2012
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APPLICATION OF TABU SEARCH FOR SOLVING THE
BIOBJECTIVE WAREHOUSE PROBLEM IN
A FUZZY ENVIRONMENT
APPLICATION OF TABU SEARCH FOR SOLVING THE
BIOBJECTIVE WAREHOUSE PROBLEM IN
A FUZZY ENVIRONMENT
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The biobjective warehouse problem in a crisp environment is often not eective in dealing with the imprecision or vagueness in the values of the problem parameters. To deal with such situations, several researchers have proposed that the parameters be represented as fuzzy numbers. We describe a new algorithm for fuzzy biobjective warehouse problem using a ranking function followed by an application of tabu search. The method is illustrated on a numerical example, demonstrating the eectiveness of the tabu search method. Numerical results are compared for both fuzzy and crisp versions of the problem.
1
The biobjective warehouse problem in a crisp environment is often not eective in dealing with the imprecision or vagueness in the values of the problem parameters. To deal with such situations, several researchers have proposed that the parameters be represented as fuzzy numbers. We describe a new algorithm for fuzzy biobjective warehouse problem using a ranking function followed by an application of tabu search. The method is illustrated on a numerical example, demonstrating the eectiveness of the tabu search method. Numerical results are compared for both fuzzy and crisp versions of the problem.
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19
Anila
Gupta
Anila
Gupta
School of Mathematics and Computer Applications, Thapar Univer
sity, Patiala147004, India
School of Mathematics and Computer Applications,
India
anilasingal@gmail.com
Amit
Kumar
Amit
Kumar
School of Mathematics and Computer Applications, Thapar University,
Patiala147004, India
School of Mathematics and Computer Applications,
India
amit rs iitr@yahoo.com
Mahesh
Kumar Sharma
Mahesh
Kumar Sharma
School of Mathematics and Computer Applications, Thapar
University, Patiala147004, India
School of Mathematics and Computer Applications,
India
mksharma@thapar.edu
Trapezoidal fuzzy numbers
Biobjective warehouse problem
Ecient solution
Tabu search
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FUZZY GRAVITATIONAL SEARCH ALGORITHM AN
APPROACH FOR DATA MINING
FUZZY GRAVITATIONAL SEARCH ALGORITHM AN
APPROACH FOR DATA MINING
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2
The concept of intelligently controlling the search process of gravitational search algorithm (GSA) is introduced to develop a novel data mining technique. The proposed method is called fuzzy GSA miner (FGSAminer). At first a fuzzy controller is designed for adaptively controlling the gravitational coefficient and the number of effective objects, as two important parameters which play major roles on search process of GSA. Then the improved GSA (namely FuzzyGSA) is employed to construct a novel data mining algorithm for classification rule discovery from reference data sets. Extensive experimental results on different benchmarks and a practical pattern recognition problem with nonlinear, overlapping class boundaries and different feature space dimensions are provided to show the powerfulness of the proposed method. The comparative results illustrate that performance of the proposed FGSAminer considerably outperforms the standard GSA. Also it is shown that the performance of the FGSAminer is comparable to, sometimes better than those of the CN2 (a traditional data mining method) and similar approach which have been designed based on other swarm intelligence algorithms (ant colony optimization and particle swarm optimization) and evolutionary algorithm (genetic algorithm).
1
The concept of intelligently controlling the search process of gravitational search algorithm (GSA) is introduced to develop a novel data mining technique. The proposed method is called fuzzy GSA miner (FGSAminer). At first a fuzzy controller is designed for adaptively controlling the gravitational coefficient and the number of effective objects, as two important parameters which play major roles on search process of GSA. Then the improved GSA (namely FuzzyGSA) is employed to construct a novel data mining algorithm for classification rule discovery from reference data sets. Extensive experimental results on different benchmarks and a practical pattern recognition problem with nonlinear, overlapping class boundaries and different feature space dimensions are provided to show the powerfulness of the proposed method. The comparative results illustrate that performance of the proposed FGSAminer considerably outperforms the standard GSA. Also it is shown that the performance of the FGSAminer is comparable to, sometimes better than those of the CN2 (a traditional data mining method) and similar approach which have been designed based on other swarm intelligence algorithms (ant colony optimization and particle swarm optimization) and evolutionary algorithm (genetic algorithm).
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37
Seyed Hamidi
Zahiri
Seyed Hamid
Zahiri
Department of Electrical Engineering, Faculty of Engineering,
Birjand University, Birjand, Iran
Department of Electrical Engineering, Faculty
Iran
hzahiri@@birjand.ac.ir
Gravitational search algorithm
Fuzzy controller
Data mining
Rule based classifier
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A NEW APPROACH TO STABILITY ANALYSIS OF FUZZY
RELATIONAL MODEL OF DYNAMIC SYSTEMS
A NEW APPROACH TO STABILITY ANALYSIS OF FUZZY
RELATIONAL MODEL OF DYNAMIC SYSTEMS
2
2
This paper investigates the stability analysis of fuzzy relational dynamic systems. A new approach is introduced and a set of sufficient conditions is derived which sustains the unique globally asymptotically stable equilibrium point in a firstorder fuzzy relational dynamic system with sumproduct fuzzy composition. This approach is also investigated for other types of fuzzy relational composition.
1
This paper investigates the stability analysis of fuzzy relational dynamic systems. A new approach is introduced and a set of sufficient conditions is derived which sustains the unique globally asymptotically stable equilibrium point in a firstorder fuzzy relational dynamic system with sumproduct fuzzy composition. This approach is also investigated for other types of fuzzy relational composition.
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48
Arya
Aghili Ashtiani
Arya
Aghili Ashtiani
Department of Electrical Engineering, Amirkabir University
of Technology (AUT), P. O. Box 15914, Tehran, Iran
Department of Electrical Engineering, Amirkabir
Iran
arya.aghili@aut.ac.ir
Sayyed Kamaloddin
Yadavar Nikravesh
Sayyed Kamaloddin
Yadavar Nikravesh
Department of Electrical Engineering, Amirk
abir University of Technology (AUT), P. O. Box 15914, Tehran, Iran
Department of Electrical Engineering, Amirk
abir
Iran
nikravsh@aut.ac.ir
Fuzzy relational dynamic system (FRDS)
Fuzzy relational model (FRM)
Linguistic stability analysis
Fuzzy relational stability
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ON SOLUTION OF A CLASS OF FUZZY BVPs
ON SOLUTION OF A CLASS OF FUZZY BVPs
2
2
This paper investigates the existence and uniqueness of solutions to rstorder nonlinear boundary value problems (BVPs) involving fuzzy dif ferential equations and twopoint boundary conditions. Some sucient condi tions are presented that guarantee the existence and uniqueness of solutions under the approach of Hukuhara dierentiability.
