2011
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A SOLUTION TO AN ECONOMIC DISPATCH PROBLEM BY A
FUZZY ADAPTIVE GENETIC ALGORITHM
A SOLUTION TO AN ECONOMIC DISPATCH PROBLEM BY A
FUZZY ADAPTIVE GENETIC ALGORITHM
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In practice, obtaining the global optimum for the economic dispatch {bf (ED)}problem with ramp rate limits and prohibited operating zones is presents difficulties. This paper presents a new andefficient method for solving the economic dispatch problem with nonsmooth cost functions using aFuzzy Adaptive Genetic Algorithm (FAGA). The proposed algorithm deals with the issue ofcontrolling the exploration and exploitation capabilities of a heuristic search algorithm in whichthe real version of Genetic Algorithm (RGA) is equipped with a Fuzzy Logic Controller (FLC)which can efficiently explore and exploit optimum solutions. To validate the results obtainedby the proposed FAGA, it is compared with a Real Genetic Algorithm (RGA). Moreover, the resultsobtained by FAGA and RGA are also compared with those obtained by other approaches reported in the literature.It was observed that the FAGA outperforms the other methods in solving the power system economicload dispatch problem in terms of quality, as well as convergence and success rates.
1
In practice, obtaining the global optimum for the economic dispatch {bf (ED)}problem with ramp rate limits and prohibited operating zones is presents difficulties. This paper presents a new andefficient method for solving the economic dispatch problem with nonsmooth cost functions using aFuzzy Adaptive Genetic Algorithm (FAGA). The proposed algorithm deals with the issue ofcontrolling the exploration and exploitation capabilities of a heuristic search algorithm in whichthe real version of Genetic Algorithm (RGA) is equipped with a Fuzzy Logic Controller (FLC)which can efficiently explore and exploit optimum solutions. To validate the results obtainedby the proposed FAGA, it is compared with a Real Genetic Algorithm (RGA). Moreover, the resultsobtained by FAGA and RGA are also compared with those obtained by other approaches reported in the literature.It was observed that the FAGA outperforms the other methods in solving the power system economicload dispatch problem in terms of quality, as well as convergence and success rates.
1
21
H.
Nezamabadipour
H.
Nezamabadipour
Electrical Engineering Department, Shahid Bahonar University
of Kerman, Kerman, Iran
Electrical Engineering Department, Shahid
Iran
nezam@mail.uk.ac.ir
S.
Yazdani
S.
Yazdani
Electrical Engineering Department, Shahid Bahonar University of Kerman,
Kerman, Iran
Electrical Engineering Department, Shahid
Iran
sajjad.yazdani@gmail.com
M. M.
Farsangi
M. M.
Farsangi
Electrical Engineering Department, Shahid Bahonar University of
Kerman, Kerman, Iran
Electrical Engineering Department, Shahid
Iran
mmaghfoori@mail.uk.ac.ir
M.
Neyestani
M.
Neyestani
Electrical Engineering Department, Shahid Bahonar University of
Kerman, Kerman, Iran
Electrical Engineering Department, Shahid
Iran
mehdi2594@yahoo.com
Economic dispatch
Genetic algorithm
%Fuzzy adaptive genetic algorithm
Nonsmooth cost functions
[bibitem{Caponio:FAMA}##A. Caponio, G. L. Cascella, F. Neri, N. Salvatore and M. Sumner, {it A fast adaptive memetic##algorithm for offline and online control design of PMSM drives}, IEEE Trans. on Systems, Man and##CyberneticsPart B, Special Issue on Memetic Algorithms, {bf 37}textbf{(1)} (2007), 2841. ##bibitem{Chatu:PSOforED}##K. T. Chaturvedi, M. Pandit and L. Srivastava, {it Selforganizing hierarchical particle swarm##optimization for nonconvex economic dispatch}, IEEE Trans. Power Syst., {bf 23}textbf{(3)}##(2008), 10791087. ##bibitem{Chen:LSED}##P. H. Chen and H. C. Chang, {it Largescale economic dispatch by genetic algorithm}, IEEE Trans.##Power Syst., {bf 10}textbf{(4)} (1995), 19191926. ##bibitem{Chiang:ImpGA}##C. L. Chiang, {it Improved genetic algorithm for power economic dispatch of units with valve##point effects and multiple fuels}, IEEE Trans. Power Syst., {bf 20}textbf{(4)} (2005), 16901699. ##bibitem{Eiben:PCinEA}##A. E. Eiben, R. Hinterding and Z. Michlewicz, {it Parameter control in evolutionary algorithms},##IEEE Transaction on Evolutionary Computation, {bf 3}textbf{(2)} (1999), 124141. ##bibitem{Gaing:PSOforED}##Z. L. Gaing, {it Particle swarm optimization to solving the economic dispatch considering the##generator constraints}, IEEE Trans. Power Syst., {bf 18}textbf{(3)} (2003), 11871195. ##bibitem{Herrera:MAwithCHC}##F. Herrera, N. Krasnogor and D. Molina, {it Realcoded memetic algorithms with crossover hill##climbing}, Evolutionary Computation, {bf 12}textbf{(3)} (2004), 273302. ##bibitem{Herrera:ACofPmbyFLC}##F. Herrera and M. Lozano, {it Adaptive control of mutation probability by fuzzy logic##controllers}, Parallel Processing Solving from Nature VI, Berlin: Springer, (2000), 335344. ##bibitem{Herrera:AFO}##F. Herrera and M. Lozano, {it Adaptive fuzzy operators based on coevolution with fuzzy##behaviours}, IEEE Transaction on Evolutionary Computation, {bf 5}textbf{(2)} (2001), 118. ##bibitem{Herrera:FAGA}##F. Herrera and M. Lozano, {it Fuzzy adaptive genetic algorithm: design, taxonomy, and future##directions}, Soft Computing, {bf 7}textbf{} (2003), 545562. ##bibitem{Krasnogor:MA}##N. Krasnogor and J. Smith, {it A tutorial for competent memetic algorithms: model, taxonomy and##design issues}, IEEE Trans. Evol. Comput., {bf 9}textbf{(5)} (2005), 474488. ##bibitem{Lee:AdpNN}##K. Y. Lee, A. SodeYome and J. H. Park, {it Adaptive Hopfield neural network for economic load##dispatch}, IEEE Trans. Power Syst., {bf 13}textbf{(2)} (1998), 519526. ##bibitem{Lin:TSforED}##W. M. Lin, F. S. Cheng and M. T. Tsay, {it An improved tabu search for economic dispatch with##multiple minima}, IEEE Trans. Power Syst., {bf 17}textbf{(1)} (2002), 108112. ##bibitem{Mehdizadeh:HPSO}##E. Mehdizadeh, S. Sadinezhad and R. Tavakolimoghaddam, {it Optimaization of fuzzy clastering##criteria by a hybrid PSO and fuzzy cmeans clustering algorithm}, Iranian Journal of Fuzzy##Systems, {bf 5}textbf{(3)} (2008), 114 ##bibitem{Net:MAhomepage}##Memetic Algorithms Home Page, http://www.densis.fee.unicamp.br/$sim$moscato /memetic_ home.##bibitem{Mrz:FLandMAforQAP}##P. Merz and B. Freisleben, {it Fitness landscape analysis and memetic algorithms for the##quadratic assignment problem}, IEEE Trans. Evol. Comput., {bf 4}textbf{(4)} (2000), 337352. ##bibitem{Moscato:MA}##P. Moscato, {it On evolution, search, optimization, genetic algorithms and martial arts: towards##memetic algorithms}, Memetic Algorithms Home Page, http://www. densis. fee. unicamp. br /$sim##$moscato /memetic_ home. html. ##bibitem{Neyestani:MAforED}##M. Neyestani, M. M. Farsangi and H. Nezamabadipour, {it Memetic algorithm for economic dispatch##with nonsmooth cost functions}, Accepted by Iranian Journal of Electrical and Computer Engineering##(IJECE) (in Farsi). ##bibitem{Oreo:EDPOZ}##S. O. Orero and M. R. Irving, {it Economic dispatch of generators with prohibited operating##zones: a genetic algorithm approach}, Proc. Inst. Elect. Eng. Gen. Transm. Distrib., {bf##143}textbf{(6)} (1996), 529534. ##bibitem{Park:PSOforED}##J. B. Park, K. S. Lee, J. R. Shin and K. Y. Lee, {it A particle swarm optimization for economic##dispatch with nonsmooth cost functions}, IEEE Trans. Power Syst., {bf 20}textbf{(1)} (2005), 34##bibitem{Rashedi:GSA}##E. Rashedi, H. Nezamabadipour and S. Saryazdi, {it GSA: a gravitational search algorithm},##Information Sciences, {bf 179}textbf{(13)} (2009), 22322248. ##bibitem{Selva:PSOforED}##A. I. Selvakumar and K. Thanushkodi, {it A new particle swarm optimization solution to nonconvex##economic dispatch problems}, IEEE Trans. Power Syst., {bf 22}textbf{(1)} (2007), 4251. ##bibitem{Sinha:EPforED}##N. Sinha, R. Chakrabarti and P. K. Chattopadhyay, {it Evolutionary programming techniques for##economic load dispatch}, IEEE Trans. Evol. Comput., {bf 7}textbf{(1)} (2003), 8394. ##bibitem{Sum:EDbyACO}##T. Sumim, {it Economic dispatch by ant colony search algorithm}, Proc. IEEE Conference on##Cybernetics and Intelligent Systems, (2004), 416421. ##bibitem{Wang:EDbyDE}##S. K. Wang, J. P. Chiou and C. W. Liu, {it Nonsmooth/nonconvex economic dispatch by a novel##hybrid differential evolution algorithm}, IET Generation Transmission & Distribution, {bf##1}textbf{(5)} (2007), 793803. ##bibitem{Wong:SA}##K. P. Wong and C. C. Fung, {it Simulated annealing based economic dispatch algorithm}, Proc.##Inst. Elect. Eng. C, {bf 140}textbf{(6)} (1993), 509515. ##bibitem{Wong:GASAED}##K. P. Wong and Y. W. Wong, {it Genetic and genetic simulatedannealing approaches to economic##dispatch}, Proc. Inst. Elect. Eng. Gen. Transm. Distrib., {bf 141}textbf{(5)} (1994), 507513. ##bibitem{Yang:EPforED}##H. T. Yang, P. C. Yang and C. L. Huang, {it Evolutionary programming based economic dispatch for##units with nonsmooth fuel cost functions}, IEEE Trans. Power Syst., {bf 11}textbf{(1)} (1996),##bibitem{Zeng:FAGA}##X. Zeng and B. Rabenasolo, {it A fuzzy logic based design for adaptive genetic algorithms},##European Congress on Intelligent Techniques and Soft Computing, (1997), 660664.##]
Fuzzy relations, Possibility theory, Measures of uncertainty, Mathematical modeling.
