Some Issues on Properties of the Extended IOWA Operators in Cubic Group Decision Making

Abstract

The concept of this paper to study some IOWA operator to aggregating the individual cubic preference relations (CPR). This paper deal further the study of their properties of group decision problems with the help of CPR, we have proved that the collective preference relation obtained by IOWA operator, then we applied the aggregation operator of individual judgment by using IOWA operators as aggregation procedure by (RAMM) method. Additionally, the result of group Consistency IOWA (C-IOWA) operator is greater than the arithmetic mean of all the individual consistency degree. The numerical application verified the result of this paper.

Keywords

• Cubic preference relation (CPR),induced ordered weighted averaging (IOWA),group decision making

References

1. [1] Atanassov K, Intuitionistic fuzzy sets, Fuzzy Sets Syst, (20) (1986) 87-96
2. [2] De S K, Biswas R, Roy A R, Some operations on intuitionistic fuzzy sets, Fuzzy Sets Syst, (14) (2000) 477-484
3. [3] Jun Y B, SKim C, Yang K O, Cubic sets, Ann. Fuzzy Math. Inf, (4) (2012) 83-98
4. [4] Szmidt E, Kacprzy J, A consensus-reaching process under intuitionistic fuzzy preference relation, International Journal of Intelligent Systems, (18) (2003) 837-852
5. [5] Xu Z S, Intuitionistic preference relations and their application in group decision making, Information Sciences, (177) (2007) 2363-2379
6. [6] Chiclana F, Herrera F, Herrera-Viedma E, Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations, Fuzzy Sets and Systems, (97) (1998) 33-48
7. [7] Fodor J, Roubens M, Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer, Dordrecht, 1994
8. [8] Satty T L, The analytic hierarchy process, New York:,McGraw-Hill,(1980)

9. [9] Tanino T, Fuzzy preference relations in group decision making, in: J. Kacprzyk, M. Roubens (Eds.), Non-Conventional Preference Relations in Decision Making, Springer-Verlag, Berlin, (1988) 54-71
10. [10] Triantaphyllou E, Multi-Criteria Decision Making Methods, A Comparative Study, Kluwer Academic Publishers, Dordrecht, 2000.
11. [11] Dubois D, Prade H, Fuzzy Sets and Systems, Theory and Application, Academic Press, New York, 1980
12. [12] Herrera F, Herrera-Viedma E, Verdegay J L, A rational consensus model in group decision making using linguistic assessments, Fuzzy Sets and Systems, (88) (1997) 31-49
13. [13] Herrera-Viedma E, Herrera F, Chiclana F & M. Luque, Some issues on consistency of fuzzy preference relations, European Journal of Operational Research, (154) (2004) 98-109
14. [14] Yager R. R, Induced aggregation operators, Fuzzy Sets and Systems, (137) (2003) 59-69