1
This paper investigates the existence and uniqueness of solutions to rstorder nonlinear boundary value problems (BVPs) involving fuzzy dif ferential equations and twopoint boundary conditions. Some sucient condi tions are presented that guarantee the existence and uniqueness of solutions under the approach of Hukuhara dierentiability.
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60
Omid
Solaymani Fard
Omid
Solaymani Fard
School of Mathematics and Computer Science, Damghan Uni
versity, Damghan, Iran
School of Mathematics and Computer Science,
Iran
osfard@du.ac.ir, omidsfard@gmail.com
Amin
Esfahani
Amin
Esfahani
School of Mathematics and Computer Science, Damghan University,
Damghan, Iran
School of Mathematics and Computer Science,
Iran
amin@impa.br, esfahani@du.ac.ir
Ali
Vahidian Kamyad
Ali
Vahidian Kamyad
Department of Mathematics, Ferdowsi University of Mashhad,
Mashhad, Iran
Department of Mathematics, Ferdowsi University
Iran
avkamyad@math.um.ac.ir
Fuzzy numbers
Fuzzy dierential equations
Boundary value problems
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SECURING INTERPRETABILITY OF FUZZY MODELS FOR
MODELING NONLINEAR MIMO SYSTEMS USING
A HYBRID OF EVOLUTIONARY ALGORITHMS
SECURING INTERPRETABILITY OF FUZZY MODELS FOR
MODELING NONLINEAR MIMO SYSTEMS USING
A HYBRID OF EVOLUTIONARY ALGORITHMS
2
2
In this study, a MultiObjective Genetic Algorithm (MOGA) is utilized to extract interpretable and compact fuzzy rule bases for modeling nonlinear Multiinput Multioutput (MIMO) systems. In the process of non linear system identi cation, structure selection, parameter estimation, model performance and model validation are important objectives. Furthermore, se curing lowlevel and highlevel interpretability requirements of fuzzy models is especially a complicated task in case of modeling nonlinear MIMO systems. Due to these multiple and conicting objectives, MOGA is applied to yield a set of candidates as compact, transparent and valid fuzzy models. Also, MOGA is combined with a powerful search algorithm namely Dierential Evolution (DE). In the proposed algorithm, MOGA performs the task of membership function tuning as well as rule base identi cation simultaneously while DE is utilized only for linear parameter identi cation. Practical applicability of the proposed algorithm is examined by two nonlinear system modeling prob lems used in the literature. The results obtained show the eectiveness of the proposed method.
1
In this study, a MultiObjective Genetic Algorithm (MOGA) is utilized to extract interpretable and compact fuzzy rule bases for modeling nonlinear Multiinput Multioutput (MIMO) systems. In the process of non linear system identi cation, structure selection, parameter estimation, model performance and model validation are important objectives. Furthermore, se curing lowlevel and highlevel interpretability requirements of fuzzy models is especially a complicated task in case of modeling nonlinear MIMO systems. Due to these multiple and conicting objectives, MOGA is applied to yield a set of candidates as compact, transparent and valid fuzzy models. Also, MOGA is combined with a powerful search algorithm namely Dierential Evolution (DE). In the proposed algorithm, MOGA performs the task of membership function tuning as well as rule base identi cation simultaneously while DE is utilized only for linear parameter identi cation. Practical applicability of the proposed algorithm is examined by two nonlinear system modeling prob lems used in the literature. The results obtained show the eectiveness of the proposed method.
61
77
Mojtaba
Eftekhari
Mojtaba
Eftekhari
Faculty of Islamic Azad University, Sirjan branch, ,Sirjan, Ker
man, Iran
Faculty of Islamic Azad University, Sirjan
Iran
m.eftekhari59@gmail.com
Mahdi
Eftekhari
Mahdi
Eftekhari
Department of Computer Engineering, School of Engineering,
Shahid Bahonar University of Kerman, Kerman, Iran
Department of Computer Engineering, School
Iran
m.eftekhari@uk.ac.ir
Maryam
Majidi
Maryam
Majidi
Department of Computer Engineering, School of Engineering, Shahid
Bahonar University of Kerman, Kerman, Iran
Department of Computer Engineering, School
Iran
majena67@yahoo.com
Hossein
Nezamabadi pour
Hossein
Nezamabadi pour
Department of Electrical Engineering, School of Engi
neering, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Electrical Engineering, School
Iran
nezam h@yahoo.com
Multiobjective
Evolutionary
Fuzzy identication
Compact
Inter pretability
[[1] J. Abonyi, Fuzzy Model Identication for Control, Birkhauser, Boston, 2003.##[2] K. Debs, Multiobjective optimization Using Evolutionary Algorithms, John Wiley and Son##Ltd, 2001.##[3] B. L. R. De Moor and ed., DaISy: Database for the Identication of Systems,##Department of Electrical Engineering, ESAT/SISTA, K. U. Leuven, Belgium, URL:##http://www.esat.kuleuven.ac.be/sista/daisy/.##[4] V. De Oliveira, Semantic constraints for membership function optimization, IEEE Trans.##SMCA, 29(1) (1999), 128138.##[5] M. Eftekhari, S. D. Katebi, M. Karimi and A. H. Jahanmiri, Eliciting transparent fuzzy model##using dierential evolution, Applied Soft Computing, 8 (2008), 466476.##[6] M. Eftekhari and S. D. Katebi, Extracting compact fuzzy rules for nonlinear system modeling##using subtractive clustering, GA and unscented lter, Applied Mathematical Modelling, 32##(2008), 26342651.