 210098, Jiangsu, China and
Business School, Hohai University, Jiangning Campus, No.8 Focheng West Road, Jiangning, Nanjing,
State Key Laboratory of HydrologyWater Resources
China


Huimin
Wang
State Key Laboratory of HydrologyWater Resources and Hydraulic
Engineering, Hohai University, No.1 Xikang Road, Nanjing, 210098, Jiangsu, China and
Business School, Hohai University, Jiangning Campus, No.8 Focheng West Road, Jiangning, Nanjing,
State Key Laboratory of HydrologyWater Resources
China
hmwang@hhu.edu.cn
Quadratic programming
Group decision making (GDM)
Multiplicative preference relation (MPR)
Fuzzy preference relation (FPR)
Ranking alternatives
[[1] S. Alonso, F. Cabrerizo, F. Chiclana, F. Herrera and E. HerreraViedma, Group decision mak##ing with incomplete fuzzy linguistic preference relations, International Journal of Intelligent##Systems, 24 (2009), 201{222.##[2] F. Chiclana, F. Herrera and E. HerreraViedma, Integrating multiplicative preference relations##in a multipurpose decisionmaking model based on fuzzy preference relations, Fuzzy Sets and##Systems, 122 (2001), 277{291.##[3] F. Chiclana, F. Herrera and E. HerreraViedma, Integrating three representation models in##fuzzy multipurpose decision making based on fuzzy preference relations, Fuzzy Sets and Sys##tems, 97 (1998), 33{48.##[4] K. O. Cogger and P. L. Yu, Eigenweight vectors and leastdistance approximation for revealed##preference in pairwise weight ratios, Journal of Optimization Theory and Applications, 46##(1985), 483{491.##[5] G. Crawford and C. Williams, A note on the analysis of subjective judgement matrices,##Journal of Mathematical Psychology, 29 (1985), 387{405.##[6] Z. P. Fan, J. Ma, Y. P. Jiang, Y. H. Sun and L. Ma, A goal programming approach to group##decision making based on multiplicative preference relations and fuzzy preference relations,##European Journal of Operational Research, 174 (2006), 311{321.##[7] Z. P. Fan, J. Ma and Q. Zhang, An approach to multiple attribute decision making based on##fuzzy preference information on alternatives, Fuzzy Sets and Systems, 131 (2002), 101{106.##[8] Z. P. Fan, S. H. Xiao and G. F. Hu, An optimization method for integrating two kinds of##preference information in group decisionmaking, Computers & Industrial Engineering, 46##(2004), 329{335.##[9] Z. P. Fan and Y. Zhang, A goal programming approach to group decisionmaking with three##formats of incomplete preference relations, Soft Computing, 14 (2010), 1083{1090.##[10] E. Fernandez and J. C. Leyva, A method based on multiobjective optimization for deriving##a ranking from a fuzzy preference relation, European Journal of Operational Research, 154##(2004), 110{124. ##[11] P. T. Harker, Alternative modes of questioning in the analytic hierarchy process, Mathemat##ical Modelling, 9 (1987), 353{360.##[12] F. Herrera, E. HerreraViedma and F. Chiclana, Multiperson decisionmaking based on multi##plicative preference relations, European Journal of Operational Research,129(2001),372{385.##[13] R. E. Jensen, An alternative scaling method for priorities in hierarchy structures, Journal of##Mathematical Psychology, 28 (1984), 317{332.