Aggregation, Non-Contradiction and Excluded-Middle
نویسندگان
چکیده
This paper investigates the satisfaction of the Non-Contradiction (NC) and Excluded-Middle (EM) laws within the domain of aggregation operators. It provides characterizations both for those aggregation operators that satisfy NC/EM with respect to (w.r.t.) some given strong negation, as well as for those satisfying them w.r.t. any strong negation. The results obtained are applied to some of the most important known classes of aggregation operators.
منابع مشابه
On Aristotle's NC and EM Principles in Three-valued Logics
By interpreting ‘p is impossible’ by ‘p is selfcontradictory’, and ‘p is always’ by ‘not p is self-contradictory’, this paper studies which of the three-valued systems of Łucasiewicz, Gödel, Kleene, Bochvar, and Post, do verify the Aristotle’s principles of Non-Contradiction (NC), and Excluded-Middle (EM). Keywords— Systems of three-valued logic, Non-Contradiction, Excluded-Middle.
متن کاملThe principle of bivalence
0. Introduction The relations between the principles of bivalence, excluded middle and non contradiction are not necessarily clear. One reason is that there are various formulations of these principles, not always equivalent. In this paper, we try to formulate precisely these principles in order to discuss their relationships and to answer the question: is the conjunction of the principles of e...
متن کاملLaws of Non-Contradiction, Laws of the Excluded Middle and Logics
There is widespread acknowledgement that the law of non-contradiction is an important logical principle. However, there is less-than-universal agreement on exactly what the law amounts to. This unclarity is brought to light by the emergence of paraconsistent logics in which contradictions are tolerated: From the point of view of proofs, not everything need follow from a contradiction — from the...
متن کاملAggregation and Non-Contradiction
This paper investigates the satisfaction of the Non-Contradiction Law (NC) within the domain of aggregation operators. It provides characterizations both for those aggregation operators that satisfy NC with respect to (w.r.t.) some given strong negation, as well as for those satisfying the law w.r.t. any strong negation. The results obtained are applied to some of the most important known class...
متن کاملIntroducing Interpolative Boolean algebra into Intuitionistic fuzzy sets
In this paper, we introduce Interpolative Boolean algebra (IBA) as a suitable algebra for intuitionistic fuzzy sets (IFSs). IBA is [0,1]-valued realization of Boolean algebra, consistent with Boolean axioms and theorems. IFS theory takes into account both membership and non-membership function, so it can be viewed as a generalization of the traditional fuzzy set theory. We propose a realization...
متن کامل