MEASURING STUDENTS MODELING CAPACITIES: A FUZZY
APPROACH
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2
A central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. In this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. The main stages of the modeling process are represented as fuzzy sets in a set of linguistic labels indicating the degree of a student's success in each of these stages. We use the total possibilistic uncertainty on the ordered possibility distribution of all student profiles as a measure of the students' modeling capacities and illustrate our results by application to a classroom experiment.
1
A central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. In this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. The main stages of the modeling process are represented as fuzzy sets in a set of linguistic labels indicating the degree of a student's success in each of these stages. We use the total possibilistic uncertainty on the ordered possibility distribution of all student profiles as a measure of the students' modeling capacities and illustrate our results by application to a classroom experiment.
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33
Michael Gr.
Voskoglou
Michael Gr.
Voskoglou
Graduate Technological Educational Institute (T.E.I.),
School of Technological Applications, 263 34 Patras, Greece
Graduate Technological Educational Institute
Greece
voskoglou@teipat.gr
Fuzzy relations
Possibility theory
Measures of uncertainty
Mathematical modeling
[bibitem{BaKo:2002}##M. Ajello and F. Spagnolo, {it Some experimental observations on common sense and fuzzy logic}, Proceedings of International Conference on Mathematics Education into the 21st Century, Napoli, (2002), 3539. ##bibitem{Bo:2007}##R. Borroneo Ferri, {it Modeling problems from a cognitive perspective}, In: C. R. Haines, P. Galbraith, W. Bloom, S. Khan, eds., Mathematical Modeling: Education, Engineering and Economics, (ICTMA 12), Horwood Publishing, Chichester, (2007), 260270. ##bibitem{Do:2007}##H. M. Doer, {it What knowledge do teachers need for teaching mathematics through applications and modeling?}, In: W. Blum, P. L. Galbraith, H. W. Henn and M. Niss, eds., Modeling and Applications in Mathematics Education, Springer, NY, (2007), 6978. ##bibitem{EsOli:1997}##E. A. Espin and C. M. L. Oliveras, {it Introduction to the use of fuzzy logic in the assessment of mathematics teachers'}, In: A. Gagatsis, ed., Proceedings of the 1$^{st}$ Mediterranean Conference on Mathematics Education, Nicosia, Cyprus, (1997), 107113. ##bibitem{GalSti:2001}##P. L. Galbraith and G. Stillman, {it Assumptions and context: pursuing their role in modeling activity}, In: J. F. Matos, W. Blum, K. Houston and S. P. Carreira, eds., Modeling and Mathematics Education: Applications in Science and Technology (ICTMA 9), Chichester, (2001), 300310. ##bibitem{HaCr:2010}## C. R. Haines and R. Crouch, {it Remarks on modeling cycle and interpretation of behaviours}, In: R. A. Lesh, P. L. Galbraith, C. R. Haines and A. Harford, eds., Modeling Students' Mathematical Modeling Competencies, (ICTMA13), London, (2010), 145154. ##bibitem{HuShi:2009}## H. L. Huang and G. Shi, {it Robust H1 control for TS timevarying delay systems with norm bounded uncertainty based on LMI approach}, Iranian Journal of Fuzzy Systems, {bf 6}textbf{(1)} (2009), 114. ##bibitem{IlSpa:2010}##L. Iliadis and S. Spartalis, {it An intelligent information system for fuzzy additive modeling (hydrological risk application)}, Iranian Journal of Fuzzy Systems, {bf 7}textbf{(1)} (2010), 114. ##bibitem{JaMaMa:2009}##N. Javiadian, Y. Maali and N. MahadaviAmiri, {it Fuzzy linear programming with grades of satisfaction in constraints}, Iranian Journal of Fuzzy Systems, {bf 6}textbf{(3)} (2009), 1735. ##bibitem{KaKa:2008}##I. Kaya and J. Kahraman, {it Fuzzy process capability analyses: an application to teaching processes}, Journal of Intelligent and Fuzzy Systems, {bf 19}textbf{(45)} (2008), 259272. ##bibitem{KeKa:2008}##C. Kezi Selva Vijila and P. Kanagasalarathy, {it Intelligent technique of cancelling maternal ECG in FECG extraction}, Iranian Journal of Fuzzy Systems, {bf 5}textbf{(1)} (2008), 2745. ##bibitem{KliFo:1988}## G. J. Klir and T. A. Folger, {it Fuzzy sets, uncertainty and information}, Prentice Hall, London, 1988. ##bibitem{KliWi:1998}##G. J. Klir and M. J. Wierman, {it Uncertaintybased information: elements of generalized information theory}, PhysikaVerlag, Heidelberg, 1998. ##bibitem{MasPAr:2005}##M. Mashinchi, A. Parchami and H. R. Maleki, {it Application of fuzzy capability indices in educational comparison}, Proceedings 3d Int. Research Convention 2005, {bf 42} (2005). ##bibitem{Me:2009}## S. Meier, {it Identifying modeling tasks}, In: L. Paditz and A. Rogerson, eds., Models in Developing Mathematics Education (MEC21), Dresden, University of Applied Sciences, (2009), 399403. ##bibitem{NaPa:2010}##P. K. Nayak and M. Pal, {it Bimatrix games with intuitionistic fuzzy goals}, In: L. Paditz and A. Rogerson, eds., Iranian Journal of Fuzzy Systems, {bf 7}textbf{(1)} (2010), 6579. ##bibitem{Perd:2004}##S. Perdikaris, {it The problem of transition across levels in the van Hiele theory of geometric reasoning}, Philosophy of Mathematics Education Journal, {bf 18} (2004). ##bibitem{Po:1979}## H. O. Pollak, {it New trends in mathematics teaching}, Unesko, Paris, {bf IV} (1979). ##bibitem{Sha:1961}##G. L. S. Shackle, {it Decision, order and time in human affairs, Cambridge}, Cambridge University Press, 1961. ##bibitem{SuBaBi:2006}##I. Y. Subbotin, H. Badkoodehi and N. N. Bilotskii, {it Fuzzy logic and iterative assessment}, Didactics of Mathematics: Problems and Investigations (Ukraine), {bf 25} (2006), 221227. ##bibitem{VoPer:1193}##M. G. Voskoglou and S. Perdikaris, {it Measuring problemsolving skills}, International Journal of Mathematical Education in Science and Technology, {bf 24}textbf{(3)} (1993), 443447. ##bibitem{Vo:1995}##M. G. Voskoglou, {it Measuring mathematical model building abilities}, International Journal of Mathematical Education in Science and Technology, {bf 26}textbf{(1)} (1995), 2935. ##bibitem{Vo:1996}##M. G. Voskoglou, {it An application of ergodic Markov chains to analogical problem solving}, The Mathematics Education (India), {bf XXX}textbf{(2)} (1996), 95108. ##bibitem{Vo:1999}##M. G. Voskoglou, {it The process of learning mathematics: a fuzzy set approach}, Heuristics and Didactics of Exact Sciences (Ukraine), {bf 10} (1999), 913. ##bibitem{Vo:2000}##M. G. Voskoglou, {it An application of Markov chains to decision making}, Studia Kupieckie (University of Lodz, Poland), {bf 6} (2000), 6976. ##bibitem{Vo:2006}##M. G. Voskoglou, {it The use of mathematical modeling as a tool for learning mathematics}, Quaderni di Ricerca in Didattica (Scienze Mathematiche), {bf 16} (2006), 5360. ##bibitem{Vo:2007}##M. G. Voskoglou, {it A stochastic model for the modeling process}, In: C. R. Haines, P. Galbraith, W. Bloom, S. Khan, eds., Mathematical Modeling: Education, Engineering and Economics, (2007), 149157. ##bibitem{Vo:2009}##M. G. Voskoglou, {it Fuzziness or probability in the process of learning? a general question illustrated by examples from teaching mathematics}, The Journal of Fuzzy Mathematics, International Fuzzy Mathematics Institute (Los Angeles), {bf 17}textbf{(3)} (2009), 697686. ##bibitem{Vo:2009a}##M. G. Voskoglou, {it Fuzzy sets in casebased reasoning}, In: Y. Chen, H. Deng, D. Zhang and Y. Xiao, eds., Fuzzy Systems and Knowledge Discovery (FSKD 2009), {bf 6} (2009), 252256. ##bibitem{Vo:2009b}##M. G. Voskoglou, {it A stochastic model for the process of learning}, In: L. Paditz and A. Rogerson, eds., Models in Developing Mathematics Education (MEC21) Dresden, (2009), 565569. ##bibitem{Vo:2010}##M. G. Voskoglou, {it Mathematizing the casebased reasoning process}, In: A. M. Leeland, ed., CaseBased Reasoning: Processes, Suitability and Applications, in press, {bf 6} (2010).##]
Optimal Control with Fuzzy Chance Constraints
Optimal Control with Fuzzy Chance Constraints
2
2
In this paper, a model of an optimal control problem with chance constraints is introduced. The parametersof the constraints are fuzzy, random or fuzzy random variables. Todefuzzify the constraints, we consider possibility levels. Bychanceconstrained programming the chance constraints are converted to crisp constraints which are neither fuzzy nor stochastic and then the resulting classical optimalcontrol problem with crisp constraints is solved by thePontryagin Minimum Principle and KuhnTucker conditions. The modelis illustrated by two numerical examples.
