On almost equitable uninorms

A general algebraic system M is considered with two binary operations. The family of all measurable functions with values in the unit interval is a motivating example. A state is a morphism from M to the unit interval, an observable is a morphism from the family of Borel sets to M. A joint distribution of two observables is constructed. It is applied for the construction of the sum of observables and for a representation of conditional probability.

Journal Article Preservation theorems for MTL-chains Get access C. J. Van Alten C. J. Van Alten School of Computer Science, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa E-mail: Clint.VanAlten@wits.ac.za Search for other works by this author on: Oxford Academic Google Scholar Logic Journal of the IGPL, Volume 19, Issue 3, June 2011, Pages 490–511, https://doi.org/10.1093/jigpal/jzp088 Published: 29 January 2010 Article history Received: 30 March 2009 Published: 29 January 2010

Uninorms, as binary operations on the unit interval, have been widely applied in fuzzy set theory. In this paper, the class of conjunctive left-continuous uninorms of which the underlying triangular norm is weak nilpotent minimum are discussed. This class of uninorms are characterized via the ordinal sum construction of Clifford for some cases.

An illustrative overview is laid out in this paper detailing the different classes of binary aggregation operations on the unit interval [0, 1] with an absorbing element. The authors focused on the characterization of specific well-known classes of these operations, including nullnorms, T-uninorms, S-uninorms and bi-uninorms, along with their interaction.

We consider a model of information aggregation in which there are two possible states of the world and agents receive private signals from the set of probability measures over the binary state space – the unit interval. For a reasonably general set of signal densities, a unique symmetric Bayesian Nash equilibrium in responsive strategies exists and voting is informative in this equilibrium. Asymptotic analysis shows that society makes the correct decision almost surely as population size grows. In contrast to findings of Feddersen and Pesendorfer (1998) in the finite signal space case and Duggan and Martinelli (1999) in an alternative model in which the signal space is a continuum, this result holds for unanimity rule. The key to the efficiency of unanimity rule is that there are perfectly informative (or at least nearly perfectly informative) signals. A corollary to the asymptotic efficiency result is that for all rules the collective performs better than a single agent's dictatorship for large but finite populations. This need not be true for arbitrary population sizes.

We give the general form of an idempotent, associative, nondecreasing and continuous binary aggregation operation in a connected order topological space. The particular case of the unit interval is studied and the choice of weights is also analized. Possible generalizations for more than two arguments are also proposed.

We study some inequalities relating the behavior of certain binary operations of the unit interval on some numerical series.

One of the basic operations required to gather more information about an object is called information aggregation or data fusion. The process requires recognition of a semantic object and gathering the new information into the collection that already exists for that object. Another related operation is collecting a set of distinct semantic objects that are similar. These operations become complicated in the presence of schema and extent heterogeneity and semantic similarity. Although a rich body of research addressed these issues in the literature, a database language support is yet available possibly because an algebraic formulation of these concepts was absent. An algebraic characterization is needed for query plan generation, optimization and query processing. In this paper, we propose two new binary operators called link (λ) and combine (χ) that capture the spirit of vertical and horizontal data fusion. The proposed operators leverage the development in schema matching and key identification technologies by casting them as user selectable functions μ and κ. We show that link and combine are generalized versions of traditional join and union operations. We also propose two extensions of SQL that exploits these two operators and opens up many optimization possibilities. We also point out that link and combine are also useful for semantic data integration and are currently being used in LifeDB data management system for Life Sciences applications.