2016
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Image Backlight Compensation Using Recurrent Functional Neural Fuzzy Networks Based on Modified Differential Evolution
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In this study, an image backlight compensation method using adaptive luminance modification is proposed for efficiently obtaining clear images.The proposed method combines the fuzzy Cmeans clustering method, a recurrent functional neural fuzzy network (RFNFN), and a modified differential evolution.The proposed RFNFN is based on the two backlight factors that can accurately detect the compensation degree. According to the backlight level, the compensation curve function of a backlight image can be adaptively adjusted. In our experiments, six backlight images are used to verify the performance of proposed method.Experimental results demonstrate that the proposed method performs well in backlight problems.
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1
19


ShengChih
Yang
Department of Computer Science and Information Engineering,
National ChinYi University of Technology, Taichung City 411, Taiwan, ROC
Department of Computer Science and Information
Taiwan


ChengJian
Lin
Department of Computer Science and Information Engineering, National ChinYi University of Technology, Taichung City 411, Taiwan, ROC
Department of Computer Science and Information
Taiwan
cjlin@ncut.edu.tw


HsuehYi
Lin
Department of Computer Science and Information Engineering, National ChinYi University of Technology, Taichung City 411, Taiwan, ROC
Department of Computer Science and Information
Taiwan
hyl@ncut.edu.tw


JyunGuo
Wang
Department of Computer Science and Information Engineering, National ChinYi University of Technology, Taichung City 411, Taiwan, ROC
Department of Computer Science and Information
Taiwan
jyunguo.wang@gmail.com


ChengYi
Yu
Department of Computer Science and Information Engineering, National ChinYi University of Technology, Taichung City 411, Taiwan, ROC
Department of Computer Science and Information
Taiwan
youjy@ncut.edu.tw
Neural fuzzy network
Recurrent network
Differential evolution
Fuzzy cmeans
Backlight compensation
Contrast enhancement
[[1] C. H. Chen, C. J. Lin and C. T. Lin, A recurrent functionallinkbased neural fuzzy system##and its applications, Proceedings of the 2007 IEEE Symposium on Computational Intelligence##in Image and Signal Processing (CIISP 2007), (2007), 415420.##[2] J. Duan and G. Qiu, Novel histogram processing for colour image enhancement, Proceedings##of the Third International Conference on Image and Graphics (ICIG04), Hong Kong, China,##(2004), 5558.##[3] A. A. Fahmy and A. M. Abdel Ghany, Adaptive functionalbased neurofuzzy PID incremental##controller structure, Neural Computing and Applications, 26(6) (2015), 14231438.##[4] M. Hojati and S. Gazor, Hybrid adaptive fuzzy identication and control of nonlinear systems,##IEEE Transactions on Fuzzy Systems, 10(2) (2002), 198210.##[5] T. H. Huang, K. T. Shih, S. L. Yeh and H. H. Chen, Enhancement of backlightscaled images,##IEEE Transactions on Image Processing, 22(12) (2013), 45874597.##[6] H. Kabir, A. AlWadud and O. Chae, Brightness preserving image contrast enhancement##using weighted mixture of global and local transformation functions, The International Arab##Journal of Information Technology, 7(4) (2010), 403410.##[7] H. Y. Lin, C. Y. Lin, C. J. Lin, S. C. Yang and C. Y. Yu, A study of digital image enlargement##and enhancement, Mathematical Problems in Engineering, Article ID 825169, (2014).##[8] D. Menotti, L. Najman, J. Facon and A. A. A. de Araujo, Multihistogram equalization meth##ods for contrast enhancement and brightness preserving, IEEE Transactions on Consumer##Electronics, 53(3) (2007), 11861194.##[9] A. H. Mohamed, A genetic based neurofuzzy controller system, International Journal of##Computer Applications, 94(1) (2014), 1417.##[10] M. Panella and A. S. Gallo, An inputoutput clustering approach to the synthesis of ANFIS##networks, IEEE Transaction on Fuzzy Systems, 13(1) (2005), 6981.##[11] O. Patel, Y. P. S. Maravi and S. Sharma, A comparative study of histogram equalization##based image enhancement techniques for brightness preservation and contrast enhancement,##Signal & Image Processing: An International Journal (SIPIJ), 4(5) (2013), 1125.##[12] T. K. S. Paterlini, Dierential evolution and particle swarm optimization in partitional clus##tering, Computational Statics & Data Analysis, 50(5) (2006), 12201247.##[13] A. P. Piotrowski, Dierential evolution algorithms applied to neural network training suer##from stagnation, Applied Soft Computing, 21(2014), 382V406.##[14] R. Storn and K. Price, Dierential evolutionA simple and ecient heuristic for global op##timization over continuous spaces, Journal of Global Optimization, 11(4) (1997), 341359.##[15] M. A.Wadudx, M. H. Kabir, M. A. A. Dewan and O. Chae, A dynamic histogram equalization##for image contrast enhancement, IEEE Transactions on Consumer Electronics, 53(2) (2007),##[16] J. Yen and R. Langari, Fuzzy Logic: intelligence, control, and information, Prentice Hall,##[17] C. Y. Yu, H. Y. Lin and R. N. Lin, Eightscale image contrast enhancement based on adaptive##inverse hyperbolic, International Symposium on Computer, Consumer and Control, Taichung,##Taiwan, (2014), 98102.##[18] C. Y. Yu, H. Y. Lin, Y. C. Ouyang and T. W. Yu, Modulated AIHT image contrast en##hancement algorithm based on contrastlimited adaptive histogram equalization, International##Journal on Applied Mathematics and Information Sciences, 7(2) (2013), 449454.##[19] C. Y. Yu, Y. C. Ouyang, C. M. Wang and C. I. Chang, Adaptive inverse hyperbolic tan##gent algorithm for dynamic contrast adjustment in displaying scenes, EURASIP Journal on##Advances in Signal Processing, 485151 (2010), 120.##[20] J. Yue, J. Liu, X. Liu and W. Tan, Identication of nonlinear system based on ANFIS with##subtractive clustering, The Sixth World Congress on Intelligent Control and Automation##(WCICA 2006), 2006, 18521856.##[21] K. Zuiderveld, Contrast limited adaptive histogram equalization, In: P. Heckbert: Graphics##Gems IV, Academic Press 1994##]
A new attitude coupled with the basic fuzzy thinking to distance between two fuzzy numbers
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Fuzzy measures are suitable in analyzing human subjective evaluation processes. Several different strategies have been proposed for distance of fuzzy numbers. The distances introduced for fuzzy numbers can be categorized in two groups:\1. The crisp distances which explain crisp values for the distance between two fuzzy numbers.\2. The fuzzy distance which introduce a fuzzy distance for normal fuzzy numbers. It was introduced by Voxman cite{33} for the first time through using $alpha$cut.\However, both mentioned concepts can lead to unsatisfactory results from the applications point of view, but there is no method, which gives a satisfactory result to all situations. In this paper, a new attitude coupled with fuzzy thinking to the fuzzy distance function on the set of fuzzy numbers is proposed. In this new fuzzy distance, we considered both mentioned attitudes, then we introduced new fuzzy distance based on a combination (hybrid) of those two. Some properties of the proposed fuzzy distance have been discussed. Finally, several examples have been provided to explain the application of the proposed method and compare this methods with others.
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39