##[14] J. Kacprzyk, Group decision making with a fuzzy linguistic majority, Fuzzy Sets and Systems,##18 (1986), 105{118.##[15] J. Kacprzyk and M. Roubens, NonConventional Preference Relations in DecisionMaking,##Springer, Berlin, 1988.##[16] S. Lipovetsky, The synthetic hierarchy method: An optimizing approach to obtaining priori##ties in the AHP, European Journal of Operational Research, 93 (1996), 550{564.##[17] S. Lipovetsky and A. Tishler, Interval estimation of priorities in the AHP, European Journal##of Operational Research, 114 (1999), 153{164.##[18] H. Nurmi, Approaches to collective decision making with fuzzy preference relations, Fuzzy##Sets and Systems, 6 (1981), 249{259.##[19] S. A. Orlovsky, Decisionmaking with a fuzzy preference relation, Fuzzy Sets and Systems, 1##(1978), 155{167.##[20] T. L. Saaty, The Analytic Hierarchy Process, McGrawHill, New York, 1980.##[21] T. Tanino, Fuzzy preference orderings in group decisionmaking, Fuzzy Sets and Systems, 12##(1984), 117{131.##[22] T. Tanino, Fuzzy preference relation in group decision making, in: J. Kacprzyk, M. Roubens##(Eds.) NonConventional Preference Relation in Decision Making, Springer, Berlin, (1988),##[23] T. Tanino, On group decision making under fuzzy preferences, in: J. Kacprzyk, M. Fedrizzi##(Eds.) Multiperson Decision Making Using Fuzzy Sets and Possibility Theory, Kluwer,##Netherlands, 1990, 172{185.##[24] L. G. Vargas, An overview of the analytic process and its applications, European Journal of##Operational Research, 48 (1990), 2{8.##[25] L. F.Wang and S. B. Xu, The Introduction to the Analytic Hierarchy Process, Chinese People##University Press, Beijing, 1990.##[26] Y. M.Wang and Z. P. Fan, Fuzzy preference relations: Aggregation and weight determination,##Computers & Industrial Engineering, 53 (2007), 163{172.##[27] Y. M. Wang and Z. P. Fan, Group decision analysis based on fuzzy preference relations:##Logarithmic and geometric least squares methods, Applied Mathematics and Computation,##194 (2007), 108{119.##[28] Y. M. Wang, Z. P. Fan and Z. S. Hua, A chisquare method for obtaining a priority vector##from multiplicative and fuzzy preference relations, European Journal of Operational Research,##182 (2007), 356{366.##[29] Y. M. Wang and C. Parkan, Multiple attribute decision making based on fuzzy preference##information on alternatives: Ranking and weighting, Fuzzy Sets and Systems, 153 (2005),##[30] D. A. Wismer, Introduction to Nonlinear Optimization: A Problem Solving Approach, North##Holland Company, New York, 1978.##[31] Y. J. Xu, L. Chen, K. W. Li and H. M. Wang, A chisquare method for priority derivation in##group decision making with incomplete reciprocal preference relations, Information Sciences,##36 (2015), 166{179.##[32] Y. J. Xu, L. Chen and H. M. Wang, A least deviation method for priority derivation in##group decision making with incomplete reciprocal preference relations, International Journal##of Approximate Reasoning, 66 (2015), 91{102.