IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.2814 unavailable Cover vol. 9, no.2, June 2012-- 01 06 2012 9 2 0 0 13 12 2016 13 12 2016 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_2814.html

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IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.186 Research Paper BEHAVIOR OF SOLUTIONS TO A FUZZY NONLINEAR DIFFERENCE EQUATION Zhang Qianhong Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, Guizhou 550004, P. R. China Yang Lihui Department of Mathematics, Hunan City University, Yiyang, Hunan 413000, P. R. China Liao Daixi Basic Science Department, Hunan Institute of Technology, Hengyang, Hunan 421002, P. R. China 08 06 2012 9 2 1 12 09 11 2010 09 06 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_186.html

In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation\$\$ x_{n+1}=frac{Ax_n+x_{n-1}}{B+x_{n-1}}, n=0,1,cdots,\$\$ where \$(x_n)\$ is a sequence of positive fuzzy number, \$A, B\$ are positive fuzzy numbers and the initial conditions \$x_{-1}, x_0\$ are positive fuzzy numbers.

Fuzzy difference equation Boundedness Persistence Equilibrium point stability
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IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.188 Research Paper GENERALIZED FUZZY VALUED \$theta\$-Choquet INTEGRALS AND THEIR DOUBLE-NULL ASYMPTOTIC ADDITIVITY Wang Gui-jun School of Mathematics Science, Tianjin Normal University, Tianjin 300387, China Li Xiao-ping School of Management, Tianjin Normal University, Tianjin 300387, China 08 06 2012 9 2 13 24 09 11 2010 09 06 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_188.html

The generalized fuzzy valued \$theta\$-Choquet integrals will beestablished for the given \$mu\$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-double-null asymptotic additivity of thefuzzy valued set functions formed are studied when the fuzzymeasure satisfies autocontinuity from above (below).\

Fuzzy measures Fuzzy valued \$theta\$-Choquet integrals Autocontinuous from above (below) Double-null asymptotic additive Pseudo-double-null asymptotic additive
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IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.190 Research Paper OPTIMIZED FUZZY CONTROL DESIGN OF AN AUTONOMOUS UNDERWATER VEHICLE Raeisy Behrooz School of Electrical and Computer Engineering, Shiraz Univer- sity, Shiraz, Iran and Iranian Space Agency, Iranian Space Center, Mechanic Institute, Shiraz, Iran, P.O. Box: 71555-414 Safavi Ali Akbar School of Electrical and Computer Engineering, Shiraz Univer- sity, Shiraz, Iran Khayatian Ali Reza School of Electrical and Computer Engineering, Shiraz Uni- versity, Shiraz, Iran 08 06 2012 9 2 25 41 09 06 2010 09 07 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_190.html

In this study, the roll, yaw and depth fuzzy control of an Au- tonomous Underwater Vehicle (AUV) are addressed. Yaw and roll angles are regulated only using their errors and rates, but due to the complexity of depth dynamic channel, additional pitch rate quantity is used to improve the depth loop performance. The discussed AUV has four aps at the rear of the vehicle as actuators. Two rule bases and membership functions based on Mamdani type and Sugeno type fuzzy rule have been chosen in each loop. By invoking the normalized steepest descent optimization method, the optimum values for the membership function parameters are found. Though the AUV is a highly nonlinear system, the simulation of the designed fuzzy logic control system based on the equations of motion shows desirable behavior of the AUV spe- cially when the parameters of the fuzzy membership functions are optimized.