Fazlollah
Abbasi
Department of Mathematics Ayatollah Amoli Branch, Islamic
Azad University, Amol, Iran
Department of Mathematics Ayatollah Amoli
Iran
k_9121946081@yahoo.com


Tofigh
Allahviranloo
Department of Mathematics, Science and Research Branch,
Islamic Azad University, Tehran, Iran
Department of Mathematics, Science and Research
Iran
alahviranlo@yahoo.com


Saeid
Abbasbandy
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Mathematics, Science and Research
Iran
abbasbandy@yahoo.com
Pseudogeometric fuzzy numbers
Transmission average (TA)
Ranking fuzzy numbers
Fuzzy absolute of fuzzy number
Fuzzy distance function (fuzzy metric)
[[1] S. Abbasbandy and T. Hajjari, A new approach for ranking of trapezoidal fuzzy numbers,##Computers and Mathematics with Applications, 57 (2009), 413419.##[2] F. Abbasi, T. Allahviranloo and S. Abbasbandy,A new attitude coupled with fuzzy thinking##to fuzzy rings and elds, Journal of Intelligent and Fuzzy Systems, 29 (2015), 851861.##[3] F. Abbasi, T. Allahviranloo and S. Abbasbandy,A new attitude coupled with fuzzy thinking##to fuzzy group and subgroup, Journal of Fuzzy Set Valued Analysis, 4 (2015), 118.##[4] F. Abbasi, T. Allahviranloo and S. Abbasbandy, A new attitude coupled with the basic think##ing to ordering for ranking fuzzy numbers, International Journal of Industrial Mathematics,##8(4) (2016), 365375.##[5] D. Altman, Fuzzy set theoretic approaches for handling imprecision in spatial analysis, International##Journal of Geographical Information Systems, 8 (1994), 271289.##[6] M. Ali Beigi, T. Hajjari and E. Ghasem Khani,An Algorithm to Determine Fuzzy Distance##Measure, 13th Iranian Conference on Fuzzy Systems (IFSC), 2013.##[7] I. Bloch,On fuzzy distances and their use in image processing under imprecisionm, Pattern##Recognition, 32(11) (1999), 18731895.##[8] C. Chakraborty and D. Chakraborty, Atheoretical development on a fuzzy distance measure##for fuzzy numbers, Mathematical and Computer Modelling, 43(34) (2006), 254261.##[9] S. H. Chen and C. C. Wang,Fuzzy distance of trapezoidal fuzzy numbers, In: Proceedings of##the 9th Joint Conference on Information Sciences, JCIS 2006. ##[10] C.H. Cheng,A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and##Systems, 95(3) (1998), 307317.##[11] S. H. Chen and C. H. Hsieh,Graded mean integration representation of generalized fuzzy##number, Proceeding of TFSA, 1998.##[12] C. Chakraborty and D. Chakraborty, A theoretical development on a fuzzy distance measure##for fuzzy numbers, Mathematical and Computer Modeling, 43( 2006), 254261, .##[13] T. C. Chu and C. T. Tsao,Ranking fuzzy numbers with an area between the centroid point##and original point, Computers Math. Applications, 43 (2002), 111117.##[14] M. M. Deza and E. Deza, Encyclopedia of Distances, 2009.##[15] P. D'Urso and P. Giordani, A weighted fuzzy cmeans clustering model for fuzzy data, Computational##Statistics and Data Analysis, 50(6) (2006), 14961523.##[16] D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, 1980.##[17] R. Fullor,Fuzzy reasoning and fuzzy optimization, On leave from Department of Operations##Research, Eotvos Lorand University, Budapest, 1998.##[18] D. Guha and D. Chakraborty,A new approach to fuzzy distance measure and similarity mea##sure between two generalized fuzzy numbers, Applied Soft Computing, 10(1) (2010), 9099.##[19] J. Kacprzyk,Multistage fuzzy control: a prescriptive approach, John Wiley and Sons, Inc,##[20] G. J. Klir and B. Yuan,Fuzzy sets and fuzzy logic: theory and applications, PrenticeHall##PTR, Upper Saddlie River, 1995.##[21] S. Nezhad, A. Noroozi and A. Makui,Fuzzy distance of triangular fuzzy numbers, Journal of##Intelligent and Fuzzy Systems, 2012.##[22] A. Rosenfeld,Distance between Fuzzy Sets. Pattern Recognition Letters, 3 (1985), 229233.##[23] H. Rouhparvar, A. Panahi and A. Noorafkan Zanjani,Fuzzy distance measure for fuzzy num##bers, Australian Journal of Basic and Applied Sciences, 5(6) (2011), 258265.