1
In this paper, a model of an optimal control problem with chance constraints is introduced. The parametersof the constraints are fuzzy, random or fuzzy random variables. Todefuzzify the constraints, we consider possibility levels. Bychanceconstrained programming the chance constraints are converted to crisp constraints which are neither fuzzy nor stochastic and then the resulting classical optimalcontrol problem with crisp constraints is solved by thePontryagin Minimum Principle and KuhnTucker conditions. The modelis illustrated by two numerical examples.
35
43
Saeed
Ramezanzadeh
Saeed
Ramezanzadeh
Department of Mathematics, Payame Noor University, Tehran,
Iran and Department of Mathematics, Faculty of Technology, Olum Entezami University,
Tehran, Iran
Department of Mathematics, Payame Noor University,
Iran
ramezanzadeh@phd.pnu.ac.ir
Aghileh
Heydari
Aghileh
Heydari
Department of Mathematics, Payame Noor University, Mashhad,
Iran
Department of Mathematics, Payame Noor University,
Iran
a_heidari@pnu.ac.ir
Fuzzy random variable
Chanceconstrained programming
Possibility level
[D. Chakraborty, {it Redefining chanceconstrained programming in##fuzzy environment}, FSS, {bf 125} (2002), 327333.## A. Charns and W. Cooper, {it Chance constrained programming}, Management Science,##{bf 6 } (1959), 7379.##D. Dubois and H. Prade, {it Ranking fuzzy numbers in the setting of##possibility theory}, Information sciences, {bf 30} (1983),##N. Javadin, Y. Maali and N. MahdaviAmiri, {it Fuzzy linear##programming with grades of satisfaction in constraints}, Iranian##Journal of Fuzzy Systems, {bf 6(3)} (2009), 1735.##H. Kuakernaak, {it Fuzzy random variables, definitions and##theorems}, Information Sciences, {bf 15} (1978), 129.## B. Liu, {it Fuzzy random chanceconstrained programming}, IEEE Transactions on##Fuzzy Systems, {bf 9(5)} (2001), 713720.## B. Liu, {it Fuzzy random dependentchance programming}, IEEE Transactions on##Fuzzy Systems, {bf 9(5)} (2001), 721726.##M. K. Maiti and M. Maiti, {it Fuzzy inventory model with two##warehouses under possibility constraints}, FSS, {bf 157} (2006),##K. Maity and M. Maiti, {it Possibility and necessity constraints and##their defuzzification a multiitem productioninventory##scenario via optimal control theory}, European Journal of##Operational Research, {bf 177} (2007), 882896.##L. S. Pontryagin and et al., {it The mathematical theory of optimal##process}, International Science, New York, 1962.##S. Ramezanzadeh, M. Memriani and S. Saati, {it Data envelopment##analysis with fuzzy random inputs and outputs: a##chanceconstrained programming approach}, Iranian Journal of Fuzzy##Systems, {bf 2(2)} (2005), 2131.##M. R. Safi, H. R. Maleki and E. Zaeimazad, {it A note on the##zimmermann method for solving fuzzy linear programming problems},##Iranian Journal of Fuzzy Systems, {bf 4(2)} (2007), 3145.##E. Shivanian, E. Khorram and A. Ghodousian, {it Optimization of##linear objective function subject to fuzzy relatin inequalities##constraints with maxaverage composition}, Iranian Journal of##Fuzzy Systems, {bf 4(2)} (2007), 1529.##]
AN EXTENDED FUZZY ARTIFICIAL NEURAL NETWORKS
MODEL FOR TIME SERIES FORECASTING
AN EXTENDED FUZZY ARTIFICIAL NEURAL NETWORKS
MODEL FOR TIME SERIES FORECASTING
2
2
Improving time series forecastingaccuracy is an important yet often difficult task.Both theoretical and empirical findings haveindicated that integration of several models is an effectiveway to improve predictive performance, especiallywhen the models in combination are quite different. In this paper,a model of the hybrid artificial neural networks andfuzzy model is proposed for time series forecasting, usingautoregressive integrated moving average models. In the proposedmodel, by first modeling the linear components, autoregressive integrated moving average models arecombined with the these hybrid models to yield amore general and accurate forecasting model than thetraditional hybrid artificial neural networks and fuzzy models. Empirical results for financialtime series forecasting indicate that the proposed model exhibitseffectively improved forecasting accuracy and hence is an appropriate forecasting tool for financial timeseries forecasting.
1
Improving time series forecastingaccuracy is an important yet often difficult task.Both theoretical and empirical findings haveindicated that integration of several models is an effectiveway to improve predictive performance, especiallywhen the models in combination are quite different. In this paper,a model of the hybrid artificial neural networks andfuzzy model is proposed for time series forecasting, usingautoregressive integrated moving average models. In the proposedmodel, by first modeling the linear components, autoregressive integrated moving average models arecombined with the these hybrid models to yield amore general and accurate forecasting model than thetraditional hybrid artificial neural networks and fuzzy models. Empirical results for financialtime series forecasting indicate that the proposed model exhibitseffectively improved forecasting accuracy and hence is an appropriate forecasting tool for financial timeseries forecasting.
45
66
Mehdi
Khashe
Mehdi
Khashe
Industrial Engineering Department, Isfahan University of Technol
ogy, Isfahan, Iran
Industrial Engineering Department, Isfahan
Iran
khashei@in.iut.ac.ir
Mehdi
Bijari
Mehdi
Bijari
Industrial Engineering Department, Isfahan University of Technology,
Isfahan, Iran
Industrial Engineering Department, Isfahan
Iran
bijari@cc.iut.ac.ir
Seyed Reza
Hejazi
Seyed Reza
Hejazi
Industrial Engineering Department, Isfahan University of Tech
nology, Isfahan, Iran
Industrial Engineering Department, Isfahan
Iran
rehejazi@cc.iut.ac.ir
Autoregressive integrated moving average (ARIMA)
Artificial neural networks (ANNs)
Fuzzy regression
Fuzzy logic
Time series forecasting
Financial markets
[bibitem{1} A. R. Arabpour and M. Tata, {it Estimating the parameters of a##fuzzy linear regression model}, Iranian Journal of Fuzzy Systems,##{bf5} (2008), 119.##bibitem{2} G. Armano, M. Marchesi and A. Murru, {it A##hybrid geneticneural architecture for stock indexes forecasting},##Information Sciences, {bf170} (2005), 333.##bibitem{1} J. M. Bates and W. J.##Granger, {it The combination of forecasts}, Operation Research,##{bf20} (1969), 451468.##bibitem{1} P. Box and G. M. Jenkins, {it Time##series analysis: forecasting and control}, Holdenday Inc, San##Francisco, CA, 1976.##bibitem{1} M. C. Brace, J. Schmidt and M. Hadlin, {it##Comparison of the forecasting accuracy of neural networks with##other established techniques}, In: Proceedings of the First Forum##on Application for weight elimination, IEEE Transactions on Neural##Networks of Neural Networks to Power Systems, Seattle, WA (1991),##bibitem{1} P. Chang, C. Liu and Y. Wang, {it A hybrid model by##clustering and evolving fuzzy rules for sales decision supports in##printed circuit board industry}, Decision Support Systems, {bf42}##(2006), 12541269.##bibitem{1} S. M. Chen, {it Forecasting enrollments##based on fuzzy time series}, Fuzzy Sets and Systems, {bf81(3)}##(1996), 311319, 1996.##bibitem{1} K. Y. Chen and C. H. Wang, {it A hybrid##SARIMA and support vector machines in forecasting the production##values of the machinery industry in Taiwan}, Expert Systems with##Applications, {bf32} (2007), 254264.##bibitem{1} S. M. Chen and N. Y. Chung,##{it Forecasting enrollments using highorder fuzzy time series##and genetic algorithms}, International J. Intell. Syst., {bf21}##(2006), 485501.##bibitem{1} R. Clemen, {it Combining forecasts: a##review and annotated bibliography with discussion}, International##Journal of Forecasting, {bf5} (1989), 559608.##bibitem{1} J. W. Denton,##{it How good are neural networks for causal forecasting?}, The##Journal of Business Forecasting, {bf14(2)} (1995), 1720.##bibitem{1}##P. A. Fishwick, {it Neural network models in simulation: a##comparison with traditional modeling approaches}, In: Proceedings##of Winter Simulation Conference, Washington, D. C., (1989),##bibitem{1} W. R. Foster, F. Collopy and L. H. Ungar, {it##Neural network forecasting of short, noisy time series}, Computers##and Chemical Engineering, {bf16(4)} (1992), 293297.