A $Gamma$-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a $Gamma$-so-ring. In this paper we introduce the notions of subdirect product and $(phi,rho)$-product of $Gamma$-so-rings and study $(phi,rho)$-represen...

We study the use of variety and quality of a product line as strategic tools, and specifically the link between quality and the composition of product assortments. We observe that individual stores offer assortments such that the same ice cream flavors from brands within the same quality tier do not appear on store shelves at the same time. This suggests that retailers may use flavor selection ...

Programs of a software product line can be synthesized by composing modules that implement features. Besides high-level domain constraints that govern the compatibility of features, there are also low-level implementation constraints: a feature module can reference elements that are defined in other feature modules. Safe composition is the guarantee that programs composed from feature modules a...

We discuss the computational complexity of approximating maximum a posteriori inference in sum-product networks. We first show NP-hardness in trees of height two by a reduction from maximum independent set; this implies non-approximability within a sublinear factor. We show that this is a tight bound, as we can find an approximation within a linear factor in networks of height two. We then show...

Picture fuzzy relation is an important and powerful concept which suitable for describing correspondences between objects. It represents the strength of association elements picture sets. In this paper we have defined min-max composition relations some properties are explored based on definition. Also discussed max-min relations. Finally, application as illustration to show how applied in decis...

The product rate variation problem minimizes the variation in the rate at which different models of a common base product are produced on the assembly lines with the assumption of negligible switch-over cost and unit processing time for each copy of each model. The assumption of significant setup and arbitrary processing times forces the problem to be a two phase problem. The first phase determ...

‎    The Narumi-Katayama index is the first topological index defined by the product of some graph theoretical quantities. Let G be a simple graph. Narumi-Katayama index of G is defined as the product of the degrees of the vertices of G. In this paper, we define the Narumi-Katayama polynomial of G. Next, we investigate some properties of this polynomial for graphs and then, we obtain ...

In this paper, we propose a Modified nested sparse grid based Adaptive Stochastic Collocation Method (MASCM) for block-based Statistical Static Timing Analysis (SSTA). The proposed MASCM employs an improved adaptive strategy derived from the existing Adaptive Stochastic Collocation Method (ASCM) to approximate the key operator MAX during timing analysis. In contrast to ASCM which uses non-neste...

This paper presents a partial-order reduction method for performance analysis of max-plus timed systems. Amax-plus timed system is a network of automata, where the timing behavior of deterministic system tasks (events in an automaton) is captured in (max,+) matrices. These tasks can be characterized in various formalisms like synchronous data flow, Petri nets, or real-time calculus. The timing ...