##[24] C. ShanHuo and W. ChienChung, Fuzzy distance using fuzzy absolute value, In: Machine##Learning and Cybernetics, International Conference, 2009.##[25] K. Sridharan and H. E. Stephanou,Fuzzy distance functions for motion planning, In: Tools##with Articial Intelligence. TAI '92, Proceedings., Fourth International Conference, 1992.##[26] S. R. Sudharsanan, Fuzzy distance approach to routing algorithms for optimal web path##estimation, In: Fuzzy Systems, The 10th IEEE International Conference, 2001.##[27] L. Stefanini, A generalization of hukuhara dierence and division for interval and fuzzy##arithmetic, Fuzzy Sets and Systems, 161 (2010), 15641584.##[28] L. Tran and L. Duckstein, Comparison of fuzzy numbers using a fuzzy distance measure,##Fuzzy Sets and Systems, 130(3) (2002), 331341.##[29] W. Voxman, Some remarks on distances between fuzzy numbers, Fuzzy Sets and Systems,##100(13) (1998), 353365.##]
A NEW MULTIOBJECTIVE OPTIMIZATION APPROACH FOR SUSTAINABLE PROJECT PORTFOLIO SELECTION: A REALWORLD APPLICATION UNDER INTERVALVALUED FUZZY ENVIRONMENT
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Organizations need to evaluate project proposals and select the ones that are the most effective in reaching the strategic goals by considering sustainability issue. In order to enhance the effectiveness and the efficiency of project oriented organizations, in this paper a new multiobjective decision making (MODM) approach of sustainable project portfolio selection is proposed which applies intervalvalued fuzzy sets (IVFSs) to consider uncertainty. In the proposed approach, in addition to sustainability criteria, other practical criteria including nonfinancial benefits, strategic alignment, organizational readiness and project risk are incorporated. The presented approach consists of three main parts: In the first part, a novel composite risk return index based on the IVFSs is introduced and used to form the first model to evaluate the financial return and risk of the proposed projects. In the second part, a new risk reduction compromise ratio model is introduced to evaluate projects versus nonfinancial criteria. Finally, an MODM model is presented to form the overall objective function of the approach. In order to make the approach more suitable for realworld situations, a group of applicable constraints is included in the proposed approach. The constraints are based on limitations and issues existing in practical project portfolio management. Due to importance of uncertainty and risk in project portfolio selection, they are addressed separately in three parts of the approach. In the first part, a novel downside risk measure is introduced and applied to assess financial risk of projects. In the second part of the approach, not only project risk is accounted for as a criterion, but also a new method is introduced to control and limit the risk of uncertainty and to use the advantages of IVFSs. Finally, the proposed IVFMODM approach is applied to select the optimal sustainable project portfolio in real case study of a holding company in a developing country. The results show that the approach can successfully address highly uncertain environments. Moreover, risk has been fully explored from different perspectives. Eventually, the approach provided the decision makers with more flexibility in focusing on financial and nonfinancial criteria in the selection process.
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Vahid
Mohagheghi
Department of Industrial Engineering, Faculty of Engineering,
Shahed University, Tehran, Iran
Department of Industrial Engineering, Faculty
Iran


S. Meysam
Mousavi
Department of Industrial Engineering, Faculty of Engineering,
Shahed University, Tehran, Iran
Department of Industrial Engineering, Faculty
Iran


