Interpretations of belief functions in approximation operators by covering

The rough set theory and the evidence theory are two important methods used to deal with uncertainty. The relationships between the rough set theory and the evidence theory have been discussed. In covering rough set theory, several pairs of covering approximation operators are characterized by belief and plausibility functions. The purpose of this paper is to review and examine interpretations of belief functions in covering approximation operators. Firstly, properties of the belief structures induced by two pairs of covering approximation operators are presented. Then, for a belief structure with the properties, there exists a probability space with a covering such that the belief and plausibility functions defined by the given belief structure are, respectively, the belief and plausibility functions induced by one of the two pairs of covering approximation operators. Moreover, two necessary and sufficient conditions for a belief structure to be the belief structure induced by one of the two pairs of covering approximation operators are presented.

A Computational View on the Nature of Reward and Value in Anhedonia

Anhedonia—a common feature of depression—encompasses a reduction in the subjective experience and anticipation of rewarding events, and a reduction in the motivation to seek out such events. The presence of anhedonia often predicts or accompanies treatment resistance, and as such better interventions and treatments are important. Yet the mechanisms giving rise to anhedonia are not well-understood. In this chapter, we briefly review existing computational conceptualisations of anhedonia. We argue that they are mostly descriptive and fail to provide anexplanatory account of why anhedonia may occur. Working within the framework of reinforcement learning, we examine two potential computational mechanisms that could give rise to anhedonic phenomena. First, we show how anhedonia can arise in multidimensional drive reduction settings through a trade-off between different rewards or needs. We then generalize this in terms of model-based value inference and identify a key role for associational belief structure. We close with a brief discussion of treatment implications of both of these conceptualisations. Insummary, computational accounts of anhedonia have provided a useful descriptive framework. Recent advances in reinforcement learning suggest promising avenues by which the mechanisms underlying anhedonia may be teased apart, potentially motivating novel approaches to treatment.

Natural Matter

Studies of lived religion have shown that from the perspective of the early modern laity, stark divisions between religion, magic, and superstition were largely absent from daily life. This chapter establishes how the division of ‘religious’ objects from secular or ‘magical’ objects in the early modern period is problematic. In particular, it shows how amulets made from natural matter, such as gemstones and animal teeth, can be reintegrated among religious objects. The evidence of amulets and rings reveals the connections of the cosmos, showing how men and women used these items to negotiate the divine and to control the ‘exigencies of daily life’. There was logic to how the divine could work through these tiny shards of stone or animal matter. From a lay perspective, the use of amulets and precious stones was not ‘enchantment’, but part of a developed belief structure that located the divine in the natural environment and that was tied to natural philosophy.

A data fusion method in wireless sensor network based on belief structure

Considering the issue with respect to the high data redundancy and high cost of information collection in wireless sensor nodes, this paper proposes a data fusion method based on belief structure to reduce attribution in multi-granulation rough set. By introducing belief structure, attribute reduction is carried out for multi-granulation rough sets. From the view of granular computing, this paper studies the evidential characteristics of incomplete multi-granulation ordered information systems. On this basis, the positive region reduction, belief reduction and plausibility reduction are put forward in incomplete multi-granulation ordered information system and analyze the consistency in the same level and transitivity in different levels. The positive region reduction and belief reduction are equivalent, and the positive region reduction and belief reduction are unnecessary and sufficient conditional plausibility reduction in the same level, if the cover structure order of different levels are the same the corresponding equivalent positive region reduction. The algorithm proposed in this paper not only performs three reductions, but also reduces the time complexity largely. The above study fuses the node data which reduces the amount of data that needs to be transmitted and effectively improves the information processing efficiency.

A Data Fusion Method in Wireless Sensor Network Based on Belief Structure

Considering the issue with respect to the high data redundancy and high cost of information collection in wireless sensor nodes, this paper proposes a data fusion method based on belief structure to reduce attribution in multi-granulation rough set. By introducing belief structure, attribute reduction is carried out for multi-granulation rough sets. From the view of granular computing, this paper studies the evidential characteristics of incomplete multi-granulation ordered information systems. On this basis, the positive region reduction, belief reduction and plausibility reduction are put forward in incomplete multi-granulation order information system, and analyze the consistency in the same level and transitivity in different levels. The positive region reduction and belief reduction are equivalent, and the positive region reduction and belief reduction is unnecessary and sufficient conditional plausibility reduction in the same level; if the cover structure order of different levels are the same, the corresponding equivalent positive region reduction. The algorithm proposed in this paper not only performs three reductions, but also reduces the time complexity largely. The above study fuses the node data which reduces the amount of data that needs to be transmitted and effectively improves the information processing efficiency.