##[7] B. Feil, J. Abonyi, J. Madar, S. Nemeth and P. A rva, Identication and analysis of MIMO##systems based on clustering algorithm, Acta Agraria Kaposvariensis, 8(3) (2004), 191203.##[8] C. M. Fonseca and P. J. Fleming, Multiobjective optimization and multiple constraint han##dling with evolutionary algorithmspart I: application example, IEEE Trans. Syst. Man and##Cybernetics, 28(1) (1998), 2637.##[9] C. M. Fonseca and P. J. Fleming, Multiobjective optimization and multiple constraint han##dling with evolutionary algorithmspart II: a unied formulation, IEEE Trans. Syst. Man and##Cybernetics, 28(1) (1998), 3847.##[10] M. J. Gacto, R. Alcala and F. Herrera, Integration of an Index to Preserve the Semantic##Interpretability in the Multiobjective Evolutionary Rule Selection and Tuning of Linguistic##Fuzzy Systems, IEEE Transactions on Fuzzy Systems, 8(3) (2010), 515531.##[11] S. Y. Ho, H. M. Chen, S. J. Ho and T. K. Cehn, Design of accurate classiers with a compact##fuzzy rule base using an evolutionary scatter partition of feature space, IEEE Tans. Systems,##Man and Cybernetics, Part B: Cybernetics, 34(2) (2004), 10311044.##[12] W. H. Ho, J. H. Chou and C. Y. Guo, Parameter identication of chaotic systems using##improved dierential evolution algorithm, Nonlinear Dynamics, 61 (2010), 2941.##[13] A. Homaifar and E. McCormick, Simultaneous design of membership functions and rule sets##for fuzzy controllers using genetic algorithms, IEEE Trans. Fuzzy Syst., 3 (1995), 129139. ##[14] H. Ishibuchi, Multiobjective genetic fuzzy systems: Review and future research directions,##Proc. of IEEE InternationalConference on Fuzzy Systems, London, UK, July 2326, (2007)##[15] C. Z. Janikow, A knowledge intensive genetic algorithm for supervised learning, Machine##Learning, 13 (1993), 198228.##[16] L. Ljung, System identication toolbox: user's guide, The MathWorks, 2004.##[17] S. Medasani, J. Kim and R. Krishnapuram, An overview of membership function generation##techniques for pattern recognition, Int. J. Approx. Reasoning, 19(34) (1998), 391417.##[18] O. Nelles, Nonlinear System Identication, SpringerVerlag, Berlin Heidelberg, 2001.##[19] A. Riid and E. Rustern, Interpretability improvement of fuzzy systems: reducing the number##of unique singletons in zeroth order TakagiSugeno systems, Proceedings of (2010) IEEE##International Conference on Fuzzy Systems, Barcelona, Spain, (2010), 20132018.##[20] K. Rodriguezvazquez, Multiobjective evolutionary algorithms in nonlinear system identi##cation. PhD thesis, Department of Automatic Control and Systems Engineering, The Uni##versity of Sheeld, 1999.##[21] R. Storn and K. Price, Dierential evolutiona simple and ecient adaptive scheme or global##optimization over continuous spaces, technical report TR95012, International Computer##Science Institute, Berkley, 1995.##[22] R. Storn and K. Price, Dierential evolution a simple and ecient heuristic for global opti##mization over continuous spaces, J. Global Optim. 11 (1997), 341359.##[23] J. T. Tsai, J. H. Chou and T. K. Liu, Tuning the structure and parameters of a neural##network by using hybrid Taguchigenetic algorithm, IEEE Trans. on Neural Networks, 17##(2006), 6980.##[24] H. Wang, S. Kwong, Y. Jin, W. Wei, and K. F. Man, Multiobjective hierarchical genetic##algorithm for interpretable fuzzy rulebased knowledge extraction, Fuzzy Sets and Systems,##149 (2005), 149186.##[25] H.Wang, S. Kwong, Y. Jin, W.Wei and K. F. Man, Agentbased evolutionary approach for in##terpretable rulebased knowledge extraction, IEEE Trans. on Systems, Man and Cybernetics##Part C, 35 (2005), 143155.##[26] S. M. Zhou and J. Q. Gan, Lowlevel interpretability and highlevel interpretability: a unied##view of datadriven interpretable fuzzy system modeling, Fuzzy Sets and Systems, 159 (2008),##30913131.##[27] S. M. Zhou and J. Q. Gan, Extracting TakagiSugeno fuzzy rules with interpretable sub##models via regularization of linguistic modiers, IEEE Transactions on Knowledge and Data##Engineering, 21(8) (2009), 11911204.##]
ESTIMATORS BASED ON FUZZY RANDOM VARIABLES AND
THEIR MATHEMATICAL PROPERTIES
ESTIMATORS BASED ON FUZZY RANDOM VARIABLES AND
THEIR MATHEMATICAL PROPERTIES
2
2
In statistical inference, the point estimation problem is very crucial and has a wide range of applications. When, we deal with some concepts such as random variables, the parameters of interest and estimates may be reported/observed as imprecise. Therefore, the theory of fuzzy sets plays an important role in formulating such situations. In this paper, we rst recall the crisp uniformly minimum variance unbiased (UMVU) and Bayesian estimators and then develop the concept of fuzzy estimators for fuzzy parameters based on fuzzy random variables.
1
In statistical inference, the point estimation problem is very crucial and has a wide range of applications. When, we deal with some concepts such as random variables, the parameters of interest and estimates may be reported/observed as imprecise. Therefore, the theory of fuzzy sets plays an important role in formulating such situations. In this paper, we rst recall the crisp uniformly minimum variance unbiased (UMVU) and Bayesian estimators and then develop the concept of fuzzy estimators for fuzzy parameters based on fuzzy random variables.
79
95
M. G.
Akbari
M. G.
Akbari
Department of Statistics, Faculty of Sciences, University of Birjand,
Southern Khorasan, Birjand
Department of Statistics, Faculty of Sciences,
Iran
mga13512@yahoo.com
M.
Khanjari Sadegh
M.