Fuzzy optimized control Autonomous underwater vehicle Normalized steepest descent Neural Network
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IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.195 Research Paper NON-FRAGILE GUARANTEED COST CONTROL OF T-S FUZZY TIME-VARYING DELAY SYSTEMS WITH LOCAL BILINEAR MODELS Li Junmin Department of Mathematics, Xidian University, 710071, Xi'an, P.R. China Zhang Guo Department of Electrical Engineering and Automation, Luoyang Insti- tute of Science and Technology, Luoyang, 471023, P.R. China 08 06 2012 9 2 43 62 09 07 2010 09 06 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_195.html

This paper focuses on the non-fragile guaranteed cost control problem for a class of T-S fuzzy time-varying delay systems with local bilinear models. The objective is to design a non-fragile guaranteed cost state feedback controller via the parallel distributed compensation (PDC) approach such that the closed-loop system is delay-dependent asymptotically stable and the closed-loop performance is no more than a certain upper bound in the presence of the additive controller gain perturbations. A sufficient condition for the existence of such non-fragile guaranteed cost controllers is derived via the linear matrix inequality (LMI) approach and the design problem of the fuzzy controller is formulated in term of LMIs. The simulation examples show that the proposed approach is effective.

Fuzzy control Non-fragile control Guaranteed cost control Delaydependent linear matrix inequality (LMI) T-S fuzzy bilinear model
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Yang, Control synthesis of continuous-time T-S fuzzy systems with local nonlinear models, IEEE Trans. Systems, Man, Cybernetics-Part B, 39 (2009), 1245-1258.  B. Z. Du, J. Lam and Z. Shu, Stabilization for state/input delay systems via static and integral output feedback, Automatica, 46 (2010), 2000-2007.  D. L. Elliott, Bilinear systems in Encyclopedia of Electrical Engineering, New York: Wiley,  H. J. Gao, J. Lam and Z. D. Wang, Discrete bilinear stochastic systems with time-varying delay: stability analysis and control synthesis, Chaos, Solitons and Fractals, 34 (2007), 394-  H. J. Gao, X. Liu and J. Lam, Stability analysis and stabilization for discrete-time fuzzy systems with time-varying delay, IEEE Trans. Systems, Man, Cybernetics-Part B, 39 (2009),  D. W. C. Ho and Y. Niu, Robust fuzzy design for nonlinear uncertain stochastic systems via sliding-mode control, IEEE Trans Fuzzy Systems, 15 (2007), 350-358.  H. L. Huang and F. G. Shi, Robust H1 control for TCS time-varying delay systems with norm bounded uncertainty based on LMI approach, Iranian Journal of Fuzzy Systems, 6 (2009), 1-14.  L. H. Keel and S. P. Bhattacharryya, Robust, fragile, or optimal, IEEE Trans. Automatic Control, 42 (1997), 1098-1105.  J. H. Kim, Delay-dependent robust and non-fragile guaranteed cost control for uncertain singular systems with time-varying state and input delays, International Journal of Control, Automation and Systems, 7 (2009), 357-364.  F. Leibfritz, An LMI-based algorithm for designing suboptimal static H2/H-in nite output- feedback controllers, SIAM J Control Optimization, 57 (2001), 1711-1735.  J. M. Li, G. Zhang and C. Du, Robust H-in nity control for a class of multiple input fuzzy bilinear systems with uncertainties, Control Theory and Applications, 26 (2009), 1298-1302.  L. Li and X. D. Liu, New approach on robust stability for uncertain T{S fuzzy systems with state and input delays, Chaos, Solitons and Fractals, 40 (2009), 2329-2339.  T. H. S. Li and S. H. Tsai, T-S fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems, IEEE Trans. Fuzzy Systems, 15 (2007), 494-505.  T. H. S. Li, S. H. Tsai and et al, Robust H-in nite fuzzy control for a class of uncertain discrete fuzzy bilinear systems, IEEE Trans. Systems, Man, Cybernetics-Part B, 38 (2008),  R. R. Mohler, Bilinear control processes, New York: Academic, 1973.  