By Vicenc Torra, Torra Narukawa
This ebook constitutes the complaints of the twelfth foreign convention on Modeling judgements for man made Intelligence, MDAI 2015, held in Skövde, Sweden, in September 2015. The 18 revised complete papers awarded have been rigorously reviewed and chosen from 38 submissions. They talk about conception and instruments for modeling judgements, in addition to functions that surround selection making strategies and knowledge fusion techniques.
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Additional info for Modeling Decisions for Artificial Intelligence: 12th International Conference, MDAI 2015, Skövde, Sweden, September 21-23, 2015, Proceedings
This is fact that if q1 is an idempotent element of a continuous t-norm T then T (x, y) = x for all x ≤ q1 ≤ y. However, we have T3 (x, y) = 0 for x ∈ [0, T1 (a, a)] and y ∈ [q1 , 1] . If T1 (a, a) = 0 then T3 is similarly as T2 an ordinal sum of three t-norms and the result can be composed from results of the previous section. 5 Conclusion We have described the strongest and the weakest t-norms that coincide with 2 the given t-norm T1 on [a, b] . These results can be applied everywhere when we search for an extremal t-norm that coincides with the given values on some subinterval of the unit interval.
6 Related Work The combination of privacy and learning has been approached in several contexts. Kasiviswanathan 2011 et al.  addressed the general problem of learning a concept class under diﬀerential privacy. Jain & Thakurta  studies the problem of releasing a diﬀerentially private predictor in the framework of kernel methods. The setting of these works is diﬀerent from ours as we do not release the output of a learning algorithm. Rather, we output private statistics used as input to learning algorithms.
14] and Blocki et al.  independently proposed schemes to provide diﬀerential privacy by bounding or truncating the degree of graphs. In this work we adopt the restricted sensitivity of Blocki et al. . There, a query on G is guaranteed to have a private response for any G, but high accuracy only if G is part of an hypothesis set G H ⊂ G (a subset of the space of graphs). Deﬁnition 22 (Restricted sensitivity. Blocki et al. (2013) ). For a query f over G H ⊂ G, with distance metric d(G, G ), the restricted sensitivity is RSf (G) = max G,G ∈G H |f (G) − f (G )| d(G, G ) .
Modeling Decisions for Artificial Intelligence: 12th International Conference, MDAI 2015, Skövde, Sweden, September 21-23, 2015, Proceedings by Vicenc Torra, Torra Narukawa