OWA Operators and Choquet Integrals in the Interval-Valued Setting

In this chapter, we make use of the notion of admissible order between intervals to extend the definition of OWA operators and Choquet integrals to the interval-valued setting. We also present an algorithm for decision making based on these developments.

[1]  Humberto Bustince,et al.  Interval-valued fuzzy sets constructed from matrices: Application to edge detection , 2009, Fuzzy Sets Syst..

[2]  Ronald R. Yager,et al.  OWA aggregation of intuitionistic fuzzy sets , 2009, Int. J. Gen. Syst..

[3]  R. Mesiar,et al.  ”Aggregation Functions”, Cambridge University Press , 2008, 2008 6th International Symposium on Intelligent Systems and Informatics.

[4]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[5]  Humberto Bustince,et al.  Interval-valued Fuzzy Sets in Soft Computing , 2010, Int. J. Comput. Intell. Syst..

[6]  Humberto Bustince,et al.  Generation of linear orders for intervals by means of aggregation functions , 2013, Fuzzy Sets Syst..

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

[8]  Humberto Bustince,et al.  Image Reduction Using Means on Discrete Product Lattices , 2012, IEEE Transactions on Image Processing.

[9]  Humberto Bustince,et al.  On averaging operators for Atanassov's intuitionistic fuzzy sets , 2011, Inf. Sci..

[10]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

[11]  Radko Mesiar,et al.  A Universal Integral as Common Frame for Choquet and Sugeno Integral , 2010, IEEE Transactions on Fuzzy Systems.

[12]  R. Aumann INTEGRALS OF SET-VALUED FUNCTIONS , 1965 .

[13]  Inmaculada Lizasoain,et al.  OWA operators defined on complete lattices , 2013, Fuzzy Sets Syst..

[14]  Humberto Bustince,et al.  A class of aggregation functions encompassing two-dimensional OWA operators , 2010, Inf. Sci..

[15]  Humberto Bustince,et al.  Construction of Interval-Valued Fuzzy Relations With Application to the Generation of Fuzzy Edge Images , 2011, IEEE Transactions on Fuzzy Systems.

[16]  Humberto Bustince,et al.  Interval-Valued Fuzzy Sets Applied to Stereo Matching of Color Images , 2011, IEEE Transactions on Image Processing.

[17]  Deli Zhang,et al.  On set-valued fuzzy integrals , 1993 .

[18]  G. Choquet Theory of capacities , 1954 .

[19]  L. Shapley A Value for n-person Games , 1988 .

[20]  菅野 道夫,et al.  Theory of fuzzy integrals and its applications , 1975 .

[21]  H. B. Mitchell An Intuitionistic Owa Operator , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[22]  Lee-Chae Jang INTERVAL-VALUED CHOQUET INTEGRALS AND THEIR APPLICATIONS , 2004 .

[23]  Radko Mesiar,et al.  Aggregation functions on bounded partially ordered sets and their classification , 2011, Fuzzy Sets Syst..

[24]  Ronald R. Yager,et al.  On Prioritized Multiple-Criteria Aggregation , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[25]  Humberto Bustince,et al.  A New Approach to Interval-Valued Choquet Integrals and the Problem of Ordering in Interval-Valued Fuzzy Set Applications , 2013, IEEE Transactions on Fuzzy Systems.