C. T. Pang and Y. Y. Lur, On the stability of Takagi-Sugeno fuzzy systems with time-varying uncertainties, IEEE Trans. Fuzzy Systems, 16 (2008), 162-170.  R. E. Precup, S. Preitl, J. K. Tar, M. L. Tomescu, M. Takacs, P. Korondi and P. Baranyi, Fuzzy control systems performance enhancement by iterative learning control, IEEE Trans. Industrial Electronics, 55 (2008), 3461-3475.  K. Tanaka and H. O. Wang, Fuzzy control systems design and analysis: a linear matrix inequality approach, John Wiley and Sons, 2001.  S. H. Tsai and T. H. S. Li, Robust fuzzy control of a class of fuzzy bilinear systems with time-delay, Chaos, Solitons and Fractals, 39 (2007), 2028-2040.  R. J. Wang, W. W. Lin and W. J. Wang, Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems, IEEE Trans. Systems, Man, Cybernetics-Part B, 34 (2004), 1288-1292.  H. N. Wu and H. X. Li, New approach to delay-dependent stability analysis and stabilization for continuous-time fuzzy systems with time-varying delay, IEEE Trans. Fuzzy Systems, 15 (2007), 482-493.  D. D. Yang and K. Y. Cai, Reliable guaranteed cost sampling control for nonlinear time-delay systems, Mathematics and Computers in Simulation, 80 (2010), 2005-2018.  G. H. Yang and J. L. Wang, Non-fragile H-in nite control for linear systems with multiplica- tive controller gain variations, Automatica, 37 (2001), 727-737.  G. H. Yang, J. L. Wang and C. Lin, H-in nite control for linear systems with additive controller gain variations, Int. J Control, 73 (2000), 1500-1506.  J. S. Yee, G. H. Yang and J. L. Wang, Non-fragile guaranteed cost control for discrete-time uncertain linear systems, Int. J Systems Science, 32 (2001), 845-853.  K. W. Yu and C. H. Lien, Robust H-in nite control for uncertain T{S fuzzy systems with state and input delays, Chaos, Solitons and Fractals, 37 (2008), 150-156.  D. Yue and J. Lam, Non-fragile guaranteed cost control for uncertain descriptor systems with time-varying state and input delays, Optimal Control Applications and Methods, 26 (2005),  B. Y. Zhang, S. S. Zhou and T. Li, A new approach to robust and non-fragile H-in nitecontrol for uncertain fuzzy systems, Information Sciences, 177 (2007), 5118-5133.  J. Zhang, Y. Xia and R. Tao, New results on H-in nite ltering for fuzzy time-delay systems, IEEE Trans. Fuzzy Systems, 17 (2009), 128-137.  J. H. Zhang, P. Shi and J. Q. Qiu, Non-fragile guaranteed cost control for uncertain stochastic nonlinear time-delay systems, Journal of the Franklin Institute, 3462009676-690.  S. S. Zhou, J. Lam and W. X. Zheng, Control design for fuzzy systems based on relaxed non-quadratic stability and H-in nite performance conditions, IEEE Trans. Fuzzy Systems, 15 (2007), 188-198.  S. S. Zhou and T. Li, Robust stabilization for delayed discrete-time fuzzy systems via basis- dependent Lyapunov-Krasovskii function, Fuzzy Sets and Systems, 151 (2005), 139-153.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.207 Research Paper Statistical Convergence and Strong \$p-\$Ces`{a}ro Summability of Order \$beta\$ in Sequences of Fuzzy Numbers Altinok H. Department of Mathematics, Firat University, 23119, Elazig, Turkey Altin Y. Department of Mathematics, Firat University, 23119, Elazig, Turkey Isik M. Department of Statistics, Firat University, 23119, Elazig, Turkey 10 06 2012 9 2 63 73 11 12 2010 11 07 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_207.html

In this study we introduce the concepts of statistical convergence of order\$beta\$ and strong \$p-\$Ces`{a}ro summability of order \$beta\$ for sequencesof fuzzy numbers. Also, we give some relations between the statisticalconvergence of order \$beta\$ and strong \$p-\$Ces`{a}ro summability of order\$beta\$ and construct some interesting examples.

