Product (mathematics)

About: Product (mathematics) is a research topic. Over the lifetime, 44382 publications have been published within this topic receiving 377809 citations.

Independence in Utility Theory with Whole Product Sets

Abstract: One of the most important concepts in value theory or utility theory is the notion of independence among variables or additivity of values. Its importance stems from numerous multiple-criteria procedures used for rating people, products, and other things. Most of these rating procedures rely on the notion of independence often implicitly for their validity. However, a satisfactory definition of independence additivity, based on multi-dimensional consequences and hypothetical gambles composed of such consequences, has not appeared. This paper therefore presents a definition of independence for cases where the set of consequences X is a product set X1 × X2 × â‹¯ × Xn, each element in X being an ordered n-tuple x1, x2, ', xn. The definition is stated in terms of indifference between special pairs of gambles formed from X. It is then shown that if the condition of the definition holds, the utility of each x1, x2, ', xn in X can be written in the additive form I†x1, x2, ', xn = I†1x1 + I†2x2 + ⋯ + I†nxn, where I†i is a real-valued function defined on the set Xi, i = 1, 2, ', n. The development is free of any specific assumptions about I† e.g., continuity, differentiability except that it be a von Neumann-Morgenstern utility function, and places no restrictions on the natures of the Xi.

Implementing product line variabilities

Abstract: Software product lines have numerous members. Thus, a product line infrastructure must cover various systems. This is the significant difference to usual software systems and the reason for additional requirements on the various assets present during software product line engineering. It is imperative that they support the description of the product line as a whole, as well as its instantiation for the derivation of individual products.Literature has already addressed how to create and instantiate generic product line assets, such as domain models and architectures to generate instance specific ones [1, 2, 3], yet little attention has been given on how to actually deal with this genericity at the code level.This paper addresses the issue of handling product line variability at the code level. To this end various implementation approaches are examined with respect to their use in a product line context.

Neural Sentiment Classification with User and Product Attention

Abstract: Document-level sentiment classification aims to predict user’s overall sentiment in a document about a product. However, most of existing methods only focus on local text information and ignore the global user preference and product characteristics. Even though some works take such information into account, they usually suffer from high model complexity and only consider wordlevel preference rather than semantic levels. To address this issue, we propose a hierarchical neural network to incorporate global user and product information into sentiment classification. Our model first builds a hierarchical LSTM model to generate sentence and document representations. Afterwards, user and product information is considered via attentions over different semantic levels due to its ability of capturing crucial semantic components. The experimental results show that our model achieves significant and consistent improvements compared to all state-of-theart methods. The source code of this paper can be obtained from https://github. com/thunlp/NSC.

Toward a Product System Modularity Construct: Literature Review and Reconceptualization

Abstract: Product modularity has been discussed in engineering and management literature for over forty years. During this time span, definitions and views on the meaning of product modularity proliferated to the extent that it is difficult to understand the essential traits of the concept. While definitional ambiguity is often a byproduct of academic debate, it hinders the advancement of scientific knowledge as well. This paper aims to move a step forward toward a more precise definition of product modularity, by articulating a product system modularity construct in the domain of tangible, assembled artifacts. More precisely, the paper constitutively defines product modularity in terms of component separability and component combinability. An indirect operational definition for product modularity is then proposed by operationalizing component separability and component combinability. The proposed definition is finally related to other definitional perspectives synthesized by a literature review: component commonality, function binding, interface standardization, and loose coupling. In this way, the nomological network of the product modularity construct is laid out. Construct validation activities are left to further research