Generalized aggregation operators for intuitionistic fuzzy sets

The generalized ordered weighted averaging (GOWA) operators are a new class of operators, which were introduced by Yager (Fuzzy Optim Decision Making 2004;3:93–107). However, it seems that there is no investigation on these aggregation operators to deal with intuitionistic fuzzy or interval‐valued intuitionistic fuzzy information. In this paper, we first develop some new generalized aggregation operators, such as generalized intuitionistic fuzzy weighted averaging operator, generalized intuitionistic fuzzy ordered weighted averaging operator, generalized intuitionistic fuzzy hybrid averaging operator, generalized interval‐valued intuitionistic fuzzy weighted averaging operator, generalized interval‐valued intuitionistic fuzzy ordered weighted averaging operator, generalized interval‐valued intuitionistic fuzzy hybrid average operator, which extend the GOWA operators to accommodate the environment in which the given arguments are both intuitionistic fuzzy sets that are characterized by a membership function and a nonmembership function, and interval‐valued intuitionistic fuzzy sets, whose fundamental characteristic is that the values of its membership function and nonmembership function are intervals rather than exact numbers, and study their properties. Then, we apply them to multiple attribute decision making with intuitionistic fuzzy or interval‐valued intuitionistic fuzzy information. © 2009 Wiley Periodicals, Inc.

[1]  Zeshui Xu,et al.  Intuitionistic Fuzzy Aggregation Operators , 2007, IEEE Transactions on Fuzzy Systems.

[2]  Zeshui Xu,et al.  On Geometric Aggregation over Interval-Valued Intuitionistic Fuzzy Information , 2007, Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007).

[3]  Jian Jhen Chen,et al.  Approach to Group Decision Making Based on Interval-Valued Intuitionistic Judgment Matrices , 2007 .

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

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

[6]  Ronald R. Yager,et al.  Generalized OWA Aggregation Operators , 2004, Fuzzy Optim. Decis. Mak..

[7]  Z. S. Xu,et al.  An overview of operators for aggregating information , 2003, Int. J. Intell. Syst..

[8]  Francisco Herrera,et al.  An Approach for Combining Linguistic and Numerical Information Based on the 2-Tuple Fuzzy Linguistic Representation Model in Decision-Making , 2000, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[9]  Ranjit Biswas,et al.  Some operations on intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[10]  Dug Hun Hong,et al.  Multicriteria fuzzy decision-making problems based on vague set theory , 2000, Fuzzy Sets Syst..

[11]  Vicenç Torra,et al.  The weighted OWA operator , 1997, Int. J. Intell. Syst..

[12]  Humberto Bustince,et al.  Vague sets are intuitionistic fuzzy sets , 1996, Fuzzy Sets Syst..

[13]  Shyi-Ming Chen,et al.  Handling multicriteria fuzzy decision-making problems based on vague set theory , 1994 .

[14]  W.-L. Gau,et al.  Vague sets , 1993, IEEE Trans. Syst. Man Cybern..

[15]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[16]  Z. Xu,et al.  Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making , 2007 .

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

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

[19]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[20]  Peter F. Fisher,et al.  Fuzzy sets , 1965 .