Khanjari Sadegh
Department of Statistics, Faculty of Sciences, University of
Birjand, Southern Khorasan, Birjand
Department of Statistics, Faculty of Sciences,
Iran
g_z_akbari@yahoo.com
Fuzzy random variable
Fuzzy parameter
Signed distance
L2 metric
Fuzzy estimator
Fuzzy unbiased estimator
Fuzzy sufficient estimator
Fuzzy risk function
[bibitem{A}##M. G. Akbari and A. Rezaei, {it An uniformly minimum variance unbiased point estimation using fuzzy observations}, Austrian Journal of Statistics, {bf 36} (2007), 307317. ##bibitem{B}##M. G. Akbari and A. Rezaei, {it Order statistics using fuzzy##random variables}, Statistics and Probability Letters, {bf 79} (2009), 10311037. ##bibitem{au}##R. J. Aumann, {it Integrals of setvalued functions}, Journal of Mathematical Analysis and Applications, {bf 12} (1965), 112. ##bibitem{bi}## P. Billingsley, {it Probability and measure}, 2nd ed., New York:##John Wiley, 1995. ##bibitem{ca}##J. J. Buckley, {it Fuzzy probabilities: new approach and applications}, SpringerVerlag, Berlin, Heidelberg, 2005. ##bibitem{cb}##J. J. Buckley, {it Fuzzy probability and statistics}, SpringerVerlag, Berlin, Heidelberg, 2006. ##bibitem{ch}##C. Cheng, {it A new approach for ranking fuzzy numbers by distance##method}, Fuzzy Sets and Systems, {bf 95} (1998), 307317. ##bibitem{g1}##G. Z. Gertner and H. Zhu, {it Bayesian estimation in forest survey##when samples or prior information are fuzzy}, Fuzzy Sets an Systems,## {bf 77} (1997), 277290. ##bibitem{ho}##H. HongZhong, J. Z. Ming and S. ZhanQuan, {it Bayesian##reliability analysis for fuzzy lifetime data}, Fuzzy Sets and##Systems, {bf 157} (2006), 16741686. ##bibitem{hr}##O. Hryniewicz, {it Possibilities approach to the Bayes statistical##decisions}, In: P. Grzegorzewski, O. Hryniewicz, M. A. Gil , eds., Soft##Methods in Probability, Statistics and Data Analysis. Physica##Verlag, HeidelbergNew York, (2002), 207218. ##bibitem{k1}##R. Kruse, {it Statistical estimation with linguistic data},##Information Sciences, {bf 33} (1984), 197207. ##bibitem{k2}##R. Kruse and K. D. Meyer, {it Statistics with vague data}, Reidel, Dordrecht, {bf 33} (1987). ##bibitem{kw}##H. Kwakernaak, {it Fuzzy random variables I}, Information Sciences, {bf 15} (1978), 129. ##bibitem{mo}##M. Modarres and S. SadiNezhad, {it Ranking fuzzy numbers by##preference ratio}, Fuzzy Sets and Systems, {bf 118} (2001), 429436. ##bibitem{na}##W. N$ddot{a}$ther, {it Regression with fuzzy data},##Computational Statistics and Data Analysis, {bf 51} (2006), 235252. ##bibitem{no}##M. Nojavan and M. Ghazanfari, {it A fuzzy ranking method by##desirability index}, Journal of Intelligent and Fuzzy Systems,##{bf 17} (2006), 2734. ##bibitem{p1}##M. L. Puri and D. A. Ralescu, {it Differential of fuzzy functions}, Journal of Mathematical Analysis and Applications, {bf 114} (1983), 552558. ##bibitem{p2}##M. L. Puri and D. A. Ralescu, {it Fuzzy random variables}, Journal of Mathematical Analysis and Applications, {bf 114} (1986), 409422. ##bibitem{p3}##M. L. Puri and D. A. Ralescu, {it Convergence theorem for fuzzy martingales}, Journal of Mathematical Analysis and Applications, {bf 160} (1991), 107122. ##bibitem{sh}##J. Shao, {it Mathematical Statistics}, 2nd ed., New York:## SpringerVerlag, 2003. ##bibitem{s11}##B. Sadeghpour Gildeh and D. Gien, {it $d_{p,q}$distance and##RaoBlackwell theorem for fuzzy random variables}, In Proc, of##the 8th international Conference of Fuzzy Theory and##Technology, Durham, USA, 2002. ##bibitem{u1}##Y. Uemura, {it A decision rule on fuzzy events}, Japanese Journal##Fuzzy Theory and Systems, {bf 3} (1991), 291300. ##bibitem{u2}##Y. Uemura, {it A decision rule on fuzzy events under an##observation}, Journal of Fuzzy Mathematics, {bf 1} (1993), 3952. ##bibitem{v1}##R. Viertl, {it Statistical methods for nonprecise data}, CRC##Press, Boca Raton, 1996. ##bibitem{v2}##R. Viertl, {it Statistics with onedimensional fuzzy data}, In C.##Bertoluzzi et al., Editor, Statistical Modeling, Analysis and##Management of Fuzzy Data, PhysicaVerlag, Heidelberg, (2002a), 199212. ##bibitem{v3}##R. Viertl, {it Statistical inference with nonprecise data}, In##Encyclopedia of Life Support Systems, UNESCO, Paris, 2002b. ##bibitem{ac}##R. Viertl, {it Univariate statistical analysis with fuzzy data},##Computational Statistics and Data Analysis, {bf 51} (2006), 133147. ##bibitem{yaa}##J. S. Yao and K. Wu, {it Ranking fuzzy numbers based on##decomposition principle and signed distance}, Fuzzy Sets and Systems, {bf 11} (2000), 275288.##]
A NEW METHOD TO REDUCE TORQUE RIPPLE IN
SWITCHED RELUCTANCE MOTOR USING
FUZZY SLIDING MODE
A NEW METHOD TO REDUCE TORQUE RIPPLE IN
SWITCHED RELUCTANCE MOTOR USING
FUZZY SLIDING MODE
2
2
This paper presents a new control structure to reduce torque ripple in switched reluctance motor. Although SRM possesses many advantages in motor structure, it suers from large torque ripple that causes some problems such as vibration and acoustic noise. In this paper another control loop is added and torque ripple is de ned as an objective function. By using fuzzy sliding mode strategy, the DC link voltage is adjusted to optimize the objective function. Simulation results have demonstrated the proposed control method.
1
This paper presents a new control structure to reduce torque ripple in switched reluctance motor. Although SRM possesses many advantages in motor structure, it suers from large torque ripple that causes some problems such as vibration and acoustic noise. In this paper another control loop is added and torque ripple is de ned as an objective function. By using fuzzy sliding mode strategy, the DC link voltage is adjusted to optimize the objective function. Simulation results have demonstrated the proposed control method.