Behnam
Vahdani
Faculty of Industrial and Mechanical Engineering, Qazvin Branch,
Islamic Azad University, Qazvin, Iran
Faculty of Industrial and Mechanical Engineering,
Iran
b.vahdani@ut.ac.ir
Sustainable project portfolio selection
Multiobjective optimization
Intervalvalued fuzzy sets (IVFSs)
Risks and uncertainties
Holding companies
[[1] B. Ashtiani, F. Haghighirad, A. Makui and A. Montazer, G, Extension of fuzzy TOPSIS##method based on intervalvalued fuzzy sets, Applied Soft Computing, 9(2) (2009), 457461.##[2] M. Better and F. Glover, Selecting project portfolios by optimizing simulations, The Engineering##Economist, 51(2) (2006), 8197.##[3] Y. P. Cai, G. H. Huang, H. W. Lu, Z. F. Yang and Q. Tan, IVFRP, An intervalvalued fuzzy##robust programming approach for municipal wastemanagement planning under uncertainty,##Engineering Optimization, 44(5) (2009), 399418.##[4] C. Carlsson, R. Fuller and J. Mezeiz, Project selection with intervalvalued fuzzy numbers,##In 2011 IEEE 12th International Symposium on Computational Intelligence and Informatics##(CINTI) (2011) ##[5] C. Carlsson, R. Fuller, M. Heikkila and P. Majlender, A fuzzy approach to R&D project##portfolio selection, International Journal of Approximate Reasoning, 44(2) (2007), 93105.##[6] C. T. Chen and H. L. Cheng, A comprehensive model for selecting information system project##under fuzzy environment, International Journal of Project Management, 27(4) (2009), 389##[7] R. H. Chen, Y. Lin and M. L. Tseng, Multicriteria analysis of sustainable development##indicators in the construction minerals industry in China, Resources Policy, 46(1) (2015),##[8] N. Chiadamrong, An integrated fuzzy multicriteria decision making method for manufactur##ing strategies selection, Computers & Industrial Engineering, 37(1) (1999), 433436.##[9] CY. Chiu and C. S. Park, Capital budgeting decisions with fuzzy projects, The Engineering##Economist 43(2) (1998), 125150.##[10] R. G. Cooper, S. J. Edgett and E. J. Kleinschmidt, New problems, new solutions: making##portfolio management more eective, ResearchTechnology Management, 43(2) (2000), 18##[11] C. Cornelis, G. Deschrijver and E. E. Kerre, Advances and challenges in intervalvalued fuzzy##logic, Fuzzy sets and systems, 175(5) (2006), 622627.##[12] T. Dyllick and K. Hockerts, Beyond the business case for corporate sustainability, Business##strategy and the environment, 11(2) (2002), 130141.##[13] S. Ebrahimnejad, M. H. Hosseinpour and A. M. Nasrabadi, A fuzzy biobjective mathemati##cal model for optimum portfolio selection by considering in##ation rate eects, International##Journal of Advanced Manufacturing Technology, 69(14) (2013), 595616.##[14] S. Ebrahimnejad, S. M. Mousavi, R. TavakkoliMoghaddam, H. Hashemi and B. Vahdani, A##novel twophase group decision making approach for construction project selection in a fuzzy##environment, Applied Mathematical Modelling, 36(9) (2012), 41974217.##[15] J. Elkington, Cannibals with forks: the triple bottom line of 21st century business, Capstone##Publishing, Ltd, Oxford, 1997.##[16] R. Z. Farahani and N. Asgari, Combination of MCDM and covering techniques in a hierar##chical model for facility location: A case study, European Journal of Operational Research,##176(3) (2007), 18391858.##[17] I. GrattanGuinness, Fuzzy Membership Mapped onto Intervals and ManyValued Quantities,##Mathematical Logic Quarterly, 22(1) (1976), 149160.##[18] L. S. Gaulke, X. Weiyang , A. Scanlon, A. Henck and T. Hinckley, Evaluation Criteria for##implementation of a sustainable sanitation and wastewater treatment system at Jiuzhaigou##National Park, Sichuan Province, China, Environmental management, 45(1) (2010), 93104.##[19] D. H. Hong and S. Lee, Some algebraic properties and a distance measure for intervalvalued##fuzzy numbers, Information Sciences, 148(1) (2002), 110.##[20] L. C. Hsu, A hybrid multiple criteria decisionmaking model for investment decision making,##Journal of Business Economics and Management, 15(3) (2014), 509529.##[21] X. Huang, Meansemivariance models for fuzzy portfolio selection, Journal of computational##and applied mathematics, 217(1) (2008), 18.##[22] M. J. Hutchins and J. W. Sutherland, An exploration of measures of social sustainability and##their application to supply chain decisions, Journal of Cleaner Production, 16(15) (2008),##16881698.##[23] C. L. Hwang and A. S. M. Masud, Multiple objective decision making, methods and applica##tions: a stateoftheart survey, Vol. 164. Berlin, Springer, 2012.##[24] S. Iamratanakul, P. Patanakul and D. Milosevic, Project portfolio selection: From past to##present, Proceedings of the 2008 IEEE ICMIT (2008), 287292.##[25] M. G. Kaiser, F. El Arbi and F. Ahlemann, Successful project portfolio management beyond##project selection techniques: Understanding the role of structural alignment, International##Journal of Project Management, 33(1) (2015), 126139.##[26] K. KhaliliDamghani and S. SadiNezhad, A hybrid fuzzy multiple criteria group decision##making approach for sustainable project selection, Applied Soft Computing, 13(1) (2013),##[27] K. KhaliliDamghani, S. SadiNezhad, F. H. Lot and M. Tavana, A hybrid fuzzy rulebased##multicriteria framework for sustainable project portfolio selection, Information Sciences, 220##(2013), 442462.##[28] D. Kuchta, Fuzzy capital budgeting, Fuzzy Sets and Systems, 11(3) (2000), 367385.##[29] S. H. Liao and S. H. Ho, Investment project valuation based on a fuzzy binomial approach,##Information Sciences, 180(11) (2010), 21242133.