##bibitem{1}##I. Ginzburg and D. Horn, {it Combined neural networks for time##series analysis}, Neural Information Processing Systems, {bf6}##(1994), 224231.##bibitem{1} T. H. Hann and E. Steurer, {it Much##ado about nothing? exchange rate forecasting: neural networks vs.##linear models using monthly and weekly data}, Neurocomputing,##{bf10} (1996), 323339.##bibitem{1} M. Haseyama and H. Kitajima,##{it An ARMA order selection method with fuzzy reasoning}, Signal##Process, {bf81} (2001), 13311335.##bibitem{1} H. Hassanpour, H.##R. Maleki and M. A. Yaghoobi, {it A note on evaluation of fuzzy##linear regression models by comparing membership functions},##Iranian Journal of Fuzzy Systems, {bf6} (2009), 16.##bibitem{1}##M. Hibon and T. Evgeniou, {it To combine or not to combine:##selecting among forecasts and their combinations}, International##Journal of Forecasting, {bf21} (2005), 1524.##bibitem{1} C. M.##Hurvich and C. L. Tsai, {it Regression and time series model##selection in small samples}, Biometrica, {bf76(2)} (1989),##bibitem{1} H. B. Hwang, {it Insights into##neuralnetwork forecasting time series corresponding to ARMA(p; q)##structures}, Omega, {bf29} (2001), 273289.##bibitem{1} H.##Ishibuchi and H. Tanaka, {it Interval regression analysis based on##mixed 01 integer programming problem}, J. Japan Soc. Ind. Eng,##{bf40(5)} (1988), 312319.##bibitem{1} J. S. R. Jang, {it ANFIS:##adaptivenetworkbased fuzzy inference system}, IEEE Trans Syst,##Man, Cybernet, {bf23} (1993), 66585.##bibitem{1} R. H.##Jones, {it Fitting autoregressions}, J. Amer. Statist. Assoc.,##{bf70(351)} (1975), 590592.##bibitem{1} M. Khashei, {it##Forecasting the Isfahan Steel Company production price in Tehran##Metals Exchange using Artificial Neural Networks (ANNs)}, Master##of Science Thesis, Isfahan University of Technology, 2005.##bibitem{1} M. Khashei, S. R. Hejazi and M. Bijari, {it A new hybrid##artificial neural networks and fuzzy regression model for time##series forecasting}, Fuzzy Sets and Systems, {bf159} (2008),##bibitem{1} Y. Lin and W. G. Cobourn, {it Fuzzy system##models combined with nonlinear regression for daily groundlevel##ozone predictions}, Atmospheric Environment, {bf41} (2007),##35023513.##bibitem{1} L. Ljung, {it System Identification##Theory for the User, PrenticeHall}, Englewood Cliffs, NJ, 1987.##bibitem{1} J. T. Luxhoj, J. O. Riis and B. Stensballe, {it A hybrid##econometricneural network modeling approach for sales##forecasting}, Int. J. Prod. Econ., {bf43} (1996), 175192.##bibitem{1} S. Makridakis, A. Anderson, R. Carbone, R. Fildes. M.##Hibdon, R. Lewandowski, J. Newton, E. Parzen and R. Winkler, {it The##accuracy of extrapolation (time series) methods: results of a##forecasting competition}, Journal of Forecasting, {bf1} (1982),##bibitem{1} E. Mehdizadeh, S. Sadinezhad and R.##Tavakkolimoghaddam, {it Optimization of fuzzy clustering##criteria by a hybrid pso and fuzzy cmeans clustering algorithm},##Iranian Journal of Fuzzy Systems, {bf5} (2008), 114##bibitem{1}##T. Minerva and I. Poli, {it Building ARMA models with genetic##algorithms}, In: Lecture Notes in Computer Science, {bf2037} (2001),##bibitem{1} C. Ong, J. J. Huang and G. H. Tzeng, {it Model##identification of ARIMA family using genetic algorithms}, Appl.##Math. Comput., {bf164(3)} (2005), 885912.##bibitem{1} P. F. Pai and##C. S. Lin, {it A hybrid ARIMA and support vector machines model in##stock price forecasting}, Omega, {bf33} (2005), 497505.##bibitem{1} E. Pelikan, C. De Groot and D. Wurtz, {it Power##consumption in WestBohemia: improved forecasts with decorrelating##connectionist networks}, Neural Network, {bf2} (1992), 701712.##bibitem{1} M. J. Reid, {it Combining three estimates of gross domestic##product}, Economica, {bf35} (1968), 431444.##bibitem{1} R.##Shibata, {it Selection of the order of an autoregressive model by##Akaike's information criterion}, Biometrika, {bf AC63(1)}##(1976), 117126.##bibitem{1} Z. Tang, C. Almeida and P. A. Fishwick,##{it Time series forecasting using neural networks us,} BoxJenkins##Methodology Simulation, {bf57(5)} (1991), 303310.##bibitem{1}##Z. Tang and P. A. Fishwick, {it Feedforward neural nets as models for##time series forecasting}, ORSA Journal on Computing, {bf5(4)}##(1993), 374385.##bibitem{1} T. Taskaya and M. C. Casey, {it##A comparative study of autoregressive neural network hybrids},##Neural Networks, {bf18} (2005), 781789.##bibitem{1} N. Terui and##H. van Dijk, {it Combined forecasts from linear and nonlinear##time series models}, International Journal of Forecasting, {bf18}##(2002), 421438.##bibitem{1} R. Tsaih, Y. Hsu and C. C. Lai, {it##Forecasting S$&$P 500 stock index futures with a hybrid AI##system}, Decision Support Systems, {bf23} (1998), 161174.##bibitem{1}##F. M. Tseng, G. H. Tzeng, H. C. Yu and B. J. C. Yuan, {it Fuzzy ARIMA##model for forecasting the foreign exchange market}, Fuzzy Sets and##Systems, {bf118} (2001), 919.##bibitem{1} F. M. Tseng,##H. C. Yu and G. H. Tzeng, {it Combining neural network model with##seasonal time series ARIMA model}, Technological Forecasting $&$##Social Change, {bf69} (2002), 7187.##bibitem{1} M. V. D. Voort and##M. Dougherty and S. Watson, {it Combining Kohonen maps with ARIMA##time series models to forecast traffic flow}, Transportation##Research Part C: Emerging Technologies, {bf4} (1996), 307318.##bibitem{1} H. Wold, {it A Study in the analysis of stationary time##series}, Almgrist $&$ Wiksell, Stockholm, 1938.##bibitem{1} H. K. Yu,##{it Weighted fuzzy timeseries models for TAIEX forecasting},##Physica A, {bf349} (2004), 609624.##bibitem{1} L. Yu, S.##Wang and K. K. Lai, {it A novel nonlinear ensemble forecasting model##incorporating GLAR and ANN for foreign exchange rates}, Computers##and Operations Research, {bf32} (2005), 25232541.##bibitem{1}##G. Yule, {it Why do we sometimes get nonsensecorrelations##between time series? a study in sampling and the nature of time##series}, J. R. Statist. Soc., {bf89} (1926), 164.##bibitem{1}##G. P. Zhang, {it Time series forecasting using a hybrid ARIMA and##neural network model}, Neurocomputing, {bf50} (2003), 159175.##bibitem{1} G. Zhang, B. E. Patuwo and M. Y. Hu, {it Forecasting with##artificial neural networks: the state of the art}, International##Journal of Forecasting, {bf14} (1998), 3562.##bibitem{1} Z. J.##Zhou and C. H. Hu, {it An effective hybrid approach based on grey and##ARMA for forecasting gyro drift, Chaos}, Solitons and Fractals,##{bf35} (2008), 525529.##]
TS FUZZY MODELBASED MEMORY CONTROL FOR
DISCRETETIME SYSTEM WITH RANDOM INPUT DELAY
TS FUZZY MODELBASED MEMORY CONTROL FOR
DISCRETETIME SYSTEM WITH RANDOM INPUT DELAY
2
2
A memory control for TS fuzzy discretetime systems with sto chastic input delay is proposed in this paper. Dierent from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delays vary randomly and satisfy some probabilistic dis tribution. A new state space model of the discretetime TS fuzzy system is derived by introducing some stochastic variables satisfying Bernoulli random binary distribution and using state augmentation method, some criterion for the stochastic stability analysis and stabilization controller design are derived for TS fuzzy systems with stochastic timevarying input delay. Finally, a nu merical example is given to demonstrate the eectiveness and the merit of the proposed method.
1
A memory control for TS fuzzy discretetime systems with sto chastic input delay is proposed in this paper. Dierent from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delays vary randomly and satisfy some probabilistic dis tribution. A new state space model of the discretetime TS fuzzy system is derived by introducing some stochastic variables satisfying Bernoulli random binary distribution and using state augmentation method, some criterion for the stochastic stability analysis and stabilization controller design are derived for TS fuzzy systems with stochastic timevarying input delay. Finally, a nu merical example is given to demonstrate the eectiveness and the merit of the proposed method.