97
108
S. R.
MousaviAghdam
S. R.
MousaviAghdam
Faculty of electrical and computer engineering, University
of Tabriz, Tabriz, Iran
Faculty of electrical and computer engineering,
Iran
rmousavi@tabrizu.ac.ir
M. B. B.
Sharifian
M. B. B.
Sharifian
Faculty of electrical and computer engineering, University of
Tabriz, Tabriz, Iran
Faculty of electrical and computer engineering,
Iran
sharifian@tabrizu.ac.ir
M. R.
Banaei
M. R.
Banaei
Department of electrical engineering, Faculty of engineering, azarbai
jan, University of tarbiat moallem, Tabriz, Iran
Department of electrical engineering, Faculty
Iran
m.banaei@azaruniv.edu
Fuzzy sliding control
Switched Reluctance Motor
Torque ripple re duction
[[1] M. R. AkbarzadehT and R. Shahnazi, Direct adaptive fuzzy PI sliding mode control of system##with unknown but bounded disturbances, Iranian Journal of Fuzzy Systems, 3(2) (2006), 33##[2] D. Cajander and H. LeHuy, Design and optimization of a torque controller for a switched##reluctance motor drive for electric vehicles by simulation, Mathematics and Computers in##Simulation, Elsevier, 71 (2006), 333344.##[3] J. Y. Chai and C. M. Liaw, Reduction of speed ripple and vibration for switched reluctance##motor drive via intelligent current proling, IET Electric Power Applications, (2010), 380##[4] N. Inanc and V. Ozbulur, Torque ripple minimization of a switched reluctance motor by##using continuous sliding mode control technique, Electric power systems research, Elsevier,##66 (2003), 241251.##[5] G. John and A. R. Eastham, Speed control of switched reluctance motor using sliding mode##control strategy, IEEE International Conference on Industrial Technology, 1 (1995), 263270.##[6] H. KhorashadiZadeh and M. R. Aghaebrahimi, A neurofuzzy technique for discrimination##between internal faults and magnetizing inrush currents in transformers, Iranian Journal of##Fuzzy Systems, 2(2) (2005), 4557.##[7] J. Li, X. Song and Y. Cho, Comparison of 12/8 and 6/4 switched reluctance motor: noise##and vibration aspects, IEEE Trans. Magn., 44(11) (2008), 41314134.##[8] J. Li and Y. Cho, Investigation into reduction of vibration and acoustic noise in switched##reluctance motors in radial force excitation and frame transfer function aspects, IEEE Trans.##Magn., 45(10) (2009), 46644667.##[9] M. A. A. Morsy, M. Said, A. Moteleb and H. T. Dorrah, Design and implementation of##fuzzy sliding mode controller for switched reluctance motor, IEEE International Conference##on Industrial Technology, (2008), 16.##[10] N. Nelvaganesan, D. Raja and S. Srinivasan, Fuzzy based fault detection and control for 6/4##switched reluctance motor, Iranian Journal of Fuzzy Systems, 45(1) (2007), 3751.##[11] H. Rouhani, C. Lucas, R. Mohammadi Milasi and M. Nikkhah bahrami, Fuzzy sliding mode##control applied to low noise switched reluctance motor control, International Conference on##Control and Automation (ICCA), 1 (2005), 325329.##[12] W. Shang, S. Zhao, Y. Shen and Z. Qi, A sliding mode ##uxlinkage controller with integral##compensation for switched reluctance motor, IEEE Trans. Magn., 45(9) (2009), 33223328.##[13] B. Singh, V. Kumar Sharma and S. S. Murthy, Comparative study of PID, sliding mode and##fuzzy logic controllers for four quadrant operation of switched reluctance motor, International##Conference on Power Electronic Drives and Energy Systems for Industrial Growth, 1 (1998),##[14] H. Vasquez and J. K. Parker, A new simplied mathematical model for a switched reluctance##motor in a variable speed pumping application, Mechatronics, Elsevier, 14 (2004), 10551068.##[15] K. Vijayakumar, R. Karthikeyan, S. Paramasivam, R. Arumugam and K. N. Srinivas,##Switched reluctance motor modeling, design, simulation, and analysis: a comprehensive re##view, IEEE Trans. Magn., 44(12) (2008), 46054617.##[16] Y. Wang, A novel fuzzy controller for switched reluctance motor drive, Second IEEE Inter##national Conference on Information and Computing Science, 2 (2009), 5558. ##]
FUZZY SOFT MATRIX THEORY AND ITS APPLICATION IN
DECISION MAKING
FUZZY SOFT MATRIX THEORY AND ITS APPLICATION IN
DECISION MAKING
2
2
In this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$set theory. We then define products of $fs$matrices andstudy their properties. We finally construct a $fs$$max$$min$decision making method which can be successfully applied to theproblems that contain uncertainties.
1
In this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$set theory. We then define products of $fs$matrices andstudy their properties. We finally construct a $fs$$max$$min$decision making method which can be successfully applied to theproblems that contain uncertainties.