##[30] C. Lin and P. J. Hsieh, A fuzzy decision support system for strategic portfolio management,##Decision Support Systems, 38(3) (2004), 383398.##[31] H. W. Lu, G. H. Huang and L. He, Development of an intervalvalued fuzzy linear##programming method based on innite cuts for water resources management, Environmental##Modelling & Software, 25(3) (2010), 354361.##[32] M. Maleti, D. Maleti, J. J. Dahlgaard, S. M. DahlgaardPark and B. Gomiek, Sustainability##exploration and sustainability exploitation: from a literature review towards a conceptual##framework, Journal of Cleaner Production, 79 (2014), 182194.##[33] K. Manley, Against the odds: small rms in Australia successfully introducing new technology##on construction projects, Research Policy, 37(10) (2008), 17511764.##[34] G. Mavrotas and O. Pechak, Combining mathematical programming and monte carlo simula##tion to deal with uncertainty in energy project portfolio selection, assessment and simulation##tools for sustainable energy systems, Springer London, (2013), 333356.##[35] J. Mezei and R. Wikstrom, Aggregation operators and intervalvalued fuzzy numbers in deci##sion making, advances in information systems and technologies, Springer Berlin Heidelberg,##(2013), 535544.##[36] V. Mohagheghi, S. M. Mousavi and B. Vahdani, A new optimization model for project port##folio selection under intervalvalued fuzzy environment, Arabian Journal for Science and##Engineering, 40(11) (2015), 33513361.##[37] S. M. Mousavi, F. Jolai and R. TavakkoliMoghaddam, A fuzzy stochastic multiattribute##group decisionmaking approach for selection problems, Group Decision and Negotiation,##22(2) (2013), 207233.##[38] S. M. Mousavi, S. A. Torabi and R. TavakkoliMoghaddam, A hierarchical group decision##making approach for new product selection in a fuzzy environment, Arabian Journal for##Science and Engineering, 38(11) (2013), 32333248.##[39] S. M. Mousavi, B. Vahdani, R. TavakkoliMoghaddam, S. Ebrahimnejad and M. Amiri, A##multistage decision making process for multiple attributes analysis under an intervalvalued##fuzzy environment, International Journal of Advanced Manufacturing Technology, 64 (2013),##12631273.##[40] T. Rashid, I. Beg and S. M. Husnine, Robot selection by using generalized intervalvalued##fuzzy numbers with TOPSIS, Applied Soft Computing, 21 (2014), 462468.##[41] B. Rebiasz, Fuzziness and randomness in investment project risk appraisal, Computers &##Operations Research, 34(1) (2007), 199210.##[42] K. W. Robert, T. M. Parris and A. A. Leiserowitz, What is sustainable development? Goals,##indicators, values, and practice, Environment: Science and Policy for Sustainable Development,##47 (3) (2005), 821.##[43] United Nations, Report of the World Commission on Environment and Development: Our##Common Future, 1987.##[44] B. Vahdani, S. M. Mousavi, R. TavakkoliMoghaddam, A. Ghodratnama and M. Mohammadi,##Robot selection by a multiple criteria complex proportional assessment method un##der an intervalvalued fuzzy environment, International Journal of Advanced Manufacturing##Technology, 73(58) (2014), 687697.##[45] B. Vahdani, R. TavakkoliMoghaddam, S. M. Mousavi and A. Ghodratnama, Soft computing##based on new intervalvalued fuzzy modied multicriteria decisionmaking method, Applied##Soft Computing, 13 (2013), 165172.##[46] B. Vahdani, S. M. Mousavi and S. Ebrahimnejad, Soft computingbased preference selection##index method for human resource management, Journal of Intelligent and Fuzzy Systems,##26(1) (2014), 393403. ##[47] J. Wang and W. L. Hwang, A fuzzy set approach for R&D portfolio selection using a real##options valuation model, Omega, 35(3) (2007), 247257.##[48] D. J. Watt, B. Kayis and K. Willey, Identifying key factors in the evaluation of tenders for##projects and services, International Journal of Project Management, 27(3) (2009), 250260.##[49] J. S. Yao and F. T. Lin, Constructing a fuzzy ##owshop sequencing model based on statistical##data, International journal of approximate reasoning, 29(3) (2002), 215234.##[50] K. K. F. Yuen, A hybrid fuzzy quality function deployment framework using cognitive net##work process and aggregative grading clustering: an application to cloud software product##development, Neurocomputing, 142 (2014), 95106.##[51] K. K. F. Yuen, Fuzzy cognitive network process: comparisons with fuzzy analytic hierarchy##process in new product development strategy, IEEE Transactions on Fuzzy Systems, 22(3)##(2014), 597610.##[52] K. K. Yuen and H. C. Lau, A Linguistic PossibilityProbability Aggregation Model for decision##analysis with imperfect knowledge, Applied Soft Computing, 9(2) (2009), 575589.##[53] W. G. Zhang, Q. Mei, Q. Lu and W. L. Xiao, Evaluating methods of investment project##and optimizing models of portfolio selection in fuzzy uncertainty, Computers & Industrial##Engineering, 61(3) (2011), 721728.##]
A new approach for solving fuzzy linear Volterra integrodifferential equations
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In this paper, a fuzzy numerical procedure for solving fuzzy linear Volterra integrodifferential equations of the second kind under strong generalized differentiability is designed. Unlike the existing numerical methods, we do not replace the original fuzzy equation by a $2times 2$ system ofcrisp equations, that is the main difference between our method and other numerical methods.Error analysis and numerical examples are given to show the convergency and efficiency of theproposed method, respectively.
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87