##[33] Y. J. Xu, Q. L. Da and L. H. Liu, Normalizing rank aggregation method for priority of a fuzzy##preference relation and its eectiveness, International Journal of Approximate Reasoning, 50##(2009), 1287{1297. ##[34] Y. J. Xu, Q. L. Da and H. M. Wang, A note on group decisionmaking procedure based on##incomplete reciprocal relations, Soft Computing, 15 (2011), 1289{1300.##[35] Y. J. Xu, J. N. D. Gupta and H. M.Wang, The ordinal consistency of an incomplete reciprocal##preference relation, Fuzzy Sets and Systems, 246(2014), 62{77.##[36] Y.J. Xu, K.W. Li and H.M. Wang, Incomplete interval fuzzy preference relations and their##applications, Computers & Industrial Engineering, 67 (2014), 93{103.##[37] Y. J. Xu, F. Ma, F. F. Tao and H. M. Wang, Some methods to deal with unacceptable##incomplete 2tuple fuzzy linguistic preference relations in group decision making, Knowledge##Based Systems, 56 (2014), 179{190.##[38] Y.J. Xu, R. Patnayakuni and H. M. Wang, Logarithmic least squares method to priority##for group decision making with incomplete fuzzy preference relations, Applied Mathematical##Modelling, 37 (2013), 2139{2152.##[39] Y. J. Xu, R. Patnayakuni and H. M. Wang, A method based on mean deviation for weight##determination from fuzzy preference relations and multiplicative preference relations, Inter##national Journal of Information Technology & Decision Making, 11 (2012), 627{641.##[40] Y. J. Xu, R. Patnayakuni and H. M. Wang, The ordinal consistency of a fuzzy preference##relation, Information Sciences, 224 (2013), 152{164.##[41] Y. J. Xu and H. M. Wang, Eigenvector method, consistency test and inconsistency repairing##for an incomplete fuzzy preference relation, Applied Mathematical Modelling, 37 (2013),##5171{5183.##[42] Z. S. Xu, Generalized chi square method for the estimation of weights, Journal of Optimiza##tion Theory and Applications, 107 (2000), 183{192.##[43] Z. S. Xu, Goal programming models for obtaining the priority vector of incomplete fuzzy##preference relation, International Journal of Approximate Reasoning, 36 (2004), 261{270.##[44] Z. S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Transations on Fuzzy Systems, 15##(2007), 1179{1187.##[45] Z. S. Xu and Q. L. Da, A least deviation method to obtain a priority vector of a fuzzy##preference relation, European Journal of Operational Research, 164 (2005), 206{216.##]
Uniform connectedness and uniform local connectedness for latticevalued uniform convergence spaces
2
2
We apply Preuss' concept of $mbbe$connectedness to the categories of latticevalued uniform convergence spaces and of latticevalued uniform spaces. A space is uniformly $mbbe$connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$connected sets, including the product theorem. Furthermore, we define and study uniform local $mbbe$connectedness, generalizing a classical definition from the theory of uniform convergence spaces to the latticevalued case. In particular it is shown that if the underlying lattice is completely distributive, the quotient space of a uniformly locally $mbbe$connected space and products of locally uniformly $mbbe$connected spaces are locally uniformly $mbbe$connected.
1

