OWA Generation Function and Some Adjustment Methods for OWA Operators With Application

We propose the concept of ordered weighted averaging (OWA) generation function with some properties, illustrative examples, and usages. A number of new properties of OWA operators and relations between some well-known OWA operators are proposed and proved using OWA Generation Functions. We discuss some orness/andness adjustment methods for a predetermined OWA operator. A practical application about investment prediction problem is given with detailed illustration and analysis, which can show the advantages of the adjustment methods proposed in this paper. In particular, the concept consistent adjustment matrix is proposed and the interests and advantages of it can be shown by its special properties.

[1]  Ronald R. Yager,et al.  OWA Operators in Regression Problems , 2010, IEEE Transactions on Fuzzy Systems.

[2]  Xinwang Liu,et al.  On the properties of equidifferent OWA operator , 2006, International Journal of Approximate Reasoning.

[3]  Radko Mesiar,et al.  Decomposition integrals , 2013, Int. J. Approx. Reason..

[4]  Xinwang Liu,et al.  Orness and parameterized RIM quantifier aggregation with OWA operators: A summary , 2008, Int. J. Approx. Reason..

[5]  Philip J. Davis,et al.  A generalization of the Bernstein polynomials , 1999 .

[6]  Luigi Troiano,et al.  Recursive and Iterative Owa Operators , 2005, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[7]  Janusz Kacprzyk,et al.  Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice , 2011, Studies in Fuzziness and Soft Computing.

[8]  Xinwang Liu,et al.  On the properties of parametric geometric OWA operator , 2004, Int. J. Approx. Reason..

[9]  Gernot D. Kleiter,et al.  Degradation in probability logic: when more information leads to less precise conclusions , 2014, Kybernetika.

[10]  Ronald R. Yager,et al.  Pythagorean Membership Grades in Multicriteria Decision Making , 2014, IEEE Transactions on Fuzzy Systems.

[11]  R. Yager.  Quantifier guided aggregation using OWA operators , 1996, Int. J. Intell. Syst..

[12]  Radko Mesiar,et al.  The Ordered Modular Averages , 2011, IEEE Transactions on Fuzzy Systems.

[13]  Shui Yu,et al.  On the Stress Function-Based OWA Determination Method With Optimization Criteria , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[14]  V. Torra.  The weighted OWA operator , 1997, International Journal of Intelligent Systems.

[15]  Ronald R. Yager,et al.  OWA aggregation over a continuous interval argument with applications to decision making , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[16]  Esther de Ves,et al.  Applying logistic regression to relevance feedback in image retrieval systems , 2007, Pattern Recognit..

[17]  R. Yager.  Families of OWA operators , 1993 .

[18]  Radko Mesiar,et al.  Weighted means and weighting functions , 2006, Kybernetika.

[19]  R. Yager,et al.  Operations for granular computing: mixing words and numbers , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[20]  LeSheng Jin,et al.  Some properties and representation methods for Ordered Weighted Averaging operators , 2015, Fuzzy Sets Syst..

[21]  Ronald R. Yager,et al.  Norms Induced from OWA Operators , 2010, IEEE Transactions on Fuzzy Systems.

[22]  Xinwang Liu,et al.  An Orness Measure for Quasi-Arithmetic Means , 2006, IEEE Transactions on Fuzzy Systems.

[23]  Jozo J. Dujmovic.  Andness and orness as a mean of overall importance , 2012, 2012 IEEE International Conference on Fuzzy Systems.

[24]  Radko Mesiar,et al.  Aggregation of infinite sequences , 2008, Inf. Sci..

[25]  Nikhil R. Pal,et al.  Orness Measure of OWA Operators: A New Approach , 2014, IEEE Transactions on Fuzzy Systems.

[26]  Zeshui Xu,et al.  An overview of methods for determining OWA weights , 2005, Int. J. Intell. Syst..

[27]  Naif Alajlan,et al.  Multicriteria Decision-Making With Imprecise Importance Weights , 2014, IEEE Transactions on Fuzzy Systems.

[28]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[29]  Byeong Seok Ahn,et al.  On the properties of OWA operator weights functions with constant level of orness , 2006, IEEE Transactions on Fuzzy Systems.

[30]  LeSheng Jin,et al.  On Obtaining Piled OWA Operators , 2015, Int. J. Intell. Syst..

[31]  Radko Mesiar,et al.  Quantitative weights and aggregation , 2004, IEEE Transactions on Fuzzy Systems.

[32]  Dimitar Filev,et al.  On the issue of obtaining OWA operator weights , 1998, Fuzzy Sets Syst..

[33]  LeSheng Jin,et al.  Discrete and continuous recursive forms of OWA operators , 2017, Fuzzy Sets Syst..

[34]  Ronald R. Yager,et al.  Time Series Smoothing and OWA Aggregation , 2008, IEEE Transactions on Fuzzy Systems.

[35]  Dimitar Filev,et al.  Induced ordered weighted averaging operators , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[36]  Jozo J. Dujmovic,et al.  LSP method and its use for evaluation of Java IDEs , 2006, Int. J. Approx. Reason..

[37]  Nikhil R. Pal,et al.  Stancu OWA Operator , 2015, IEEE Transactions on Fuzzy Systems.

[38]  Wei Xiong,et al.  An Axiomatic Foundation for Yager's Decision Theory , 2014, Int. J. Intell. Syst..

[39]  Ronald R. Yager,et al.  Induced aggregation operators , 2003, Fuzzy Sets Syst..

[40]  R. Yager,et al.  PARAMETERIZED AND-UKE AND OR-LIKE OWA OPERATORS , 1994 .

[41]  Jozo J. Dujmovic,et al.  Continuous Preference Logic for System Evaluation , 2007, IEEE Transactions on Fuzzy Systems.

[42]  Zhongsheng Hua,et al.  Aggregating preference rankings using OWA operator weights , 2007, Inf. Sci..

[43]  Vicenç Torra,et al.  Modeling decisions - information fusion and aggregation operators , 2007 .

[44]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decision-making , 1988 .

[45]  Radko Mesiar,et al.  On linear and quadratic constructions of aggregation functions , 2015, Fuzzy Sets Syst..

[46]  Radko Mesiar,et al.  On the Transformation of Fuzzy Measures to the Power Set and Its Role in Determining the Measure of a Measure , 2015, IEEE Transactions on Fuzzy Systems.

[47]  R. Mesiar,et al.  Aggregation operators: new trends and applications , 2002 .

[48]  Naif Alajlan,et al.  Probabilistically Weighted OWA Aggregation , 2014, IEEE Transactions on Fuzzy Systems.