67
79
Jinliang
Liu
Jinliang
Liu
Department of Applied Mathematics, Nanjing University of Finance
and Economics, Nanjing, 210046, P. R. China and the College of Information Sciences,
Donghua University, Shanghai, 201620, P. R. China
Department of Applied Mathematics, Nanjing
China
liujinliang@vip.163.com
Zhou
Gu
Zhou
Gu
Power Engineering, Nanjing Normal University, Nanjing, Jiangsu, 210042,
P. R. China
Power Engineering, Nanjing Normal University,
China
guzhouok@yahoo.com.cn
Hua
Han
Hua
Han
College of Information Science and Technology, Donghua University,
Shanghai, 201620, P. R.China
College of Information Science and Technology,
China
2070967@mail.dhu.edu.cn
Songlin
Hu
Songlin
Hu
Department of Control Science and Engineering, Huazhong University
of Science and Technology, Wuhan, Hubei, 430074, P. R. China
Department of Control Science and Engineering,
China
songlin621@126.com
Memory control
Fuzzy system
Random input delay
Discretetime system
[[1] Y. Cao and P. Frank, Analysis and synthesis of nonlinear timedelay systems via fuzzy control##approach, IEEE Trans. On fuzzy systems, 8(2) (2000), 200211.##[2] Y. Cao and P. Frank, Stability analysis and synthesis of nonlinear timedelay systems via##linear Takagi{Sugeno fuzzy models, Fuzzy Sets and Systems, 142(2) (2001), 213229. ##[3] B. Chen, X. Liu, S. Tong and C. Lin, Observerbased stabilization of TS fuzzy systems with##input delay, IEEE Trans. On Fuzzy Systems, 16(3) (2008), 652663.##[4] B. Chen, X. Liu, C. Lin and K. Liu, Robust H1 control of Takagi{Sugeno fuzzy systems with##state and input time delays, Fuzzy Sets and Systems, 160(4) (2009), 403422.##[5] G. Feng and X. Guan, Delaydependent stability analysis and controller synthesis for discrete##time TS fuzzy systems with time delays, IEEE Trans. On Fuzzy Systems, 13(5) (2005),##[6] G. Feng, A survey on analysis and design of modelbased fuzzy control systems, IEEE Trans.##On Fuzzy systems, 14(5) (2006), 676697.##[7] E. Fridman and U. Shaked, Delaydependent H1 control of uncertain discrete delay systems,##European Journal of Control, 11(1) (2005), 2937.##[8] E. Fridman and U. Shaked, Stability and guaranteed cost control of uncertain discrete delay##systems, International Journal of Control, 78(4) (2005), 235246.##[9] H. Gao and T. Chen, New results on stability of discretetime systems with timevarying##state delay, IEEE Trans. on Automatic Control, 52(2) (2007), 328334.##[10] H. Gao, X. Meng and T. Chen, Stabilization of networked control systems with a new delay##characterization, IEEE Trans. On Automatic Control, 53(9) (2008), 21422148.##[11] X. Guan and C. Chen, Delaydependent guaranteed cost control for TS fuzzy systems with##time delays, IEEE Trans. On Fuzzy Systems, 12(2) (2004), 236249.##[12] H. Huang and F. Shi, Robust H1 control for TCS timevarying delay systems with norm##bounded uncertainty based on LMI approach, Iranian Journal of Fuzzy Systems, 6(1) (2009),##[13] J. Liu, W. Yu, Z. Gu and S. Hu, H1 ltering for timedelay systems with markovian jumping##parameters: delay partitioning approach, Journal of the Chinese Institute of Engineers, 33(3)##(2010), 357365.##[14] J. Liu, Z. Gu, E. Tian and R. Yan, New results on H1 lter design for nonlinear systems with##timedelay through a TS fuzzy model approach, International Journal of Systems Science,##First published on: 16 August 2010 (iFirst).##[15] X. Liu and Q. Zhang, Approaches to quadratic stability conditions and H1 control designs##for TS fuzzy systems, IEEE Trans. On Fuzzy Systems, 11(6) (2003), 830839.##[16] K. Lee, J. Kim, E. Jeung and H. Park, Output feedback robust H1 control of uncertainfuzzy##dynamic systems with timevarying delay, IEEE Trans. On Fuzzy systems, 8(6) (2000), 657##[17] C. Peng, Y. Tian and E. Tian, Improved delaydependent robust stabilization conditions of##uncertain T{S fuzzy systems with timevarying delay, Fuzzy Sets and Systems, 159(20)##(2008), 27132729.##[18] C. Peng, D. Yue and Y. Tian, New approach on robust delaydependent H1 control for##uncertain TS fuzzy systems with interval timevarying delay, IEEE Trans. On Fuzzy Systems,##17(4) (2009), 890900.##[19] T. Takagi and M. Sugeno, Fuzzy identication of systems and its applications to modeling##and control, IEEE Transactions on Systems, Man, and Cybernetics, 15(1) (1985), 116132.##[20] E. Tian and C. Peng, Delaydependent stability analysis and synthesis of uncertain T{S fuzzy##systems with timevarying delay, Fuzzy Sets and Systems, 157(4) (2006), 544559.##[21] H. Wang, K. Tanaka and M. Grin, An approach to fuzzy control of nonlinear systems:##stability and design issues, IEEE Trans. On Fuzzy Systems, 4(1) (1996), 1423.##[22] J. Yoneyama, Robust stability and stabilization for uncertain Takagi{Sugeno fuzzy timedelay##systems, Fuzzy Sets and Systems, 158(2) (2007), 115134.##[23] D. Yue, Q. Han and J. Lam, Networkbased robust H1 control of systems with uncertainty,##Automatica, 41(6) (2005), 9991007.##[24] D. Yue, Q. Han and C. Peng, State feedback controller design of networked control systems,##IEEE Trans. On Circuits and Systems Part II: Express Briefs, 51(11) (2004), 640644. ##]
EXPECTED PAYOFF OF TRADING STRATEGIES INVOLVING
EUROPEAN OPTIONS FOR FUZZY FINANCIAL MARKET
EXPECTED PAYOFF OF TRADING STRATEGIES INVOLVING
EUROPEAN OPTIONS FOR FUZZY FINANCIAL MARKET
2
2
Uncertainty inherent in the financial market was usually consid ered to be random. However, randomness is only one special type of uncer tainty and appropriate when describing objective information. For describing subjective information it is preferred to assume that uncertainty is fuzzy. This paper defines the expected payoof trading strategies in a fuzzy financial market within the framework of credibility theory. In addition, a computable integral form is obtained for expected payoof each strategy.
1
Uncertainty inherent in the financial market was usually consid ered to be random. However, randomness is only one special type of uncer tainty and appropriate when describing objective information. For describing subjective information it is preferred to assume that uncertainty is fuzzy. This paper defines the expected payoof trading strategies in a fuzzy financial market within the framework of credibility theory. In addition, a computable integral form is obtained for expected payoof each strategy.
81
94
Zhongfeng
Qin
Zhongfeng
Qin
School of Economics and Management, Beihang University, Beijing
100191, China
School of Economics and Management, Beihang
China
qin@buaa.edu.cn, qzf05@mails.tsinghua.edu.cn
Xiang
Li
Xiang
Li
The State Key Laboratory of Rail Traffic Control and Safety, Beijing
Jiaotong University, Beijing 100044, China
The State Key Laboratory of Rail Traffic
China
xiangli04@mail.tsinghua.edu.cn
Credibility measure
Liu process
Expected value
Fuzzy process
[[1] M. Baxter and A. Rennie, Financial calculus: an introduction to derivatives pricing, Cam##bridge University Press, 1996.##[2] F. Black and M. Scholes, The pricing of option and corporate liabilities, J. Polit. Econ., 81##(1973), 637654.##[3] K. A. Chrysas and B. K. Papadopoulos, On theoretical pricing of options with fuzzy esti##mators, J. Comput. Appl. Math., 223 (2009), 552566.##[4] J. Hull, Options, futures and other derivative securities, 5th ed., PrenticeHall, 2006.##[5] Z. Landsman, Minimization of the root of a quadratic functional under a system of ane##equality constraints with application to portfolio management, J. Comput. Appl. Math., 220##(2008), 739748.##[6] C. Lee, G. Tzeng and S. Wang, A new application of fuzzy set theory to the BlackScholes##option pricing model, Expert Syst. Appl., 29 (2005), 330342.##[7] X. Li and B. Liu, A sucient and necessary condition for credibility measures, Int. J. Un##certain. Fuzz., 14 (2006), 527535.##[8] X. Li and B. Liu, Maximum entropy principle for fuzzy variables, Int. J. Uncertain. Fuzz.,##15 (2007), 4352.##[9] X. Li and Z. Qin, Expected value and variance of geometric Liu process, Far East Journal of##Experimental and Theoretical Artical Intelligence, 1(2) (2008), 127135.##[10] B. Liu, Uncertainty theory, lst ed., SpringerVerlag, Berlin, 2004.##[11] B. Liu, Uncertainty theory, 2nd ed., SpringerVerlag, Berlin, 2007.##[12] B. Liu, Uncertainty theory, 3nd ed., http://orsc.edu.cn/liu/ut.pdf.##[13] B. Liu, Fuzzy process, hybrid process and uncertain process, J. Uncertain Syst., 2 (2008),##[14] B. Liu and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE##T. Fuzzy Syst., 10 (2002), 445450.##[15] Y. K. Liu and J. Gao, The independence of fuzzy variables in credibility theory and its##applications, Int. J. Uncertain. Fuzz., 15(Supp.2) (2007), 120.##[16] R. Merton, Theory of rational option pricing, Bell J. Econ. Manage. Sci., 4 (1973), 141183.##[17] S. Muzzioli and C. Torricelli, A multiperiod binomial model for pricing options in a vague##world, J. Econ. Dynam. Control, 28 (2004), 861887.##[18] Z. Qin and X. Li, Option pricing formula for fuzzy nancial market, J. Uncertain Syst., 2##(2008), 1721.##[19] Z. Qin, X. Li and X. Ji, Portfolio selection based on fuzzy crossentropy, J. Comput. Appl.##Math., 228 (2009), 139149.##[20] Z. Qin and X. Li, Fuzzy calculus for nance, http://orsc.edu.cn/process/fc.pdf.##[21] P. A. Samuelson, Rational theory of warrant prices, Ind. Manage. Rev., 6 (1965), 1331.##[22] K. Thiagarajah, S. S. Appadoo and A. Thavaneswaran, Option valuation model with adaptive##fuzzy numbers, Comput. Math. Appl., 53 (2007), 831841.##[23] E. Vercher, Portfolios with fuzzy returns: Selection strategies based on semiinnite program##ming, J. Comput. Appl. Math., 217 (2008), 381393.##[24] Y. Wang, Mining stock price using fuzzy rough set system, Expert Syst. Appl., 24 (2003),##[25] H. Wu, Pricing European options based on the fuzzy pattern of BlackScholes formula, Com##put. Oper. Res., 31 (2004), 10691081.##[26] H. Wu, Using fuzzy sets theory and BlackScholes formula to generate pricing boundaries of##European options, Appl. Math. Comput., 185 (2007), 136146.##[27] Y. Yoshida, The valuation of European options in uncertain environment, Eur. J. Oper. Res.,##145 (2003), 221229.##[28] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338353.##]
AGILITY EVALUATION IN PUBLIC SECTOR USING FUZZY
LOGIC
AGILITY EVALUATION IN PUBLIC SECTOR USING FUZZY
LOGIC
2
2
Agility metrics are difficult to define in general, mainly due to the multidimensionality and vagueness of the concept of agility itself. In this paper, a knowledgebased framework is proposed for the measurement and assessment of public sector agility using the A.T.Kearney model. Fuzzy logic provides a useful tool for dealing with decisions in which the phenomena are imprecise and vague. In the paper, we use the absolute agility index together with fuzzy logic to address the ambiguity in agility evaluation in public sector in a case study.
