Search results for "De Morgan's laws"
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A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms
1983
All known connectives 'and'/'or' for fuzzy sets or some classes can be introduced as t-norms/t-conorms, where Ling's representation theorem is used as a basic tool, and which is illustrated by various known and new examples (Section 2). Given a strict negation function and one connective, the other can be constructed, so that the corresponding De Morgan law is valid. In case of given Archimedean connectives, there can be constructed negation functions (Section 3). Given a non-strict Archimedean connective, a negation function and the other connective can be constructed, so that in addition to the De Morgan laws, the excluded middle law and the law of non-contradiction are valid, i.e. the ne…
Conjunction and Disjunction Among Conditional Events
2017
We generalize, in the setting of coherence, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. Given a prevision assessment on the conjunction of two conditional events, we study the set of coherent extensions for the probabilities of the two conditional events. Then, we introduce by a progressive procedure the notions of conjunction and disjunction for n conditional events. Moreover, by defining the negation of conjunction and of disjunction, we show that De Morgan’s Laws still hold. We also show that the associative and commutative properties are satisfied. Finally, we examine in detail the conjunction for a family \(\mathcal F\) of t…