Fuzzy number Statistical convergence Cesro summability
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IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.208 Research Paper A MODIFICATION ON RIDGE ESTIMATION FOR FUZZY NONPARAMETRIC REGRESSION Farnoosh Rahman School of Mathematics, Iran University of Science and Tech- nology, Narmak, Tehran-16846, Iran Ghasemian Javad School of Mathematics, Iran University of Science and Technol- ogy, Narmak, Tehran-16846, Iran Solaymani Fard Omid School of Mathematics and Computer Science, Damghan Uni- versity, Damghan, Iran 10 06 2012 9 2 75 88 11 07 2010 11 07 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_208.html

This paper deals with ridge estimation of fuzzy nonparametric regression models using triangular fuzzy numbers. This estimation method is obtained by implementing ridge regression learning algorithm in the La- grangian dual space. The distance measure for fuzzy numbers that suggested by Diamond is used and the local linear smoothing technique with the cross- validation procedure for selecting the optimal value of the smoothing param- eter is fuzzi ed to t the presented model. Some simulation experiments are then presented which indicate the performance of the proposed method.

Fuzzy regression Ridge estimation Fuzzy nonparametric regression Local linear smoothing
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IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.210 Research Paper Delay-dependent robust stabilization and \$H_{infty}\$ control for uncertain stochastic T-S fuzzy systems with multiple time delays Senthilkumar T. Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram - 624 302, Tamilnadu, India Balasubramaniam P. Department of Mathematics, Gandhigram Rural Institute- Deemed University, Gandhigram - 624 302, Tamilnadu, India 10 06 2012 9 2 89 111 11 09 2010 11 07 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_210.html

In this paper, the problems of robust stabilization and\$H_{infty}\$ control for uncertain stochastic systems withmultiple time delays represented by the Takagi-Sugeno (T-S) fuzzymodel have been studied. By constructing a new Lyapunov-Krasovskiifunctional (LKF) and using the bounding techniques, sufficientconditions for the delay-dependent robust stabilization and \$H_{infty}\$ control scheme are presented in terms of linear matrixinequalities (LMIs). By solving these LMIs, a desired fuzzycontroller can be obtained which can be easily calculated byMatlab LMI control toolbox. Finally, a numerical simulation isgiven to illustrate the effectiveness of the proposed method.

Takagi-Sugeno (T-S) fuzzy systems Robust \$H_{infty}\$ control Stochastic system Linear matrix inequalities (LMIs) Multiple time delays Lyapunov-Krasovskii functional (LKF)
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Lee, {it Delay-dependent robust             stabilization of uncertain state-delayed systems},               Int. J. Control, {bf 74} (2001), 1447-1455. bibitem{P}  V. N. Phat, {it Memoryless \$H_{infty}\$ controller design for switched               non-linear systems with mixed time-varying delays}, Int. J. Control, {bf 82} (2009), 1889-1898. bibitem{SN}  P. Shi and S. K. Nguang, {it \$H_{infty}\$ output feedback control of fuzzy system models              under sampled measurements}, Comput. Math. Appl., {bf 46} (2003), 705-717. bibitem{TIW}  K. Tanaka, T. Ikeda and H. O. Wang, {it Fuzzy regulators and fuzzy                observers: relaxed stability conditions and LMI-based designs},               IEEE Trans. Fuzzy Syst., {bf 6} (1998), 250-265. bibitem{TS} T. Takagi and M. Sugeno, {it Fuzzy identification systems and  it's application to modeling                and control}, IEEE Trans. Syst. Man Cybern., {bf 15} (1985), 116-132. bibitem{WHL} Z. Wang, D. W. C. Ho and X. 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IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.213 Research Paper ON GENERALIZED FUZZY MULTISETS AND THEIR USE IN COMPUTATION Syropoulos Apostolos Greek Molecular Computing Group, 366, 28th October St., GR-67100 Xanthi, Greece 10 06 2012 9 2 113 125 11 04 2010 11 05 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_213.html

An orthogonal approach to the fuzzification of both multisets and hybridsets is presented. In particular, we introduce \$L\$-multi-fuzzy and\$L\$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. In addition, we study the properties ofthese structures. Also, the usefulness of these structures is examined inthe framework of mechanical multiset processing. More specifically, weintroduce a variant of fuzzy P~systems and, since simplefuzzy membrane systems have been introduced elsewhere, we simply extendpreviously stated results and ideas.

