In this paper, we investigate po-purity using finitely presented S-posets, and give some equivalent conditions under which an S-poset is absolutely po-pure. We also introduce strongly finitely presented S-posets to characterize absolutely pure S-posets. Similar to the acts, every finitely presented cyclic S-posets is isomorphic to a factor S-poset of a pomonoid S by a finitely generated right con...

By utilizing the ideas of fuzzy-weighted entropy and directed divergence appropriately selecting weights, several new measures fuzzy cross-entropy have been generated. Concurrently, some weighted suggested based on

We investigate the number of samples required for testing the monotonicity of a distribution with respect to an arbitrary underlying partially ordered set. Our first result is a nearly linear lower bound for the sample complexity of testing monotonicity with respect to the poset consisting of a directed perfect matching. This is the first nearly linear lower bound known for a natural non-symmet...

A join-completion of a poset is a completion for which each element is obtainable as a supremum, or join, of elements from the original poset. It is well known that the join-completions of a poset are in one-to-one correspondence with the closure systems on the lattice of up-sets of the poset. A ∆1-completion of a poset is a completion for which, simultaneously, each element is obtainable as a ...

A join-completion of a poset is a completion for which each element is obtainable as a supremum, or join, of elements from the original poset. It is well known that the join-completions of a poset are in one-to-one correspondence with the closure systems on the lattice of up-sets of the poset. A ∆1-completion of a poset is a completion for which, simultaneously, each element is obtainable as a ...

We give a generalization of possibility and necessity measures: their domains are extended towards fields of sets, and their codomains towards arbitrary complete lattices. In this way, these measures can be associated with (Q,≤)-fuzzy sets, where (Q,≤) is at least a poset. An important inconsistency problem, intricately linked with this association, is solved. It is argued that order lies at th...

In this contribution we present uniform goal-directed rules for the implicational fragments of the three main formalizations of fuzzy logic; namely, Łukasiewicz logic Ł, Gödel logic G, and Product logic Π. We begin with a historical overview of the goal-directed methodology, focussing in particular on the pioneering work of Dov Gabbay, then proceed by recalling the fundamental systems of fuzzy ...