95
111


Gunther
Jager
School of Mechanical Engineering, University of Applied Sciences
Stralsund, 18435 Stralsund, Germany
School of Mechanical Engineering, University
Germany
g.jager@ru.ac.za, gunther.jaeger@fhstralsund.de
$L$topology
$L$uniform convergence space
Uniform connectedness
Local connectedness
[[1] J. Adamek, H. Herrlich, and G.E. Strecker, Abstract and Concrete Categories, Wiley, New##York, 1989. ##[2] G. Cantor, Uber unendliche lineare Punktmannichfaltigkeiten, Math. Ann., 21 (1883), 545{##[3] A. Craig and G. Jager, A common framework for latticevalued uniform spaces and probabilistic##uniform limit spaces, Fuzzy Sets and Systems, 160 (2009), 1177 { 1203.##[4] J. Fang, Latticevalued semiuniform convergence spaces, Fuzzy Sets and Systems, 195 (2012),##[5] W. Gahler, Grundstrukturen der Analysis I, Birkhauser Verlag, Basel and Stuttgart, 1977.##[6] J. Gutierrez Garca, A unied approach to the concept of fuzzy Luniform space, Thesis,##Universidad del Pais Vasco, Bilbao, Spain, 2000.##[7] J. Gutierrez Garca, M.A. de Prada Vicente and A. P. Sostak, A unied approach to the##concept of fuzzy Luniform space, In: S. E. Rodabaugh, E. P. Klement (Eds.), Topological##and algebraic structures in fuzzy sets, Kluwer, Dordrecht, (2003), 81{114.##[8] F. Hausdor, Grundzuge der Mengenlehre, Leipzig, 1914.##[9] U. Hohle and A. P. Sostak, Axiomatic foundations of xedbasis fuzzy topology, In: U. Hohle,##S.E. Rodabauch (Eds.), Mathematics of Fuzzy Sets. Logic, Topology and Measure Theory,##Kluwer, Boston/Dordrecht/London (1999), 123{272.##[10] G. Jager, A category of Lfuzzy convergence spaces, Quaestiones Math., 24 (2001), 501{517.##[11] G. Jager, Subcategories of latticevalued convergence spaces, Fuzzy Sets and Systems, 156##(2005), 1{24.##[12] G. Jager and M. H. Burton, Stratied Luniform convergence spaces, Quaest. Math., 28##(2005), 11 { 36.##[13] G. Jager, Latticevalued convergence spaces and regularity, Fuzzy Sets and Systems, 159##(2008), 2488{2502.##[14] G. Jager, Level spaces for latticevalued uniform convergence spaces, Quaest. Math., 31##(2008), 255{277.##[15] G. Jager, Compactness in latticevalued function spaces, Fuzzy Sets and Systems, 161 (2010),##2962{2974.##[16] G. Jager, Latticevalued Cauchy spaces and completion, Quaest. Math., 33 (2010), 53{74.##[17] G. Jager, Connectedness and local connectedness for latticevalued convergence spaces, Fuzzy##Sets and Systems, to appear, doi:10.1016/j.fss.2015.11.013.##[18] G. Kneis, Contributions to the theory of pseudouniform spaces, Math. Nachrichten, 89##(1979), 149{163.##[19] S. G. Mrowka and W. J. Pervin, On uniform connectedness, Proc. Amer. Math. Soc., 15##(1964), 446{449.##[20] G. Preu, EZusammenhangende Raume, Manuscripta Mathematica, 3 (1970), 331{342.##[21] G. Preu, Trennung und Zusammenhang, Monatshefte fur Mathematik, 74(1970), 70{87.##[22] W. W. Taylor, Fixedpoint theorems for nonexpansive mappings in linear topological spaces,##J. Math. Anal. Appl., 40 (1972), 164{173.##[23] R. Vainio, A note on products of connected convergence spaces, Acta Acad. Aboensis, Ser.##B, 36(2) (1976), 1{4.##[24] R. Vainio, The locally connected and the uniformly locally connected core##ector in general##convergence theory, Acta Acad. Aboensis, Ser. B, 39(1) (1979), 1{13.##[25] R. Vainio, On connectedness in limit space theory, in: Convergence structures and applications##II, Abhandlungen der Akad. d. Wissenschaften der DDR, Berlin (1984), 227{232.##]
Optimal coincidence best approximation solution in nonArchimedean Fuzzy Metric Spaces
2
2
In this paper, we introduce the concept of best proximal contraction theorems in nonArchimedean fuzzy metric space for two mappings and prove some proximal theorems. As a consequence, it provides the existence of an optimal approximate solution to some equations which contains no solution. The obtained results extend further the recently development proximal contractions in nonArchimedean fuzzy metric spaces and famous Banach contraction principle.
1

113
124


Naeem
Saleem
Department of Mathematics, National University of Computer and
Emerging Sciences, Lahore  Pakistan
Department of Mathematics, National University
Pakistan
naeem.saleem2@gmail.com


Mujahid
Abbas
Department of Mathematics and Applied Mathematics, University of
Pretoria, Lynnwood road, Pretoria 0002, South Africa and Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Department of Mathematics and Applied Mathematics,
Saudi Arabia
abbas.mujahid@gmail.com


