Maximum M-Entropy model- type ΙΙ for obtaining the ordered weighted averaging operator weights

Document Type : Original Paper

Authors

1 Shohadaie Hovaizeh University of Technology, Susangerd, Iran

2 Department of Mathematics, Iran University of Science and Technology

Abstract

One key issue in the theory of the OWA operator is to determine its associated weights. In this paper, based upon the M-Entropy measures, new models for obtaining the ordered weighted averaging (OWA) operators are proposed. In the models it is assumed, according to available information that the OWA weights are in decreasing or increasing order. Some properties of the models are analyzed and the method of Lagrange multipliers is used to provide a direct way to find these weights. The models are solved with specific level of Orness comparing the results with some other related models and with the other maximum M-entropy model. The results demonstrate the efficiency of the M-Entropy models in generating the OWA operator weights. Also, the obtained weights of the two M-entropy models confirm the difference between two types of the models. Finally, an applied example is presented to illustrate the applications of the proposed model.

Keywords

Main Subjects


[1] Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multi-criteria decision- making. IEEE Transactions on Systems, Man and Cybernetics18, 183–190.
[2] Merigó.José, M and Casanovas, Montserrat. (2010). The Fuzzy generalized OWA operator and its application in strategic decision making, Cybernetics and Systems41, 359-370.
[3] Yager, R. R. (2004). OWA aggregation over a continuous interval argument with applications to decision making, IEEE Transactions on Systems, Man, and Cybernetics, Part B 34, 1952-1963.
[4] Yager, R. R. (2009). Weighted Maximum Entropy OWA Aggregation with Applications to Decision Making Under Risk, IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans39(3), 555-564.
[5] Torra, V. (2004). OWA operators in data modeling and reidentication, IEEE Trans. Fuzzy Systems12, 652-660.
[6] Yager, R. R. and Filew, D.P. (1992). Fuzzy logic controllers with flexible structures. In: Proc Second IntConf on Fuzzy Sets and Neural Networks, Izuka, Japan; 317–320.
[7] Kacprzyk, J. and Zadrozny, S. (2001). Computing with words in intelligent database querying: standalone and internet-based applications, Information Sciences134, 71-109.
[8] Peláez, J.I. and Doña, J.M. (2003). Majority additive-ordered weighting averaging: a new neat ordered weighting averaging operator based on the majority process, international Journal of Intelligent Systems, 18, 469-481.
[9] Fuller, R. (2007). On obtaining OWA operator weights: a short survey of recent developments, in: Proceedings of the 5-th IEEE International Conference on Computational Cybernetics (ICCC)
[10]Yager, R.R. (1998). Including importances in OWA aggregations using fuzzy systems modeling. IEEE Trans Fuzzy Syst6(1); 286–294.
[11] Herrera-Viedma, E, Cordón. O, Luque. M, Lopez. A.G and Muñoz. A.M. (2003). A model of fuzzy linguistic IRS based on multi-granular linguistic information, International Journal of Approximate Reasoning34, 221239.
[12] Herrera-Viedma. E, Cordón. O, Luque. M, Lopez. A.G and Muñoz. A.M. (2007). A Model of Information Retrieval System with Unbalanced Fuzzy Linguistic Information, International Journal of Intelligent Systems22(11), 1197-1214.
[13] Herrera-Viedma, E and Pasi, G. (2003). Evaluating the Informative Quality of Documents in SGML-Format Using Fuzzy Linguistic Techniques Based on Computing with Words, Information Processing and Management, 39(2), 233-249.
 [14] O’Hagan, M. (1988). Aggregating template rule antecedents in real-time expert systems with fuzzy set logic. In Proceedings of 22nd annual IEEE Asilomar conference on signals, systems, and computers Pacific Grove, CA, 681–689.
[15] Majlender, P. (2005). OWA operators with maximal Rényi entropy. Fuzzy Sets andSystems155, 340–360.
[16] Jian, Wu., Bo-Liang Sun, Chang-Yong Liang and Shan-Lin Yang. (2009). A linear programming model for determining ordered weighted averaging operator weights with maximal Yager’s entropy. Computers & Industrial Engineering57, 742–747
[17] Kapur, J. N and Sharma, S. (1999). On measures of M-Entropy, Indian J. pure appl. Math30(2), 129-145.
[18] Kapur, J. N and Sharma, S. (2002). Some new measures of M-Entropy, Indian J. pure appl. Math33(6), 869-893.
[19] Yari, G and Chaji, A. (2012). Determination of Ordered Weighted Averaging Operator Weights Based on the M-Entropy Measures. International Journal of Intelligent Systems27(12),1020–1033.
[20] Yager, R. R. (1995). Measures of entropy and fuzziness related to aggregation operators, Information Sciences82, 147-166.
[21] Filev, D. and Yager, R. (1995) Analytic Properties of Maximum Entropy OWA Operators. Information Sciences,85, 11 – 27.
[22] Carlsson, C., Fuller, R. and Fuller, S. (1997) OWA Operators for Doctoral Student Selection Problem, in: R.R. Yager, J. Kacprzyk (Eds.), The Ordered Weighted Averaging Operators: Theory, Methodology and Applications, Kluwer Academic Publishers, Boston, 167–178.
[23] Bordogna, G. Fedrizzi, M. and Pasi, G. (1997). A Linguistic Modeling of Consensus in Group Decision Making Based on OWA Operators, IEEE Trans. Systems, Man, Cybernet.-Pt. A: Systems Humans27(1), 126–132.
 [24] Davey, A., Olson, D. and Wallenius, J. (1994). The Process of Multi Attribute Decision Making: a Case Study of Selecting Applicants for a Ph.D. Program, European J. Oper. Res.(72), 469–484,
[25] Smolíková, R. and Wachowiak, M.P. (2002) Aggregation Operators for Selection Problems, Fuzzy Sets and Systems131 (1).,23-34
]26[ میان آبادی، حجت؛ افشار، عباس (1386). تصمیم‌گیری گروهی فازی، محاسبه وزن نسبی تصمیم‌گیرندگان؛ مطالعه کاربردی: انتخاب دانشجویان مقطع دکترا. فصلنامه آموزش مهندسی ایران، شماره 35، سال نهم، صص 53-31.