In some statistical process monitoring applications, quality of a process or product is described by more than one ordinal factors called ordinal multivariate process. To show the relationship between these factors, an ordinal contingency table is used and modeled with ordinal log-linear model. In this paper, a new control charts based on ordinal-normal statistic is developed to monitor the ord...

Recently, the topic related to construction of triangular norms and conorms on bounded lattices using ordinal sums has been extensively studied. In this paper, we introduce a new sum an appropriate lattice. Also, give some illustrative examples for clarity. Then, show that method can be generalized by induction modified lattice, respectively. And provide examples.

For a regular cardinal κ, a formula of the modal μ-calculus isκ-continuous in a variable x if, on every model, its interpretation as a unaryfunction of x is monotone and preserves unions of κ-directed sets. We define thefragment Cא1 (x) of the modal μ-calculus and prove that all the formulas in thisfragment are א1-continuous. For each formula φ(x) of the modal μ-calculus,we ...

A subrecursive rewriting framework for the classical Kirby and Paris hydra battle is introduced. The termination of a natural rewrite system RH for the Hydra battle is shown by using ordinals and additionally by proving an upper bound on the derivation lengths in terms of a fast growing function of ordinal index ε0. It is shown that the RH -derivation lengths cannot be bounded by a fast growing...

Palindrome number conjecture: Take any non-palindromic natural with two or more digits, add its inverse ordinal number, continue to use the inverted of sum plus sum, repeat this process continuously. After a finite operations, palindrome must be obtained. We firstly give out several definitions: The pure-single-digit-of-sum is single digits that only count numbers same digit in vertical operati...

We study the problem of finding a small subset of items that is agreeable to all agents, meaning that all agents value the subset at least as much as its complement. Previous work has shown worst-case bounds, over all instances with a given number of agents and items, on the number of items that may need to be included in such a subset. Our goal in this paper is to efficiently compute an agreea...

For a regular cardinal κ, a formula of the modal μ-calculus is κ-continuous in a variable x if, on every model, its interpretation as a unary function of x is monotone and preserves unions of κ-directed sets. We define the fragment Cא1 (x) of the modal μ-calculus and prove that all the formulas in this fragment are א1-continuous. For each formula φ(x) of the modal μ-calculus, we construct a for...

For a regular cardinal $\kappa$, a formula of the modal $\mu$-calculus is $\kappa$-continuous in a variable x if, on every model, its interpretation as a unary function of x is monotone and preserves unions of $\kappa$-directed sets. We define the fragment C $\aleph 1 (x) of the modal $\mu$-calculus and prove that all the formulas in this fragment are $\aleph 1-continuous. For each formula $\ph...

We prove that when divisibility is added to a residuated multilattice, this causes the multilattice structure to collapse down to a residuated lattice. This motivates the study of semi-divisibility and regularity on residuated multilattices. The ordinal sum construction is also applied to residuated multilattices as a way to construct new examples of both residuated multilattices and consistent...

Triangular subnorms are associative commutative non-decreasing operations on the unit interval, upper bounded by the minimum. Continuous triangular subnorms are shown to be ordinal sum of Archimedean continuous t-subnorms with at most one proper t-subnorm summand. Special attention is paid to generate continuous t-subnorms. An application of continuous t-subnorms to the construction of left-con...