Uninorm aggregation operators.(English)Zbl 0871.04007

Summary: A generalization of the $$t$$-norm and $$t$$-conorm called the uni-norm is defined. These operators allow for an identity element lying anywhere in the unit interval rather than at one or zero as in the case of $$t$$-norms and $$t$$-conorms, respectively. Various important properties of these uni-norms are investigated. We next introduce two particular families of these uni-norms, $$R^*$$ and $$R_*$$, study their behavior and suggest some semantics. Finally, withdrawing the requirement of associativity, we introduce a class of operators called $$R_{Q\text{-star}}$$ aggregation operators which are useful for aggregations guided by imperatives such as “if most of the scores are above the identity take the Max else use the Min”.

MSC:

 3e+72 Theory of fuzzy sets, etc.
Full Text:

References:

 [1] Alsina, C.; Trillas, E.; Valverde, L., On some logical connectives for fuzzy set theory, J. math. anal. appl., 93, 15-26, (1983) · Zbl 0522.03012 [2] Dubois, D.; Prade, H., A review of fuzzy sets aggregation connectives, Inform. sci., 36, 85-121, (1985) · Zbl 0582.03040 [3] Klement, E.P., Characterization of fuzzy measures constructed by means of triangular norms, J. math. anal. appl., 86, 345-358, (1982) · Zbl 0491.28004 [4] Mamdani, E.H.; Assilian, S., An experiment in linguistic synthesis with a fuzzy logic controller, Int. J. man-machine studies, 7, 1-13, (1975) · Zbl 0301.68076 [5] Yager, R.R., MAM and MOM operators for aggregation, Inform. sci., 69, 259-273, (1993) · Zbl 0783.04007 [6] Yager, R.R., Aggregation operators and fuzzy systems modeling, Fuzzy sets and systems, 67, 129-146, (1994) · Zbl 0845.93047 [7] Yager, R.R., On inference structures for fuzzy systems modeling, (), 1252-1256 [8] Yager, R.R.; Ovchinnikov, S.; Tong, R.; Nguyen, H., Fuzzy sets and applications: selected papers by L.A. zadeh, (1987), Wiley New York [9] Zadeh, L.A., A theory of approximate reasoning, (), 149-194 [10] Zadeh, L.A., A computational approach to fuzzy quantifiers in natural languages, Comput. math. applic., 9, 149-184, (1983) · Zbl 0517.94028
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.