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Probability‐Generated Aggregators
Author(s) -
Kagan Evgeny,
Rybalov Alexander,
Siegelmann Hava,
Yager Ronald
Publication year - 2013
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21598
Subject(s) - probabilistic logic , probability distribution , t norm , applied probability , computer science , fuzzy logic , unit interval , norm (philosophy) , algebraic operation , theoretical computer science , algebra over a field , mathematics , algebraic number , fuzzy set , discrete mathematics , fuzzy number , artificial intelligence , pure mathematics , statistics , mathematical analysis , political science , law
The paper addresses a relation between logical reasoning and probability and presents probability‐generated aggregators. The obtained aggregators implement probability distributions for specification of generator functions; as it was proven in the paper, such implementation is always possible. In the paper, the relation between neutral element of the probabilistic uninorm and parameters of the underlying probability distribution is demonstrated, and a method for specification of the probabilistic uninorm, and thus—of the probability distribution using t ‐norm and t ‐conorm—is constructed. In addition, the obtained probabilistic uninorm and probabilistic absorbing norm or nullnorm are briefly considered as algebraic operations on the open unit interval. In is demonstrated, that, in general, the obtained algebra is nondistributive and depends on the distributions, which are used for generating probabilistic uninorm and absorbing norm. The obtained results bridge several gaps between fuzzy and probabilistic logics and provide a basis both for theoretical studies in the field and for practical techniques of digital/analog schemes synthesis and analysis.