Yager, Ronald R.; Rybalov, Alexander Bipolar aggregation using the uninorms. (English) Zbl 1304.91068 Fuzzy Optim. Decis. Mak. 10, No. 1, 59-70 (2011). Summary: In bipolar aggregation the total score depends not just on previous score and the value of additional argument but on distribution of all other arguments as well. In addition the process of bipolar aggregation is not Markovian, i.e. aggregation is not associative. To model bipolar aggregation was introduced general \({R_{G}^\ast}\) aggregation based on uninorms. By discarding associativity we built a variation of the uninorm using generating functions that can be applied as an intuitively appealing bipolar aggregation operator. This modified uninorm operator will allow us to control the aggregation depending on distribution of the arguments above and below the neutral element: the closer proportion of arguments below the neutral value to 1 or to 0 the closer bipolar aggregation is to some t-norm or t-conorm with desirable properties. Cited in 19 Documents MSC: 91B06 Decision theory Keywords:bipolar; uninorm; fuzzy sets; decision making × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Aczel J. (1949) Sur les operations definies pour des nombres reels. Bulletin of the France Mathematical Society 76: 59–64 [2] De Baets B. (1998) Uninorms: The known classes. In: Ruan D., Abderrahim H. A., D’hondt P., Kerre E. E. (eds) Fuzzy logic and intelligent technologies for nuclear science and industry. World Scientific, Singapore, pp 21–28 [3] De Baets B. (1999) Idempotent uninorms. European Journal of Operations Research 118: 631–642 · Zbl 0933.03071 · doi:10.1016/S0377-2217(98)00325-7 [4] De Baets B., Fodor J. (1999) Residual operators of uninorms. Soft Computing 3: 89–100 · doi:10.1007/s005000050057 [5] Dombi J. (1982) Basic concepts for a theory of evaluation: The aggregative operator. European Journal of Operational Research 10: 282–293 · Zbl 0488.90003 · doi:10.1016/0377-2217(82)90227-2 [6] Dubois D., Prade H. (2008a) Special issue on bipolar representations of information and preference. International Journal of Intelligent Systems, Wiley 23(10): 999–1152 · Zbl 1147.68708 · doi:10.1002/int.20304 [7] Dubois D., Prade H. (2008) An introduction to bipolar representations of information and preference. International Journal of Intelligent Systems, Wiley 23(10): 866–877 · Zbl 1147.68708 · doi:10.1002/int.20297 [8] Dubois D., Fargier H., Bonnefon J. F. (2008) On the qualitative comparison of decisions having positive and negative features. Journal of Artificial Intelligence Research 32: 385–417 · Zbl 1183.68573 [9] Fodor J. C., Yager R. R., Rybalov A. (1997) Structure of Uninorms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems (IJUFKS) 5(4): 411–427 · Zbl 1232.03015 · doi:10.1142/S0218488597000312 [10] Grabisch, M. (2006). Aggregation on bipolar scales. In H. C. M. de Swart, E. Orlowska, G. Schmidt, M. Roubens (Eds.), Theory and applications of relational structures as knowledge instruments II’ (pp. 355–371). · Zbl 1177.68214 [11] Grabisch M., Marichal J.-L., Mesiar R. (2009) Aggregation functions. Cambridge University Press, Cambridge · Zbl 1196.00002 [12] Klement E. P., Mesiar R., Pap E. (1996) On the relationship of associative compensatory operators to triangular norms and conorms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 4: 129–144 · Zbl 1232.03041 · doi:10.1142/S0218488596000081 [13] Osgood C., Tannenbaum P., Suci G. (1957) The measurement of meaning. University of Illinois Press, Urbana, IL [14] Saminger, S., Dubois, D., & Mesiar, R. (2006). On consensus functions in the bipolar case. In Proceedings of 27th linz seminar on fuzzy set theory (pp. 116–119). [15] Sicilia, M.-A., & Garcia, E. (2004). On the use of bipolar scales in preference–based recommender systems, in lecture notes in computer science (Vol. 3182/2004, pp. 268–276). Berlin, Heidelberg: Springer. [16] Yager R. R. (1994) Aggregation operators and fuzzy systems modeling. Fuzzy Sets and Systems 67: 129–146 · Zbl 0845.93047 · doi:10.1016/0165-0114(94)90082-5 [17] Yager R. R., Rybalov A. (1996) Uninorm aggregation operators. Fuzzy Sets and Systems 80: 111–120 · Zbl 0871.04007 · doi:10.1016/0165-0114(95)00133-6 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.