1
Agility metrics are difficult to define in general, mainly due to the multidimensionality and vagueness of the concept of agility itself. In this paper, a knowledgebased framework is proposed for the measurement and assessment of public sector agility using the A.T.Kearney model. Fuzzy logic provides a useful tool for dealing with decisions in which the phenomena are imprecise and vague. In the paper, we use the absolute agility index together with fuzzy logic to address the ambiguity in agility evaluation in public sector in a case study.
95
111
Nazar
Dahmardeh
Nazar
Dahmardeh
Department of Economics, University of Sistan and Baluchestan,
Zahedan, Iran
Department of Economics, University of Sistan
Iran
nazar@hamoon.usb.ac.ir
vahid
Pourshahabi
vahid
Pourshahabi
Member of Young Researchers Club, Islamic Azad University,
Zahedan, Iran
Member of Young Researchers Club, Islamic
Iran
pourshahabi.vahid@gmail.com
Agility index
Agility measuring
Fuzzy logic
Agile government
Public sector
[[1] B. M. Arteta and R. E. Giachetti, A measure of agility as the complexity of the enterprise##system, Robotics and Computerintegrated Manufacturing, 20 (2004), 495503.##[2] A. T. Kearney, Improving Performance in the Public Sector, 2003.##[3] E. Bottani, A fuzzy QFD approach to achieve agility, International Journal of Production##Economics, 2009.##[4] S. J. Chen and C. L. Hwang, Fuzzy multiple attribute decision making methods and application,##Springer, Berlin, Heidelberg, 1992.##[5] H. Hassanpour, H. R. Maleki and M. A. Yaghooni, A note on evaluation of fuzzy linear##regression models by comparing membership functions, Iranian Journal of Fuzzy Systems, 6##(2) (2009), 16.##[6] R. Hefner and N. Grumman, Six sigma applied throughout the lifecycle of an automated##decision system, (2006), 588.##[7] M. Jackson and C. Johansson, An agility analysis from a production system perspective,##Integrated Manufacturing Systems, 14(6) (2002), 482488.##[8] C. T. Lin, H. Chiu and P. Y. Chu, Agility index in the supply chain, Int. J. Production##Economics, 100 (2006), 285299.##[9] A. Maturo, On some structures of fuzzy numbers, Iranian Journal of Fuzzy Systems, 6(4)##(2009), 4959. ##[10] S. Parker and J. Barlett, Toward agile government, State service authority, 2008.##[11] A. W. Scheer, H. Kruppke, W. Jost and H. Kinderman, AGILITY, Aris Business process##management, 2007.##[12] B. Sherehiy, W. Karwowski and J. K. Layer, A review of enterprise agility: concepts, frameworks,##and attributes, International Journal of Industrial Ergonomics, 37 (2007), 445460.##[13] P. M. Swafford, S. Ghosh and N. Murthy, The antecedents of supply chain agility of a firm:##scale development and model testing, Journal of Operations Management, 24 (2006), 170##[14] N. C. Tsourveloudis and K. P. Valavanis, On the measurement of enterprise agility, Journal##of Intelligent and Robotics Systems, 33 (2002), 329342.##[15] M. Zain, R. C. Rose, I. Abdollah and M. Masrom, The relationship between information##technology acceptance and organizational agility in Malaysia, Information and Management,##42 (2005), 829839.##]
FUZZY GOULD INTEGRABILITY ON ATOMS
FUZZY GOULD INTEGRABILITY ON ATOMS
2
2
In this paper we study the relationships existing between total measurability in variation and Gould type fuzzy integrability (introduced and studied in [21]), giving a special interest on their behaviour on atoms and on finite unions of disjoint atoms. We also establish that any continuous real valued function defined on a compact metric space is totally measurable in the variation of a regular finitely purely atomic multisubmeasure and it is also Gould integrable with respect to regular finitely purely atomic multisubmeasures.
1
In this paper we study the relationships existing between total measurability in variation and Gould type fuzzy integrability (introduced and studied in [21]), giving a special interest on their behaviour on atoms and on nite unions of disjoint atoms. We also establish that any continuous real valued function de ned on a compact metric space is totally measurable in the variation of a regular nitely purely atomic multisubmeasure and it is also Gould integrable with respect to regular nitely purely atomic multisubmeasures.
113
124
Alina
Cristiana Gavrilut
Alina
Cristiana Gavrilut
Faculty of Mathematics, Al. I. Cuza University, Iasi,
Romania
Faculty of Mathematics, Al. I. Cuza University,
Romania
gavrilut@uaic.ro
Fuzzy Gould integral
Totally measurability (in variation)
(Multi) (sub) measure
Atom
Finitely purely atomic
Regularity
[[1] M. Abbas, M. Imdad and D. Gopal, "weak contractions in fuzzy metric spaces, Iranian##Journal of Fuzzy Systems, in print.##[2] M. Alimohammady, E. Ekici, S. Jafari and M. Roohi, On fuzzy upper and lower contra##continuous multifunctions, Iranian Journal of Fuzzy Systems, in print.##[3] I. Altun, Some xed point theorems for single and multivalued mappings on ordered non##archimedean fuzzy metric spaces, Iranian Journal of Fuzzy Systems, 7(1) (2010), 9196.##[4] I. Chitescu, Finitely purely atomic measures and Lpspaces, An. Univ. Bucuresti St. Natur.,##24 (1975), 2329.##[5] I. Chitescu, Finitely purely atomic measures: coincidence and rigidity properties, Rend. Circ.##Mat. Palermo(2), 50(3) (2001), 455476.##[6] I. Dobrakov, On submeasures, I, Dissertationes Math., 112 (1974), 535.##[7] L. Drewnowski, Topological rings of sets, continuous set functions, Integration, I, II, III,##Bull. Acad. Polon. Sci. Ser. Math. Astron. Phys., 20 (1972), 269286.##[8] A. Gavrilut, A Gould type integral with respect to a multisubmeasure, Math. Slovaca, 58(1)##(2008), 120.##[9] A. Gavrilut, On some properties of the Gould type integral with respect to a multisubmeasure,##An. St. Univ. Iasi, 52(1) (2006), 177194.##[10] A. Gavrilut, Nonatomicity and the Darboux property for fuzzy and nonfuzzy Borel/Baire##multivalued set functions, Fuzzy Sets and Systems, 160 (2009), 13081317.##[11] A. Gavrilut, Regularity and autocontinuity of set multifunctions, Fuzzy Sets and Systems,##160 (2009), 681693.##[12] A. Gavrilut, A Lusin type theorem for regular monotone uniformly autocontinuous set mul##tifunctions, Fuzzy Sets and Systems, 161 (2010), 29092918.##[13] A. Gavrilut and A. Croitoru, Nonatomicity for fuzzy and nonfuzzy multivalued set functions,##Fuzzy Sets and Systems, 160 (2009), 21062116.##[14] A. Gavrilut and A. Petcu, A Gould type integral with respect to a submeasure, An. St. Univ.##Iasi, Tomul LIII, 2 (2007), 351368.##[15] A. Gavrilut and A. Petcu, Some properties of the Gould type integral with respect to a##submeasure, Bul. Inst. Pol. Iasi, LIII (LVII), 5 (2007), 121131.##[16] G. G. Gould, On integration of vectorvalued measures, Proc. London Math. Soc., 15 (1965),##[17] S. Hu and N. S. Papageorgiou, Handbook of multivalued analysis, Kluwer Acad. Publ., Dor##drecht, I (1997).##[18] E. Pap, Nulladditive set functions, Kluwer Academic Publishers, DordrechtBostonLondon,##[19] Q. Jiang and H. Suzuki, Fuzzy measures on metric spaces, Fuzzy Sets and Systems, 83 (1996),##[20] A. Precupanu and A. Croitoru, A Gould type integral with respect to a multimeasure, I, An.##St. Univ. Iasi, 48 (2002), 165200.##[21] A. Precupanu, A. Gavrilut and A. Croitoru, A fuzzy Gould type integral, Fuzzy Sets and##Systems, 161 (2010), 661680.##[22] H. Suzuki, Atoms of fuzzy measures and fuzzy integrals, Fuzzy Sets and Systems, 41 (1991),##[23] C. Wu and S. Bo, Pseudoatoms of fuzzy and nonfuzzy measures, Fuzzy Sets and Systems,##158 (2007), 12581272.##]
ON GENERAL FUZZY RECOGNIZERS
ON GENERAL FUZZY RECOGNIZERS
2
2
In this paper, we de ne the concepts of general fuzzy recognizer, language recognized by a general fuzzy recognizer, the accessible and the coac cessible parts of a general fuzzy recognizer and the reversal of a general fuzzy recognizer. Then we obtain the relationships between them and construct a topology and some hypergroups on a general fuzzy recognizer.