Mojtaba
Ghanbari
Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran
Department of Mathematics, Aliabad Katoul
Iran
mojtaba.ghanbari@gmail.com
Fuzzy number
Fuzzy linear Volterra integrodifferential equation
Generalized differentiability
Fuzzy trapezoidal rule
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Universal Approximation of Intervalvalued Fuzzy Systems Based on Intervalvalued Implications
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2
It is firstly proved that the multiinputsingleoutput (MISO) fuzzy systems based on intervalvalued $R$ and $S$implications can approximate any continuous function defined on a compact set to arbitrary accuracy. A formula to compute the lower upper bounds on the number of intervalvalued fuzzy sets needed to achieve a prespecified approximation accuracy for an arbitrary multivariate continuousfunction is then presented. In addition, a method to design the intervalvalued fuzzy systems based on $R$ and $S$implications in order to approximate a given continuousfunction with a required approximation accuracy is represented. Finally, two numerical examples are provided to illustrate the proposed procedure.
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89
110


Dechao
Li
School of Mathematics, Physics and Information Science, Zhejiang Ocean
University, Zhoushan, Zhejiang, 316022, China and Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan, Zhejiang, 316022,
China
School of Mathematics, Physics and Information
China


Yongjian
Xie
College of Mathematics and Information Science, Shaanxi Normal
University, Xi'an, 710062, China
College of Mathematics and Information Science,
China
Intervalvalued fuzzy sets
Intervalvalued fuzzy implications
Intervalvalued fuzzy systems
Universal approximator
Sufficient condition
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Tsao, A type2 selforganizing neural fuzzy system and its FPGA implementation,##IEEE Transaction on System Man Cybernet. Part B: Cybernet, 38(6) (2008),##1537–1548.##[18] H. K. Lam, H. Li, C. Deters, E. L. Secco, H. A. Wurdemann and K. Althoefer, Control design##for interval type2 fuzzy systems under imperfect premise matching, IEEE Transactions on##Industrial Electronics, 61(2) (2014), 956–968, art. no. 6480840.##[19] D. C. Li, Y. M. Li and Y. J. Xie, Robustness of intervalvalued fuzzy inference, Information##Science, 181 (2011), 4754–4764.##[20] Y. M. Li and Y. J. Du, Indirect adaptive fuzzy observer and controller design based on interval##type2 TS fuzzy model, Applied Mathematical Modelling, 36(4) (2012), 1558–1569.##[21] Y. M. Li, Z. K. Shi and Z. H. Li, Approximation theory of fuzzy systems based upon genuine##manyvalued implications: SISO cases, Fuzzy Sets and Systems, 130 (2002), 147–157.##[22] Y. M. Li, Z. K. Shi and Z. H. 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Mˇckˇcr, Mathematical Principles of Fuzzy Logic, Kluwer Academic##Publishers, Boston, 1999.##[29] I. Perfilieva, Normal forms in BLalgebra off unctions and their contribution to universal##approximation, Fuzzy Sets and Systems, 143(1) (2004), 111–127.##[30] I. Perfilieva and V. Kreinovich, A new universal approximation result for fuzzy systems,##which reflects CNFDNF duality, Int. J. Intell. Syst. 17(12) (2002), 1121–1130.##[31] Y. M. Tang and X. P. Liu, Differently implicational universal triple I method of (1, 2, 2)##type, Computers and Mathematics with Applications, 59(6) (2010), 1965–1984.##[32] I. B. T¨urksen, Type 2 representation and reasoning for CWW, Fuzzy Sets and Systems, 127##(2002), 17–36.##[33] I. B. T¨urksen and Y. Tian, Intervalvalued fuzzy sets representation on multiple antecedent##fuzzy Simplications and reasoning, Fuzzy Sets and Systems, 52(2) (1992), 143–167.##[34] G. Wang and X. Li, Correlation and information energy of intervalvalued fuzzy numbers,##Fuzzy Sets and Systtem, 103(1) (1999), 169–175.##[35] D. Wu, On the fundamental differences between interval type2 and type1 fuzzy logic controllers,##IEEE Transactions on Fuzzy Systems, art. no. 6145645, 20(5) (2012), 832–848.##[36] D. Wu and W. W. Tan, A type2 fuzzy logic controller for the liquidlevel process, in: 2004##IEEE International Conference on Fuzzy Systems, (2004), Proceedings. 2 (2004), 953–958.##[37] H. Ying, Sufficient conditions on general fuzzy systems as function approximators, Automatic,##30(3) (1994), 521–525.##[38] H. Ying, General interval type2 Mamdani fuzzy systems are universal approximators, Proceedings##of North American Fuzzy Information Processing Society Conference, New York,##NY, May 19–22, 2008. ##[39] H. Ying, Interval type2 TakagiSugeno fuzzy systems with linear rule consequent are universal##approximators, The 28th North American Fuzzy Information Processing Society Annual##Conference, Cincinnati, Ohio, June 14–17, 2009.##[40] L. A. Zadeh, The concepts of a linguistic variable and its application to approximate reasoning##(I), (II), Information Science, 8 (1975), 199–249; 301–357.##[41] L. A. Zadeh, The concepts of a linguistic variable and its application to approximate reasoning##(III), Information Science, 9 (1975), 43–80.##[42] W. Y. Zeng and S. Feng, Approximate reasoning algorithm of intervalvalued fuzzy sets based##on least square method, Information Sciences, 272 (2014), 73–83.##[43] H. Zhou and H. Ying, A method for deriving the analytical structure of a broad class of##typical interval type2 mamdani fuzzy controllers, in: IEEE Transactions on Fuzzy Systems,##art. no. 6341818, 21(3) (2013), 447–458.##]
Stability analysis and feedback control of TS fuzzy hyperbolic delay model for a class of nonlinear systems with timevarying delay
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In this paper, a new TS fuzzy hyperbolic delay model for a class of nonlinear systems with timevarying delay, is presented to address the problems of stability analysis and feedback control. Fuzzy controller is designed based on the parallel distributed compensation (PDC), and with a new Lyapunov function, delay dependent asymptotic stability conditions of the closedloop system are derived via linear matrix inequalities (LMIs). Besides, considering the differences between the model and the real system, we extent the model to uncertain TS fuzzy hyperbolic delay model. Based on the uncertain model, a robust $H_{infty}$ fuzzy controller is obtained and stability conditions are developed in terms of LMIs. The main advantage of the control based on TS fuzzy hyperbolic delay model is that it can achieve small control amplitude via ``soft'' constraint approach. Finally, a numerical example and the Van de Vusse example are given to validate the advantages of the proposed method.
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111
134


