In this article we introduce and study the notion of operational closure: a transitive set d is called operationally closed iff it contains all constants of OST and any operation f ∈ d applied to an element a ∈ d yields an element fa ∈ d, provided that f applied to a has a value at all. We will show that there is a direct relationship between operational closure and stability in the sense that ...

Publications are increasingly (often wrongly) being used as research outputs. Furthermore, ‘impacts’ of such publications are often (wrongly as well) measured using ‘citations’. Popular metric, like the ‘Hirsch index’, or ‘h-index’ is used as yardstick for judging the quality of individual researchers. However, there are many controversies around it, whether it is a good yardstick, which could ...

The Operational Transformation (OT) approach, used in many collaborative editors, allows a group of users to concurrently update replicas of a shared object and exchange their updates in any order. The basic idea of this approach is to transform any received update operation before its execution on a replica of the object. This transformation aims to ensure the convergence of the different repl...

Small-step semantics and big-step semantics are two styles for operationally defining the meaning of programming languages. Small-step semantics are given as a relation between program configurations, relation which denotes one computational step; big-step semantics are given as a relation directly associating to each program configuration the corresponding final configuration. Small-step seman...

Item parameter calibration is important for tests based on item response theory, because the scoring, equating, bias analysis of the test, and item selection in adaptive tests are all based on the item parameters. As a test is continuously administered, item calibration needs to be conducted for new items at intervals to replace overexposed, obsolete, or flawed items in the item bank. Although ...

In this paper, we construct a fully homomorphic encryption (FHE) scheme over integers with the message space ZQ for any prime Q. Even for the binary case Q = 2, our decryption circuit has a smaller degree than that of the previous scheme; the multiplicative degree is reduced from O(λ(log λ)) to O(λ), where λ is the security parameter. We also extend our FHE scheme to a batch FHE scheme.

The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators for neutrosophic sets by the extension of the Dombi operations, this paper firstly presents the Dombi operations of s...