Zahid
Raza
Department of Mathematics, National University of Computer and
Emerging Sciences, Lahore  Pakistan
Department of Mathematics, National University
Pakistan
zahid.raza@nu.edu.pk
Fuzzy metric space
Optimal approximate solution
Fuzzy proximal contraction
Fuzzy expansive
Fuzzy isometry
sincreasing sequence
tnorm
[[1] S. Chauhan, W. Shatanawi, S. Kumar and S. Radenovic, Existence and uniqueness of xed##points in modied intuitionistic fuzzy metric spaces, Journal of Nonlinear Sciences and Ap##plications, 7(1) (2014), 28{41.##[2] K. Fan, Extensions of two xed point theorems of F. E. Browder, Mathematische Zeitschrift,##112(3) (1969), 234{240. ##[3] J. G. Garcia and S. Romaguera, Examples of nonstrong fuzzy metrics, Fuzzy sets and sys##tems, 162(1) (2011), 91{93.##[4] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems,##64(3) (1994), 395{399.##[5] A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets##and Systems, 90(3) (1997), 365{368.##[6] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27(3) (1983),##[7] V. Gregori and A. Sapena, On xedpoint theorems in fuzzy metric spaces, Fuzzy Sets and##Systems, 125(2) (2002), 245{252.##[8] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11(5)##(1975), 336{344.##[9] C. Mongkolkeha, Y. J. Cho and P. Kumam, Best proximity points for generalized proxi##mal contraction mappings in metric spaces with partial orders, Journal of Inequalities and##Applications, 94(1) (2013), 94{105.##[10] S. Sadiq Basha, Best proximity points, optimal solutions, Journal of Optimal Theory and##Applications, 151(1) (2011), 210{216.##[11] S. Sadiq Basha, Common best proximity points: Global minimization of multiobjective func##tions, Journal of Global Optimization, 54(2) (2012), 367{373.##[12] N. Saleem, B. Ali, M. Abbas and Z. Raza, Fixed points of Suzuki type generalized multivalued##mappings in fuzzy metric spaces with applications, Fixed Point Theory and Applications,##(36)(1) (2015).##[13] M. Sangurlu and D. Turkoglu, Fixed point theorems for ( o') contractions in a fuzzy metric##spaces, Journal of Nonlinear Sciences and Applications. 8(5) (2015), 687{694.##[14] B. Schweizer and A. Sklar, Statistical metric spaces, Pacic Journal of Mathematics, 10(1)##(1960), 313{334.##[15] C. Vetro and P. Salimi, Best proximity point results in nonArchimedean fuzzy metric spaces,##Fuzzy Information and Engineering, 5(4) (2013), 417{429.##[16] L. A. Zadeh, Fuzzy Sets, Informations and Control, 8(3) (1965), 338{353.##]
On $L$double fuzzy rough sets
2
2
ur aim of this paper is to introduce the concept of $L$double fuzzy rough sets in whichboth constructive and axiomatic approaches are used. In constructive approach, a pairof $L$double fuzzy lower (resp. upper) approximation operators is defined and the basic properties of them are studied.From the viewpoint of the axiomatic approach, a set of axioms is constructed to characterize the $L$double fuzzy upper (resp. lower) approximation of $L$double fuzzy rough sets. Finally, from $L$double fuzzy approximation operators, we generated Alexandrov $L$double fuzzy topology.
1

125
142


A. A.
Abd Ellatif
Department of Mathematics, Faculty of Science and Arts at
Belqarn, P. O. Box 60, Sabt AlAlaya 61985, Bisha University, Saudi Arabia
Department of Mathematics, Faculty of Science
Saudi Arabia


A. A.
Ramadan
Department of Mathematics, Benisuef University, Benisuef, Egypt
Department of Mathematics, Benisuef University,
Egypt
$L$fuzzy sets
$L$double fuzzy relations
$L$double fuzzy rough sets
$L$double fuzzy approximation operators
$L$double fuzzy topology
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On The Bicompletion of Intuitionistic Fuzzy QuasiMetric Spaces
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Based on previous results that study the completion of fuzzy metric spaces, we show that every intuitionistic fuzzy quasimetric space, using the notion of fuzzy metric space in the sense of Kramosil and Michalek to obtain a generalization to the quasimetric setting, has a bicompletion which is unique up to isometry.
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Francisco
CastroCompany
Gilmation S.L., Calle 232, 66 La Ca~nada, Paterna,
46182, Spain
Gilmation S.L., Calle 232, 66 La Ca~nada,
Spain
fracasco@mat.upv.es


Pedro
Tirado
Instituto Universitario de Matematica Pura y Aplicada, Universidad
Politecnica de Valencia, 46022, Valencia, Spain
Instituto Universitario de Matematica Pura
Spain
pedtipe@mat.upv.es
Intuitionistic fuzzy quasimetric
Bicomplete
Isometry
Bicompletion
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Persian Translation of Abstracts
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