L-fuzzy sets Fuzzy Multisets Computability P Systems
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IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.215 Research Paper GLOBAL ROBUST STABILITY CRITERIA FOR T-S FUZZY SYSTEMS WITH DISTRIBUTED DELAYS AND TIME DELAY IN THE LEAKAGE TERM Balasubramaniam P. Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram - 624 302, Tamilnadu, India Lakshmanan S. Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram - 624 302, Tamilnadu, India Rakkiyappan R. Department of Mathematics, Bharathiar University, Coimbatore - 641 046, Tamilnadu, India 10 06 2012 9 2 127 146 11 07 2010 11 04 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_215.html

The paper is concerned with robust stability criteria for Takagi- Sugeno (T-S) fuzzy systems with distributed delays and time delay in the leakage term. By exploiting a model transformation, the system is converted to one of the neutral delay system. Global robust stability result is proposed by a new Lyapunov-Krasovskii functional which takes into account the range of delay and by making use of some inequality techniques. Based on the interval time-varying delays, new stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, three numerical examples and their simulations are given to show the effectiveness and advantages of our results.

Delay-dependent stability Linear matrix inequality Lyapunov–Krasovskii functional T-S fuzzy systems
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Sano, textit{A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer}, IEEE  Trans. Fuzzy Syst., textbf{2} (1994), 119-134 bibitem{F1}  E. Tian and C. Peng, textit{Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay}, Fuzzy Sets and  Systems, textbf{157} (2006), 544-559. bibitem{Unc4} M. Wu, Y. He, J. H. She and G. P. Liu, textit{Delay-dependent criteria for robust stability of time-varying delay systems}, Automatica, textbf{40} (2004), 1435-1439. bibitem{F2}  J. Yoneyama, textit{New delay-dependent approach to robust stability and stabilization for Takagi-Sugeno fuzzy time-delay systems}, Fuzzy Sets and  Systems, textbf{158} (2007), 2225-2237. bibitem{F32} J. Yoneyama, textit{Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays}, Information Sciences, textbf{178} (2008), 1935-1947. bibitem{Unc11} D. Yue, E. Tian, Y. Zhang and C. Peng, textit{Delay-distribution-dependent robust stability of uncertain systems with time-varying delay}, Int. J. Robust Nonlinear  Control, textbf{19} (2009), 377-393. bibitem{In3}  W. Zhang, X. S. Cai and Z. Z. Han, textit{Robust stability criteria for systems with interval time-varying delay and nonlinear perturbations}, J. Comput. Appl. Math., textbf{234} (2010), 174-180.
IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.218 Research Paper \$L-\$ordered Fuzzifying Convergence Spaces Wu Wenchao Department of Mathematics, Ocean University of China, 266100 Qing- dao, P. R. China Fang Jinming Department of Mathematics, Ocean University of China, 266100 Qing- dao, P. R. China 10 06 2012 9 2 147 161 11 07 2010 11 06 2011 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_218.html

Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of \$L-\$ordered fuzzifying convergence spaces, in whichthe category of \$L-\$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called thecategory of principal \$L-\$ordered fuzzifying convergence spaces andthat of topological \$L-\$ordered fuzzifying convergence spaces, andit is shown that they are isomorphic to the category of\$L-\$fuzzifying neighborhood spaces and that of \$L-\$fuzzifyingtopological spaces respectively.

\$L-\$fuzzifying topology \$L-\$ordered fuzzifying convergence structure \$L-\$filter Cartesian-closed category Reflective subcategory
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IJFS University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 University of Sistan and Baluchestan 21 10.22111/ijfs.2012.2815 unavailable Persian-translation vol. 9, no.2, June 2012 01 06 2012 9 2 165 174 13 12 2016 13 12 2016 Copyright © 2012, University of Sistan and Baluchestan. 2012 http://ijfs.usb.ac.ir/article_2815.html

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