1
In this paper, we de ne the concepts of general fuzzy recognizer, language recognized by a general fuzzy recognizer, the accessible and the coac cessible parts of a general fuzzy recognizer and the reversal of a general fuzzy recognizer. Then we obtain the relationships between them and construct a topology and some hypergroups on a general fuzzy recognizer.
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135
M.
Horry
M.
Horry
Shahid Chamran University of Kerman, Kerman, Iran
Shahid Chamran University of Kerman, Kerman,
Iran
mohhorry@chamranedu.ir
M. M.
Zahedi
M. M.
Zahedi
Department of Mathematics, Shahid Bahonar University of Kerman,
Kerman, Iran
Department of Mathematics, Shahid Bahonar
Iran
zahedi mm@mail.uk.ac.ir
(General) Fuzzy automata
General fuzzy recognizer
Accessibility
Coaccessibility
Topology
Hypergroup
[[1] S. Bozapalidis and O. L. Bozapalidoy, On the recognizability of fuzzy languages I, Fuzzy Sets##and Systems, 157 (2006), 23942402.##[2] S. Bozapalidis and O. L. Bozapalidoy, On the recognizability of fuzzy languages II, Fuzzy Sets##and Systems, 159(1) (2008), 107113. ##[3] S. Bozapalidis and O. L. Bozapalidoy, Fuzzy tree language recognizability, Fuzzy Sets and##Systems, 161(5) (2010), 716734.##[4] P. Corsini, Prolegomena of hypergroup theory, Aviani Editore, 1993.##[5] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Pub##lishers, Advances in Mathematics, 2003.##[6] M. Doostfatemeh and S. C. Kremer, New directions in fuzzy automata, International Journal##of Approximate Reasoning, 38 (2005), 175214.##[7] M. Horry and M. M. Zahedi, Hypergroups and general fuzzy automata, Iranian Journal of##Fuzzy Systems, 6(2) (2009), 6174.##[8] K. Kuratowski, Topology, Academic Presss, 1966.##[9] H. V. Kumbhojkar and S. R. Chaudhari, Fuzzy recognizers and recognizable sets, Fuzzy Sets##and Systems, 131(3) (2002), 381392.##[10] J. N. Mordeson and D. S. Malik, Fuzzy automata and languages, theory and applications,##Chapman and Hall/CRC, London/Boca Raton, FL, 2002.##[11] D. S. Malik, J. N. Mordeson and M. K. Sen, On subsystems of fuzzy nite state machines,##Fuzzy Sets and Systems, 68 (1994), 8392.##[12] M. Mizumoto, J. Tanaka and K. Tanaka, Some consideration on fuzzy automata, J. Compute.##Systems Sci., 3 (1969), 409422.##[13] W. Omlin, K. K. Giles and K. K. Thornber, Equivalence in knowledge representation: au##tomata, rnns, and dynamic fuzzy systems, Proc. IEEE, 87(9) (1999), 16231640.##[14] W. Omlin, K. K. Thornber and K. K. Giles, Fuzzy nitestate automata can be determinis##tically encoded into recurrent neural networks, IEEE Trans. Fuzzy Syst., 5(1) (1998), 7689.##[15] E. S. Santos, Realization of fuzzy languages by probabilistic, maxprod and maximin au##tomata, Information Sciences, 8 (1975), 3953.##[16] W. G. Wee, On generalization of adaptive algorithm and application of the fuzzy sets concept##to pattern classif ication, Ph.D. dissertation Purdue University, IN, 1967.##[17] W. G. Wee and K. S. Fu, A formulation of fuzzy automata and its applicationset as a modele##of learning systems, IEEE Trans. Systems Sci. Cybernet., 5 (1969), 215223.##[18] M. M. Zahedi, M. Horry and K. Abolpor, Bifuzzy (General) topology on maxmin general##fuzzy automata, Advanced in Fuzzy Mathematics, 3(1) (2008), 5168.##]
FUZZY SOFT SET THEORY AND ITS APPLICATIONS
FUZZY SOFT SET THEORY AND ITS APPLICATIONS
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2
In this work, we define a fuzzy soft set theory and its related properties. We then define fuzzy soft aggregation operator that allows constructing more efficient decision making method. Finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.
1
In this work, we define a fuzzy soft set theory and its related properties. We then define fuzzy soft aggregation operator that allows constructing more efficient decision making method. Finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.
137
147
Naim
Cagman
Naim
Cagman
Department of Mathematics, Faculty of Arts and Sciences, Gazios
manpasa University, 60150 Tokat, Turkey
Department of Mathematics, Faculty of Arts
Turkey
naim.cagman@gop.edu.tr
Serdar
Enginoglu
Serdar
Enginoglu
Department of Mathematics, Faculty of Arts and Sciences, Gazios
manpasa University, 60150 Tokat, Turkey
Department of Mathematics, Faculty of Arts
Turkey
serdar.enginoglu@gop.edu.tr
Filiz
Citak
Filiz
Citak
Department of Mathematics, Faculty of Arts and Sciences, Gaziosman
pasa University, 60150 Tokat, Turkey
Department of Mathematics, Faculty of Arts
Turkey
filiz.citak@gop.edu.tr
Fuzzy sets
Soft sets
Fuzzy soft sets
Soft aggregation
Fuzzy soft aggregation
Aggregate fuzzy set
[[1] M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set##theory, Comput. Math. Appl., 57 (2009), 15471553.##[2] H. Aktas. and N. C.##agman, Soft sets and soft groups, Information Sciences, 177 (2007), 2726##agman and S. Enginoglu, Soft set theory and uniint decision making, Eur. J. Oper.##Res., 207 (2010), 848855.##agman and S. Enginoglu, Soft matrix theory and its decision making, Comput. Math.##Appl., 59(10) (2010), 33083314.##agman, F. Ctak and S. Enginoglu, Fuzzy parameterized fuzzy soft set theory and its##applications, Turk. J. Fuzzy Syst., 1(1) (2010), 2135.##[6] D. Chen, E. C. C. Tsang, D. S. Yeung and X. Wang, The parameterization reduction of soft##sets and its applications, Comput. Math. Appl., 49 (2005), 757763.##[7] D. Dubois, and H. Prade, Fuzzy set and systems: theory and applications, Academic Press,##New York, 1980.##[8] F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Comput. Math. Appl., 56(10) (2008),##26212628.##[9] Y. B. Jun, Soft BCK/BCIalgebras, Comput. Math. Appl., 56 (2008), 14081413.##[10] Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCIalgebras,##Information Sciences, 178 (2008), 24662475.##[11] Y. B. Jun, K. J. Lee and C. H. Park, Soft set theory applied to commutative ideals in BCK##algebras, J. Appl. Math. and Informatics, 26 (2008), 707720.##[12] Y. B. Jun and C. H. Park, Applications of soft sets in Hilbert algebras, Iranian Journal of##Fuzzy Systems, 6(2) (2009), 7588.##[13] Y. B. Jun, H. S. Kim and J. Neggers, Pseudo dalgebras, Information Sciences, 179 (2009),##17511759.##[14] Y. B. Jun, K. J. Lee and C. H. Park, Soft set theory applied to ideals in dalgebras, Comput.##Math. Appl., 57 (2009), 367378.##[15] Z. Kong, L. Gao, L. Wang and S. Li, The normal parameter reduction of soft sets and its##algorithm, Comput. Math. Appl., 56 (2008), 30293037.##[16] Z. Kong, L. Gao and L. Wang, Comment on A fuzzy soft set theoretic approach to decision##making problems", J. Comput. Appl. Math., 223 (2009), 540542.##[17] D. V. Kovkov, V. M. Kolbanov and D. A. Molodtsov, Soft sets theorybased optimization, J.##Comput. Sys. Sc. Int., 46(6) (2007), 872880.##[18] P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, J. Fuzzy Math., 9(3) (2001), 589602.##[19] P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making##problem, Comput. Math. Appl., 44 (2002), 10771083.##[20] P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003),##[21] P. Majumdar and S. K. Samanta, Similarity measure of soft sets, New. Math. Nat. Comput.,##4(1) (2008), 112.##[22] A. Mukherjee and S. B. Chakraborty, On intuitionistic fuzzy soft relations, Bull. Kerala##Math. Assoc., 5(1) (2008), 3542.##[23] D. A. Molodtsov, Soft set theoryrst results, Comput. Math. Appl., 37 (1999), 1931.##[24] D. A. Molodtsov, The description of a dependence with the help of soft sets, J. Comput. Sys.##Sc. Int., 40(6) (2001), 977984. ##[25] D. A. Molodtsov, The theory of soft sets (in Russian), URSS Publishers, Moscow, 2004.##[26] D. A. Molodtsov, V. Yu. Leonov and D. V. Kovkov, Soft sets sechnique and its application,##Nechetkie Sistemi I Myakie Vychisleniya, 1(1) (2006), 839.##[27] M. M. Mushrif, S. Sengupta and A. K. Ray, Texture classication using a novel, softset##theory based classication, Algorithm. Lecture Notes In Computer Science, 3851 (2006),##[28] C. H. Park, Y. B. Jun and M. A. Ozturk, Soft WSalgebras, Commun. Korean Math. Soc.,##23(3) (2008), 313324.##[29] Z. Pawlak, Rough sets, Int. J. Comput. Inform. Sci., 11 (1982), 341356.##[30] D. Pei and D. Miao, From soft sets to information systems, In: X. Hu, Q. Liu, A. Skowron,##T. Y. Lin, R. R. Yager, B. Zhang ,eds., Proceedings of Granular Computing, IEEE, 2 (2005),##[31] A. R. Roy and P. K. Maji, A fuzzy soft set theoretic approach to decision making problems,##J. Comput. Appl. Math., 203 (2007), 412418.##[32] T. Som, On the theory of soft sets, soft relation and fuzzy soft relation, Proc. of the National##Conference on Uncertainty: A Mathematical Approach, UAMA06, Burdwan, (2006), 19.##[33] Q. M. Sun, Z. L. Zhang and J. Liu, Soft sets and soft modules, In: G. Wang, T. Li, J. W.##GrzymalaBusse, D. Miao, A. Skowron, Y. Yao, eds., Rough Sets and Knowledge Technology,##RSKT08, Proceedings, Springer, (2008), 403409.##[34] Z. Xiao, Y. Li, B. Zhong and X. Yang, Research on synthetically evaluating method for##business competitive capacity based on soft set, Stat. Methods. Med. Res., (2003), 5254.##[35] Z. Xiao, L. Chen, B. Zhong and S. Ye, Recognition for soft information based on the theory##of soft sets, In: J. Chen ,eds., Proceedings of ICSSSM05, 2 (2005), 11041106.##[36] Z. Xiao, K. Gong and Y. Zou, A combined forecasting approach based on fuzzy soft sets, J.##Comput. Appl. Math., 228 (2009), 326333.##[37] X. Yang, D. Yu, J. Yang and C. Wu, Generalization of soft set theory: from crisp to fuzzy##case, In: BingYuan Cao ,eds., Fuzzy Information and Engineering: Proceedings of ICFIE##2007, Advances in Soft Computing 40, Springer, (2007), 345355.##[38] X. Yang, T. Y. Lin, J. Yang, Y. Li and D. Yu, Combination of intervalvalued fuzzy set and##soft set, Comput. Math. Appl., 58 (2009), 521527.##[39] L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338353.##[40] Y. Zou and Y. Chen, Research on soft set theory and parameters reduction based on relational##algebra, In: Intelligent Information Technology Application, IITA, 1 (2008), 152  156.##[41] H. J. Zimmermann, Fuzzy set theory and its applications, Kluwer Academic Publishers, 1993.##[42] Y. Zou and Z. Xiao, Data analysis approaches of soft sets under incomplete information,##Knowl. Base. Syst., 21 (2008), 941945.##]
ON FUZZY UPPER AND LOWER CONTRACONTINUOUS
MULTIFUNCTIONS
ON FUZZY UPPER AND LOWER CONTRACONTINUOUS
MULTIFUNCTIONS
2
2
This paper is devoted to the concepts of fuzzy upper and fuzzy lower contracontinuous multifunctions and also some characterizations of them are considered.