109
119
Naim
Cagman
Naim
Cagman
Department of Mathematics, Faculty of Arts and Sciences, Gazios
manpasa University, 60250 Tokat, Turkey
Department of Mathematics, Faculty of Arts
Turkey
ncagman@gop.edu.tr
Serdar
Enginoglu
Serdar
Enginoglu
Department of Mathematics, Faculty of Arts and Sciences, Gazios
manpasa University, 60250 Tokat, Turkey
Department of Mathematics, Faculty of Arts
Turkey
serdarenginoglu@gop.edu.tr
Fuzzy soft sets
Fuzzy soft matrix
Products of fuzzy soft matrices
Fuzzy soft maxmin decision making
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Enginou{g}lu, {it Soft matrix theory and its decision making},##Computers and Mathematics with Applications, {bf59} (2010), 33083314. ##bibitem{cagea10a} N. d{C}au{g}man, F. C{i}tak and S. Enginou{g}lu, {it Fuzzy parameterized fuzzy soft set##theory and its applications}, Turkish Journal of Fuzzy Systems, {bf 1(1)} (2010), 2135. ##bibitem{cagea10b} N. d{C}au{g}man, S. Enginou{g}lu and F. C{i}tak,##{it Fuzzy soft set theory and its applications}, Iranian Journal of Fuzzy##Systems, {bf 8(3)} (2011), 137147. ##bibitem{fenea10} F. Feng, Y. B. Jun, X. Liu and L. Li, {it An adjustable approach to##fuzzy soft set based decision making}, Journal of Computational and##Applied Mathematics, {bf 234} (2010), 1020. ##bibitem{fenea08} F. Feng, Y. B. Jun and X. Zhao, {it Soft semirings}, Fuzzy Sets and##Systems: Theory and Applications, {bf 56(10)} (2008), 26212628. ##bibitem{herea09} T. Herawan, A. N. M. Rose and M. M. Deris, {it Soft set theoretic##approach for dimensionality reduction}, In Database Theory and##Application, Springer Berlin Heidelberg, {bf 64} (2009), 171178. ##bibitem{jiaea10} Y. Jiang, Y. Tang, Q. Chen, J. Wang and S. Tang, {it Extending soft##sets with description logics}, Computers and Mathematics with##Applications, {bf 59} (2010), 20872096. ##bibitem{jun08}Y. B. Jun, {it Soft BCK/BCIalgebras}, Computers and Mathematics with##Applications, {bf56} (2008), 14081413. ##bibitem{junpar08} Y. B. Jun and C. H. Park, {it Applications of soft sets in ideal theory##of BCK/BCIalgebras}, Information Sciences, {bf178} (2008), 24662475. ##bibitem{junpar09}Y. B. Jun and C. H. Park, {it Applications of soft sets in Hilbert##algebras}, Iranian Journal of Fuzzy Systems, {bf6(2)} (2009), 5586. ##bibitem{junea09a}Y. B. Jun, H. S. Kim and J. Neggers, {it Pseudo dalgebras}, Information##Sciences, {bf179} (2009), 17511759. ##bibitem{junea10a} Y. B. Jun, K. J. Lee and A. Khan, {it Soft ordered semigroups},##Mathematical Logic Quarterly, {bf56(1)} (2010), 4250. ##bibitem{junea08} Y. B. Jun, K. J. Lee and C. H. Park, {it Soft set theory applied to##commutative ideals, in BCKalgebras}, Journal of Applied Mathematics##Informatics, {bf26(34)} (2008), 707720. ##bibitem{junea09b} Y. B. Jun, K. J. Lee and C. H. Park, {it Soft set theory applied to##ideals in dalgebras}, Computers and Mathematics with Applications, {bf 57} (2009), 367378. ##bibitem{junea10b} Y. B. Jun, K. J. Lee and C. H. Park, {it Fuzzy soft set theory applied##to BCK/BCIalgebras}, Computers and Mathematics with Applications, {bf 59} (2010), 31803192. ##bibitem{junea09c} Y. B. Jun, K. J. Lee and J. Zhan, {it Soft pideals of soft##BCIalgebras}, Computers and Mathematics with Applications, {bf58} (2009), 20602068. ##bibitem{kalea10} S. J. Kalayathankal and G. S. Singh, {it A fuzzy soft flood alarm model},##Mathematics and Computers in Simulation, {bf 80} (2010), 887893. ##bibitem{khaahm09} A. Kharal and B. Ahmad, {it Mappings on fuzzy soft classes}, Advances in##Fuzzy Systems, (2009), 16. ##bibitem{konea08} Z. Kong, L. Gao, L. Wang and S. Li, {it The normal parameter reduction##of soft sets and its algorithm}, Computers and Mathematics with##Applications, {bf56} (2008), 30293037. ##bibitem{kovea07} D. V. Kovkov, V. M. Kolbanov and D. A. Molodtsov, {it Soft sets##theorybased optimization}, Journal of Computer and Systems Sciences##International, {bf46(6)} (2007), 872880. ##bibitem{majea01a} P. K. Maji, R. Biswas and A. R. Roy, {it Fuzzy soft sets}, Journal of Fuzzy##Mathematics, {bf9(3)} (2001), 589602. ##bibitem{majea01b} P. K. Maji, R. Biswas and A. R. Roy, {it Intuitionistic fuzzy soft sets},##Journal of Fuzzy Mathematics, {bf 9(3)} (2001), 677691. ##bibitem{majea03} P. K. Maji, R. Biswas and A. R. Roy, {it Soft set theory}, Computers and##Mathematics with Applications, {bf45} (2003), 555562. ##bibitem{majea02} P. K. Maji, A. R. Roy and R. Biswas, {it An application of soft sets in a##decision making problem}, Computers and Mathematics with##Applications, {bf44} (2002), 10771083. ##bibitem{majsam08} P. Majumdar and S. K. Samanta, {it Similarity measure of soft sets}, New##Mathematics and Natural Computation, {bf4(1)} (2008), 112. ##bibitem{majsam10} P. Majumdar and S. K. Samanta, {it Generalised fuzzy soft sets}, Computers##and Mathematics with Applications, {bf 59} (2010), 14251432. ##bibitem{mol99} D. A. Molodtsov, {it Soft set theoryfirst results}, Computers and##Mathematics with Applications, {bf37} (1999), 1931. ##bibitem{mukcha08} A. Mukherjee and S. B. Chakraborty, {it On intuitionistic fuzzy soft##relations}, Bulletin of Kerala Mathematics Association, {bf5(1)} (2008), 3542. ##bibitem{musea06} M. M. Mushrif, S. Sengupta and A. K. Ray, {it Texture classification using##a novel}, SoftSet Theory Based Classification, Algorithm. Lecture##Notes in Computer Science., {bf3851} (2006), 246254. ##bibitem{parea08} C. H. Park, Y. B. Jun and M. A. "{O}zt"{u}rk, {it Soft WSalgebras},##Communications of the Korean Mathematical Society, {bf23(3)} (2008), 313324. ##bibitem{peimia05} D. Pei and D. Miao, {it From soft sets to information systems}, In:##Proceedings of Granular Computing (eds: X. Hu, Q. Liu, A. Skowron,##T. Y. Lin, R. R. Yager, B. Zhang) IEEE 2005, {bf 2} (2005), 617 621. ##bibitem{qinhon10} K. Qin and