Induced and Linguistic Generalized Aggregation Operators and Their Application in Linguistic Group Decision Making
- 362 Downloads
We introduce a wide range of induced and linguistic generalized aggregation operators. First, we present the induced linguistic generalized ordered weighted averaging (ILGOWA) operator. It is a generalization of the OWA operator that uses linguistic variables, order inducing variables and generalized means in order to provide a more general formulation. One of its main results is that it includes a wide range of linguistic aggregation operators such as the induced linguistic OWA (ILOWA), the induced linguistic OWG (ILOWG) and the linguistic generalized OWA (LGOWA) operator. We further generalize the ILGOWA operator by using quasi-arithmetic means obtaining the induced linguistic quasi-arithmetic OWA (Quasi-ILOWA) operator and by using hybrid averages forming the induced linguistic generalized hybrid average (ILGHA) operator. We also present a further extension with Choquet integrals. We call it the induced linguistic generalized Choquet integral aggregation (ILGCIA). We end the paper with an application of the new approach in a linguistic group decision making problem.
KeywordsLinguistic aggregation operators OWA operator Choquet integral Linguistic group decision making
Unable to display preview. Download preview PDF.
- Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, BerlinGoogle Scholar
- Bonissone PP (1982) A fuzzy sets based linguistic approach: theory and applications. In: Gupta MM, Sanchez E (eds) Approximate reasoning in decision analysis. North-Holland, Amsterdam, pp 329–339Google Scholar
- Calvo T, Mayor G, Mesiar R (2002) Aggregation operators: new trends and applications. Physica-Verlag, New YorkGoogle Scholar
- Merigó JM, Casanovas M (2010b) Fuzzy generalized hybrid aggregation operators and its application in decision making. Int J Fuzzy Syst 12: 15–24Google Scholar
- Merigó JM, Casanovas M (2010c) Induced and heavy aggregation operators with distance measures. J Syst Eng Electron 21: 431–439Google Scholar
- Merigó JM, Casanovas M (2010d) Decision making with distance measures and linguistic aggregation operators. Int J Fuzzy Syst 12: 190–198Google Scholar
- Merigó JM, Gil-Lafuente AM (2008) The induced linguistic generalized OWA operator. In: Proceedings of the FLINS 2008 international conference, Madrid, pp 325–330Google Scholar
- Sugeno M (1974) Theory of fuzzy integrals and its applications. PhD Thesis, Tokyo Institute of TechnologyGoogle Scholar
- Xu YJ, Da QL, Liu XW (2010) Some properties of linguistic preference relation and its ranking in group decision making. J Syst Eng Electron 21: 244–249Google Scholar
- Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Part 1. Inf Sci 8:199–249; Part 2. Inf Sci 8:301–357; Part 3. Inf Sci 9:43–80Google Scholar
- Zhou LG, Chen HY (2010b) Continuous generalized OWA operator and its application to decision making. Fuzzy Sets Syst (in press). doi: 10.1016/j.fss.2010.05.009