Jiaxian
Wang
School of Mathematics and Statistics, Xidian University, Xi'an, 710071,
China
School of Mathematics and Statistics, Xidian
China


Junmin
Li
School of Mathematics and Statistics, Xidian University, Xi'an, 710071,
China
School of Mathematics and Statistics, Xidian
China
jmli@mail.xidian.edu.cn
TS fuzzy hyperbolic delay model
Small control amplitude
LMIs
robust $H_{infty}$ fuzzy control
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Kung and K. H. Su, The piecewise Lyapunov functions based the delay##independent H1 controller design for a class of timedelay TS fuzzy system, IEEE Interna##tional Conference on Systems, Man and Cybernetics, (2007), 121{126.##[7] C. S. Chiu, W. T. Yang and T. S. Chiang, Robust output feedback control of TS fuzzy time##delay systems, IEEE Symposium on Computational Intelligence in Control and Automation,##(2013), 45{50.##[8] G. Feng, A survey on analysis and design of modelbased fuzzy control systems, IEEE Trans##actions on Fuzzy Systems, 14(5) (2006), 676{697.##[9] Daniel W. C. Ho and Y. Niu, Robust fuzzy design for nonlinear uncertain stochastic systems##via slidingmode control, IEEE Transactions on Fuzzy Systems, 15(3) (2007), 350{358.##[10] Z. Hong and Z. F. Li, Stabilization for a class of TS uncertain nonlinear systems with##TimeDelay, Chinese Control and Decision Conference, (2012), 375{380.##[11] M. Y. Hsiao, C. H. Liu, S. H. Tsai and et al, A TakagiSugeno fuzzymodelbased modeling##method, IEEE International Conference on Fuzzy Systems, (2010), 1{6.##[12] J. M. Li, G. Zhang, Nonfragile guaranteed cost control of TS fuzzy time varying delay##systems with local bilinear models, Iranian Journal of Fuzzy Systems, 9(2) (2012), 43{62.##[13] Y. M. Li and S. C. Tong, Prescribed performance adaptive fuzzy outputfeedback dynamic##surface control for nonlinear largescale systems with time delays, Information Sciences, 292##(2015), 125{142.##[14] C. H. Lien and K. W. Yu, Robust control for TakagiSugeno fuzzy systems with timevarying##state and input delays, Chaos, Solitons and Fractals, 35(5) (2008), 1003{1008.##[15] C. Lin, Q. G. Wang and T. H. Lee, Delaydependent LMI conditions for stability and stabi##lization of TS fuzzy systems with bounded timedelay, Fuzzy Sets Systems, 157(9) (2006),##1229{1247.##[16] C. Lin, Q. G. Wang, T. H. Lee and Y. He, Fuzzy weightingdependent approach to H1 lter##design for timedelay fuzzy systems, IEEE Transactions on Signal Processing, 55(6) (2007),##2746{2751.##[17] T. Takagi and M. Sugeno, Fuzzy identication of systems and its applications to modelling##and control, IEEE Transactions on Systems, Man and Cybernetics, 15(1) (1985), 116{132. ##[18] K. Tanaka, T. Ikeda and H. O. Wang, Fuzzy regulators and fuzzy observers: relaxed stability##conditions and LMIbased designs, IEEE Transactions on Fuzzy Systems, 6(2) (1998), 250{##[19] K. Tanaka and H. O. Wang, Fuzzy control systems design and analysis: A linear matrix##inequality approach, John Wiley and Sons, 2002.##[20] S. H. Tsai and C. J. Fang, A novel relaxed stabilization condition for a class of TS timedelay##fuzzy systems, IEEE International Conference on Fuzzy Systems, (2014), 2294{2299.##[21] C. S. Tseng, B. S. Chen and H. J. Uang, Fuzzy tracking control design for nonlinear dynamic##systems via TS fuzzy model, IEEE Transactions on Fuzzy Systems, 9(3)(2001), 381{392.##[22] G. Wang, Y. Wang and D. S. Yang, New sucient conditions for delaydependent robust##H1 control of uncertain nonlinear system based on fuzzy hyperbolic model with timevarying##delays, Chinese Control and Decision Conference, (2012), 1138{1143.