Z. Hong, {it On soft equality}, Journal of Computational and##Applied Mathematics, {bf 234} (2010), 13471355. ##bibitem{roymaj07} A. R. Roy and P. K. Maji, {it A fuzzy soft set theoretic approach to##decision making problems}, Journal of Computational and Applied##Mathematics, {bf203} (2007), 412418. ##bibitem{sezata11} A. Sezgin and A. O. Atag"{u}n, {it On operations of soft sets},##Comput. Math. Appl., {bf61(5)} (2011), 14571467. ##bibitem{sezea11} A. Sezgin, A. O. Atag"{u}n and E. Ayg"{u}n, {it A note on soft nearrings##and idealistic soft nearrings}, Filomat, {bf25} (2011), 5368. ##bibitem{som06} T. Som, {it 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), 1{}9. ##bibitem{son07} M. J. Son, {it Intervalvalued fuzzy soft sets}, Journal of Fuzzy Logic##and Intelligent Systems, {bf17(4)} (2007), 557562. ##bibitem{sunea08} Q. M. Sun, Z. L. Zhang and J. Liu, {it Soft sets and soft modules},##Proceedings of Rough Sets and Knowledge Technology, Third##International Conference, RSKT 2008, 1719 May, Chengdu, China, (2008), 403409. ##bibitem{xiaea09}Z. Xiao, K. Gong and Y. Zou, {it A combined forecasting approach based##on fuzzy soft sets}, Journal of Computational and Applied##Mathematics, {bf 228} (2009), 326333. ##bibitem{xiaea10}Z. Xiao, K. Gong, S. Xia and Y. 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FUZZY LINEAR REGRESSION BASED ON
LEAST ABSOLUTES DEVIATIONS
FUZZY LINEAR REGRESSION BASED ON
LEAST ABSOLUTES DEVIATIONS
2
2
This study is an investigation of fuzzy linear regression model for crisp/fuzzy input and fuzzy output data. A least absolutes deviations approach to construct such a model is developed by introducing and applying a new metric on the space of fuzzy numbers. The proposed approach, which can deal with both symmetric and nonsymmetric fuzzy observations, is compared with several existing models by three goodness of t criteria. Three wellknown data sets including two small data sets as well as a large data set are employed for such comparisons.
1
This study is an investigation of fuzzy linear regression model for crisp/fuzzy input and fuzzy output data. A least absolutes deviations approach to construct such a model is developed by introducing and applying a new metric on the space of fuzzy numbers. The proposed approach, which can deal with both symmetric and nonsymmetric fuzzy observations, is compared with several existing models by three goodness of t criteria. Three wellknown data sets including two small data sets as well as a large data set are employed for such comparisons.
121
140
S. M.
Taheri
S. M.
Taheri
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 8415683111, Iran and Department of Statistics, School of Mathematical
Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Mathematical Sciences, Isfahan
Iran
sm_taheri@yahoo.com
M.
Kelkinnama
M.
Kelkinnama
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 8415683111, Iran
Department of Mathematical Sciences, Isfahan
Iran
m_ kelkinnama@yahoo.com
Fuzzy regression
Least absolutes deviations
Metric on fuzzy numbers
Similarity measure
Goodness of fit
[bibitem{tata}##A. R. Arabpour and M. Tata, {it Estimating the parameters of a##fuzzy linear regression model}, Iranian Journal of Fuzzy Systems,##{bf 5} (2008), 120. ##bibitem{bar2007}##A. Bargiela, W. Pedrycz and T. Nakashima, {it Multiple regression##with fuzzy data}, Fuzzy Sets and Systems, {bf 158} (2007),##21692188. ##bibitem{cel87}##A. Celmins, {it Least squares model fitting to fuzzy vector##data}, Fuzzy Sets and Systems, {bf 22} (1987), 260269. ##bibitem{ctISI2011}##J. Chachi and S. M. Taheri, {it A leastabsolutes approach to multiple##fuzzy regression}, In: Proc. of##58th ISI Congress, Dublin, Ireland, (2011), CPS07701. ##bibitem{ctr}##J. Chachi, S. M. Taheri and R. H. Rezaei Pazhand, {it An intervalbased approach##to fuzzy regression for fuzzy inputoutput data}, In: Proc. of##the IEEE Int. Conf. Fuzzy Syst. (FUZZIEEE 2011), Taipei, Taiwan, (2011), 28592863. ##bibitem{lee94}##P. T. Chang and C. H. 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Coppi, P. D'urso, P. Giordani and A. Santoro, {it Least##squares estimation of a linear regression model with LR fuzzy##response}, Computational Statistics and Data Analysis, {bf 51} (2006), 267286. ##bibitem{diamond}##P. Diamond, {it Least squares fitting of several fuzzy##variables}, In: Proc. of Second IFSA Congress, Tokyo, (1987), 2025. ##bibitem{dodge}## Y. Dodge and ed., {it Statistical data analysis based on the L1Norm##and related methods}, Elsevier Science Publishers B. V., Netherlands, 1987. ##bibitem{durso}## P. D'Urso and A. Santoro, {it Goodness of fit and variable selecion in##the fuzzy multiple linear regression},## Fuzzy Sets and Systems, {bf 157} (2006), 26272647. ##bibitem{fth}## S. Fattahi, S. M. Taheri and S. A. Hoseini Ravandi, {it Cotton yarn engineering via fuzzy## least squares regression},## Fibers and Polymers, to appear. ##bibitem{guo}##P. Guo and H. Tanaka, {it Dual models for posibilistic regression##analysis}, Computational Statistics and Data Analysis, {bf 51} (2006), 253266. ##bibitem{hasanpour}##H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, {it A goal programming approach to fuzzy linear regresion with nonfuzzy input and fuzzy output data}, AsiaPacific Journal of Operational Research, {bf26} (2009), 587604. ##bibitem{hasanpour2010}##H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, {it Fuzzy linear regression model with crisp coefficients: a goal programming approach}, Iranian Journal of Fuzzy Systems, {bf7} (2010), 1939. ##bibitem{kao}##C. Kao and C. L. Chyu, {it A fuzzy linear regesion model with##better explanatory power}, Fuzzy Sets and Systems, {bf126} (2002), 401409. ##bibitem{bishu}##B. Kim and R. R. Bishu, {it Evalaution of fuzzy linear##regresssion models by comparing