1
This paper is devoted to the concepts of fuzzy upper and fuzzy lower contracontinuous multifunctions and also some characterizations of them are considered.
149
158
mohsen
Alimohammady
mohsen
Alimohammady
Department of Mathematics, University of Mazandaran, Babolsar,
Iran
Department of Mathematics, University of
Iran
amohsen@umz.ac.ir
E.
Ekici
E.
Ekici
Department of Mathematics, Canakkale Onsekiz Mart University, Terzioglu
Campus, 17020 Canakkale, Turkey
Department of Mathematics, Canakkale Onsekiz
Turkey
eekici@comu.edu.tr
S.
Jafari
S.
Jafari
College of Vestsjaelland South, Herrestraede 11, 4200 Slagelse, Denmark
College of Vestsjaelland South, Herrestraede
Denmark
jafari@stofanet.dk
M.
Roohi
M.
Roohi
Ghaemshahr branch Islamic Azad University, Ghaemshahr, Iran
Ghaemshahr branch Islamic Azad University,
Iran
mehdi.roohi@gmail.com
Fuzzy topological space
Fuzzy multifunctions
Fuzzy lower contracontinuous multifunction
Fuzzy upper contracontinuous multifunction
[[1] J. Albrycht and M. Maltoka, On fuzzy multivalued function, Fuzzy Sets and Systems, 12##(1984), 6169.##[2] M. Alimohammady and M. Roohi, On fuzzy ' continuous multifunction, J. Appl. Math.##Stoch. Anal., (2006), 17.##[3] J. P. Aubin and H. Frankowska, Setvalued analysis, Birkhauser, Boston, 1990.##[4] I. Beg, Continuity of fuzzy multifunction, J. Appl. Math. Stochastic Anal., 12(1) (1999),##[5] I. Beg, Fuzzy closed graph fuzzy multifunctions, Fuzzy Sets and Systems, 115 (2000), 451454.##[6] I. Beg, Fuzzy multivalued functions, Bull. Allahabad Math. Soc., 21 (2006), 41104.##[7] I. Beg, Fixed points of fuzzy multivalued mappings with values in fuzzy ordered sets, J. Fuzzy##Math., 6(1) (1998), 127131. ##[8] K. R. Bhutani, J. Mordeson and A. Rosenfeld, On degrees of end nodes and cut nodes in##fuzzy graphs, Iranian Journal of Fuzzy Systems, 1(1) (2004), 5764.##[9] J. M. Cadenas and J. L. Verdegay, A primer on fuzzy optimization models and methods,##Iranian Journal of Fuzzy Systems, 3(1) (2006), 121.##[10] M. Caldas, E. Ekici, S. Jafari and T. Noiri, On the class of contra continuous functions,##Annales Univ. Sci. Budapest Sec. Math., 49 (2006), 7586.##[11] C. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 191201.##[12] J. Dontchev, Contracontinuous functions and strongly Sclosed spaces, Internat. J. Math.##Math. Sci., 19(2) (1996), 303310.##[13] E. Ekici, On some types of continuous fuzzy functions, Appl. Math. ENot., 4 (2004), 2125.##[14] E. Ekici and E. E. Kerre, On fuzzy contracontinuities, Advances in Fuzzy Mathematics, 1(1)##(2006), 3544.##[15] E. Ekici, S. Jafari and T. Noiri, On upper and lower contracontinuous multifunctions,##Analele Stii. Univ. Cuza Iasi Mat., LIV, 1 (2008), 7585.##[16] E. Ekici, New forms of contracontinuity, Carpathian J. Math., 24(1) (2008), 3745.##[17] E. Ekici, On (LC,s)continuous functions, Chaos, Solitons and Fractals, 38(2) (2008), 430##[18] H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, Fuzzy linear regression model with crisp##coefficients: a goal programming approach, Iranian Journal of Fuzzy Systems, 7(2) (2010),##[19] J. E. Joseph and M. H. Kwack, On Sclosed spaces, Proc. Amer. Math. Soc., 80 (1980),##[20] S. B. Mordukhovich and Y. Shao, Fuzzy calculus for coderivatives of multifunctions, Nonlinear##Anal., 29(6) (1997), 605626.##[21] M. N. Mukherjee and S. Malakar, On almost continuous and weakly continuous fuzzy multifunctions,##Fuzzy Sets and Systems, 41 (1991), 113125.##[22] T. Noiri and S. Jafari, Properties of (, s)continuous functions, Topology and its Appl., 123##(2002), 167179.##[23] D. Noll, Baire spaces and graphtheorems, Proc. amer. Math. Soc., 96 (1986), 141151.##[24] A. A. Nouh and M. E. ElShafei, Cluster sets of functions and multifunctions in fuzzy topological##spaces, J. Fuzzy Math., 15(4) (2007), 759768.##[25] P. PaoMing and L. YingMing, Fuzzy topology I. neighborhood structure of a fuzzy point and##MooreSmith convergence, J. Math. Anal. Appl., 76 (1980), 571599.##[26] P. PaoMing and L. YingMing, Fuzzy topology II. product and quotient spaces, J. Math.##Anal. Appl., 77 (1980), 2037.##[27] N. S. Papageorgiou, Fuzzy topology and fuzzy multifunctions, J. Math. Anal. Appl., 109##(1985), 397425.##[28] V. I. Ponomarev, Properties of topological spaces preserved under multivalued continuous##mappings on compacta, Amer. Math. Soc. Translations, 38(2) (1964), 119140.##[29] K. S. Raja Sethupathy and S. Laksmivarahan, Connectedness in fuzzy topology, Kybernetika,##13(3) (1977), 190193.##[30] M. R. Safi, H. R. Maleki and E. Zaeimazad, A note on the Zimmermann method for solving##fuzzy linear programming problems, Iranian Journal of Fuzzy Systems, 4(2) (2007), 3145.##[31] A. Stouti, Fixed points of expanding fuzzy multifunctions, J. Fuzzy Math., 13(1) (2005),##[32] A. Stouti, An fuzzy version of Amann’s fixed point theorem for fuzzy monotone multifunctions,##J. Fuzzy Math., 14(1) (2006), 175183##[33] T. Thompson, Sclosed spaces, Proc. Amer. Math. Soc., 60 (1976), 335338.##[34] E. Tsiporkova, B. De Baets and E. Kerre, Continuity of fuzzy multivalued mappings, Fuzzy##Sets and Systems, 94 (1998), 335348.##[35] R. Viertl and D. Hareter, Fuzzy information and stochastics, Iranian Journal of Fuzzy Systems,##1(1) (2004), 4356.##[36] C. K. Wong, Fuzzy topology: product and quotient theorems, J. Math. Anal. Appl., 45 (1974),##[37] M. A. Yaghoobi and M. A. Tamiz, A short note on the relationship between goal programming##and fuzzy programming for vectormaximum problems, Iranian Journal of Fuzzy Systems, 2(2)##(2005), 3136.##[38] L. A. Zadeh, Fuzzy sets, Information and Control., 8 (1965), 338353.##[39] M. M. Zahedi and M. R. KhorashadiZadeh, Category of (POM)Lfuzzy graphs and hypergraphs,##Iranian Journal of Fuzzy Systems, 2(1) (2005), 4963.##]
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