##[23] S. B. Wang, Y. Y. Wang and L. K. Zhang, Timedelay dependent state feedback fuzzy##predictive control of timedelay TS fuzzy model, Fifth International Conference on Fuzzy##Systems and Knowledge Discovery, (2008), 129{133.##[24] T. T. Wang, H. C. Yan, H. B. Shi and H. Zhang, Eventtriggered H1 control for networked##TS fuzzy systems with time delay, IEEE International Conference on Information and Au##tomation, (2014), 194{199.##[25] Y. Y. Wang, H. G. Zhang, J. Y. 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Gong and et al, New sucient conditions for robust H1 fuzzy##hyperbolic tangent control of uncertain nonlinear systems with timevarying delay, Fuzzy Sets##and Systems, 161(15) (2010), 1993{2011.##[31] H. G. Zhang, S. X. Lun and D. R. Liu, Fuzzy H1 lter design for a class of nonlinear discrete##time systems with multiple time delays, IEEE Transactions on Fuzzy Systems, 15(3) (2007),##[32] H. G. Zhang and Y. B. Quan, Modeling, identication and control of a class of nonlinear##system, IEEE Transactions on Fuzzy Systems, 9(2) (2001), 349{354.##[33] H. G. Zhang and X. P. Xie, Relaxed Stability Conditions for ContinuousTime TS Fuzzy##Control Systems Via Augmented MultiIndexed Matrix Approach, IEEE Transactions on##Fuzzy Systems, 19(3) (2011), 478{492.##[34] H. G. Zhang, J. L. Zhang, G. H. Yang and et al, Leaderbased optimal coordination con##trol for the consensus problem of multiagent dierential games via fuzzy adaptive dynamic##programming, IEEE Transactions on Fuzzy Systems, 23(1) (2015), 152{163.##[35] J. H. Zhang, P. Shi and J. Q. Qiu, Nonfragile guaranteed cost control for uncertain stochastic##nonlinear timedelay systems, Journal of the Franklin Institute, 346(7) (2009), 676{690.##[36] Z. Y. Zhang, C. Lin and B. Chen, New stability and stabilization conditions for TS fuzzy##systems with time delay, Fuzzy Sets and Systems, 263(C) (2015), 82{91.##[37] Y. Zhao and H. J. Gao, Fuzzymodelbased control of an overhead crane with input delay and##actuator saturation, IEEE Transactions on Fuzzy Systems, 20(1) (2012), 181{186.##]
Some results on $L$complete lattices
2
2
The paper deals with special types of $L$ordered sets, $L$fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a special element of $L^P$. A relation between $L$fuzzy complete lattices and fixpoints is found and fuzzy versions of monotonicity, rolling, fusion and exchange rules on $L$complete lattices are stated.Finally, we investigate the set of all monotone maps on a fuzzy directed complete posets, $DCPO$s, andfind a condition which under the set of all fixpoints of a monotone map on a fuzzy $DCPO$ is a fuzzy $DCPO$.
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135
152


Anatolij
Dvurecenskij
Mathematical Institute, Slovak Academy of Sciences, Stefanikova 49, SK814 73 Bratislava, Slovakia and Depart. Algebra Geom, Palacky Univer.,
17. listopadu 12, CZ771 46 Olomouc, Czech Republic
Mathematical Institute, Slovak Academy of
Czech Republic


Omid
Zahiri
University of Applied Science and Technology, Tehran, Iran
University of Applied Science and Technology,
Iran
Fuzzy complete lattice
Fixpoint
Fuzzy DCPO
Fuzzy directed poset
Monotone map
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RSBLalgebras are MValgebras
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2
We prove that RSBLalgebras are MValgebras.
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153
154


Esko
Turunen
Department of Mathematics, Technical University of Tampere, P.O.
Box 553, 33101, Tampere , Finland
Department of Mathematics, Technical University
Finland
esko.turunen@tut.fi
BLalgebra
MValgebra
Mathematical fuzzy logic
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Persiantranslation vol. 13, no. 6, December 2016
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