membership functions}, Fuzzy Sets##and Systems, {bf 100} (1998), 343352. ##bibitem{kimetal}##K. J. Kim, D. H. Kim and S. H. Choi, {it Least absolute deviation##estimator in fuzzy regression}, Journal of Applied Mathematics and Computing, {bf18} (2005), 649656. ##bibitem{korner}##R. K"orner and W. N"ather, {it Linear regression with random##fuzzy variables extended classical estimates, best linear##estimates, least squares estimates}, Information Sciences, {bf109} (1998), 95118. ##bibitem{mohamadi}##J. Mohammadi and S. M. Taheri, {it Pedomodels fitting with fuzzy least squares regression}, Iranian Journal of Fuzzy Systems,##{bf 1} (2004), 4561. ##bibitem{pappis}##C. P. Pappis and N. I. Karacapilidis, {it A comparative##assessment of measure of similarity of fuzzy values}, Fuzzy Sets##and Systems, {bf 56} (1993), 171174. ##bibitem{porahmad1}##S. Pourahmad, S. M. T. Ayatollahi and S. M. Taheri, {it Fuzzy logistic regression: a new possibilistic model and its application in clinical vague status}, Iranian Journal of Fuzzy Systems,##{bf 8} (2011), 117. ##bibitem{porahmad2}##S. Pourahmad, S. M. T. Ayatollahi, S. M. Taheri and Z. Habib Agahi, {it Fuzzy logistic regression based on the least squares approach with application in clinical studies}, Computers and Mathematics with Applications, {bf 62} (2011), 33533365. ##bibitem{rezaee}##H. Rezaei, M. Emoto and M. Mukaidono, {it New similarity measure##between two fuzzy sets}, Journal of Advanced Computational Intelligence and Intelligent Informatics, {bf 10} (2006), 946953. ##bibitem{rosu}##P. J. Rosseeuw and A. M. Leroy, {it Robust regression and outlier##detection}, Wiley, 1987. ##bibitem{sakawa}## M. Sakawa and H. Yano, {it##Multiobjective fuzzy linear regression analysis for fuzzy##inputoutput data}, Fuzzy Sets and Systems, {bf 47} (1992), 173181. ##bibitem{kelkin}##S. M. Taheri and M. Kelkinnama, {it Fuzzy least absolutes regression}, In: Proc. 4th Internatinal IEEE Conferance on Intelligent Systems, Varna, Bulgaria, (2008), 5558. ##%bibitem{robust}##%W. Stahel and S. Weisberg, (ed.s), {it Directions in robust##%Statistics and Diagnistics}, Springer Verlag, New York, 1991.##bibitem{tanakaGuo}##H. Tanaka and P. Guo, {it Possibilistic data analysis for operations##research}, SpringerVerlag, New York, 1999. ##bibitem{tanaka}##H. Tanaka, S. Vejima and K. Asai, {it Linear regression analysis##with fuzzy model}, IEEE Transactions on Systems, Man, Cybernetics, {bf12} (1982), 903907. ##bibitem{torabi}##H. Torabi and J. Behboodian, {it Fuzzy leastabsolutes estimates##in linear models}, Communications in StatisticsTheory and##Methods, {bf 36} (2007), 19351944.##%bibitem[Yang and Ko]{}##%M.S. Yang,##bibitem{ko}## M. S. Yang and C. H. Ko, {it On a class of fuzzy cnumbers##clustering procedures for fuzzy data}, Fuzzy Sets and Systems,##{bf 84} (1996), 4960.##bibitem{koccc}## M. S. Yang and C. H. Ko, {it On clusterwise fuzzy regression##analysis}, IEEE Transactions on Systems, Man, Cybernetics B, {bf 27} (1997), 113. ##bibitem{lin}##M. S. Yang and T. S. Lin, {it Fuzzy leastsquares linear##regression analysis for fuzzy inputoutput data}, Fuzzy Sets and##Systems, {bf 126} (2002), 389399. ## bibitem{yen}## K. K. Yen, G. Ghoshray and G. Roig, {it A linear regression## model using triangular fuzzy number coefficient}, Fuzzy Sets and## Systems, {bf 106} (1999), 167177. ##bibitem{z}##H. J. Zimmermann, {it Fuzzy set theory and its applications},##Kluwer, Dodrecht, 3rd ed., 1995.##]
TRANSPORT ROUTE PLANNING MODELS BASED
ON FUZZY APPROACH
TRANSPORT ROUTE PLANNING MODELS BASED
ON FUZZY APPROACH
2
2
Transport route planning is one of the most important and frequent activities in supply chain management. The design of information systems for route planning in real contexts faces two relevant challenges: the complexity of the planning and the lack of complete and precise information. The purpose of this paper is to nd methods for the development of transport route planning in uncertainty decision making contexts. The paper uses an approximation that integrates a speci c fuzzybased methodology from Soft Computing. We present several fuzzy optimization models that address the imprecision and/or exibility of some of its components. These models allow transport route planning problems to be solve with the help of metaheuristics in a concise way. A simple numerical example is shown to illustrate this approach.
1
Transport route planning is one of the most important and frequent activities in supply chain management. The design of information systems for route planning in real contexts faces two relevant challenges: the complexity of the planning and the lack of complete and precise information. The purpose of this paper is to nd methods for the development of transport route planning in uncertainty decision making contexts. The paper uses an approximation that integrates a speci c fuzzybased methodology from Soft Computing. We present several fuzzy optimization models that address the imprecision and/or exibility of some of its components. These models allow transport route planning problems to be solve with the help of metaheuristics in a concise way. A simple numerical example is shown to illustrate this approach.
141
158
Julio
Brito
Julio
Brito
I. U. D. R., University of La Laguna, E38271 Tenerife, Spain
I. U. D. R., University of La Laguna, E38271
Spain
jbrito@ull.es
Jose A.
Moreno
Jose A.
Moreno
I. U. D. R., University of La Laguna, E38271 Tenerife, Spain
I. U. D. R., University of La Laguna, E38271
Spain
jamoreno@ull.es
Jose L.
Verdegay
Jose L.
Verdegay
Department C. C. I. A., University of Granada, E18071 Granada,
Spain
Department C. C. I. A., University of Granada,
Spain
verdegay@decsai.ugr.es
Fuzzy optimization
Route planning
Soft computing
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