for every positive integer k, a set s of vertices in a graph g = (v;e) is a k- tuple dominating set of g if every vertex of v -s is adjacent to at least k vertices and every vertex of s is adjacent to at least k - 1 vertices in s. the minimum cardinality of a k-tuple dominating set of g is the k-tuple domination number of g. when k = 1, a k-tuple domination number is the well-studied domination...

With the current heightened promotion of environmental awareness, issues related to protection have become a critical component economic development. The emergence new environment-friendly materials and simple packaging, other awareness demands in recent years, prompted manufacturers pay more attention planning greener production supply processes than before. Many scholars been urged investigat...

‎For any integer $kgeq 1$‎, ‎a set $S$ of vertices in a graph $G=(V,E)$ is a $k$-‎tuple total dominating set of $G$ if any vertex‎ ‎of $G$ is adjacent to at least $k$ vertices in $S$‎, ‎and any vertex‎ ‎of $V-S$ is adjacent to at least $k$ vertices in $V-S$‎. ‎The minimum number of vertices of such a set‎ ‎in $G$ we call the $k$-tuple total restrained domination number of $G$‎. ‎The maximum num...

Ngram-based Statistical Machine Translation relies on a standard Ngram language model of tuples to estimate the translation process. In training, this translation model requires a segmentation of each parallel sentence, which involves taking a hard decision on tuple segmentation when a word is not linked during word alignment. This is especially critical when this word appears in the target lan...

Building green airports can be regarded as among the most promising routes to sustainable development of ecosystems and human health. This study aims at addressing problem airport plan selection under an uncertain context by developing multiattribute group decision making (MAGDM) model. In proposed model, assessment information is characterized in form a proportional hesitant 2-tuple linguistic...