Weighted ordinal means

The concept of weighted ordinal arithmetic means and other related weighted ordinal means is studied. Based on the relevant results on the scale [0,1], new types of weighted ordinal means are proposed. In some cases these ordinal means coincide with those proposed by Godo and Torra, but not in the case when ordinal means introduced by them are not idempotent. Based on divisible ordinal t-conorms and modifying the approach of Godo and Torra, we show how the previously introduced weighted ordinal means can be obtained without exploiting the formal similarity of the structure of continuous t-conorms on [0,1] and divisible ordinal t-conorms.

[1]  R. Mesiar,et al.  Logical, algebraic, analytic, and probabilistic aspects of triangular norms , 2005 .

[2]  R. Mesiar,et al.  Weighted means based on triangular conorms , 2001 .

[3]  G. Mayor,et al.  t‐Operators and uninorms on a finite totally ordered set , 1999 .

[4]  Radko Mesiar,et al.  A review of aggregation operators , 2001 .

[5]  Josep Domingo-Ferrer,et al.  Regression for ordinal variables without underlying continuous variables , 2006, Inf. Sci..

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

[7]  Witold Pedrycz,et al.  Regranulation: A granular algorithm enabling communication between granular worlds , 2007, Inf. Sci..

[8]  Radko Mesiar,et al.  Quasi- and pseudo-inverses of monotone functions, and the construction of t-norms , 1999, Fuzzy Sets Syst..

[9]  Francesc Esteva,et al.  Review of Triangular norms by E. P. Klement, R. Mesiar and E. Pap. Kluwer Academic Publishers , 2003 .

[10]  G. Mayor,et al.  Triangular norms on discrete settings , 2005 .

[11]  Luis Martínez-López,et al.  Dealing with heterogeneous information in engineering evaluation processes , 2007, Inf. Sci..

[12]  Joan Torrens,et al.  On a class of operators for expert systems , 1993, Int. J. Intell. Syst..

[13]  Jean-Luc Marichal,et al.  Aggregation operators for multicriteria decision aid , 1998 .

[14]  Vicenç Torra,et al.  On aggregation operators for ordinal qualitative information , 2000, IEEE Trans. Fuzzy Syst..

[15]  J. Aczél,et al.  Sur les opérations définies pour nombres réels , 1948 .

[16]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[17]  C. Sierra,et al.  A new approach to connective generation in the framework of expert systems using fuzzy logic , 1988, [1988] Proceedings. The Eighteenth International Symposium on Multiple-Valued Logic.

[18]  Zeshui Xu,et al.  A method based on linguistic aggregation operators for group decision making with linguistic preference relations , 2004, Inf. Sci..