Subsethood Measures of Spatial Granules

Subsethood, which is to measure the degree of set inclusion relation, is predominant in fuzzy set theory. This paper introduces some basic concepts of spatial granules, coarse-fine relation, and operations like meet, join, quotient meet and quotient join. All the atomic granules can be hierarchized by set-inclusion relation and all the granules can be hierarchized by coarse-fine relation. Viewing an information system from the micro and the macro perspectives, we can get a micro knowledge space and a micro knowledge space, from which a rough set model and a spatial rough granule model are respectively obtained. The classical rough set model is the special case of the rough set model induced from the micro knowledge space, while the spatial rough granule model will be play a pivotal role in the problem-solving of structures. We discuss twelve axioms of monotone increasing subsethood and twelve corresponding axioms of monotone decreasing supsethood, and generalize subsethood and supsethood to conditional granularity and conditional fineness respectively. We develop five conditional granularity measures and five conditional fineness measures and prove that each conditional granularity or fineness measure satisfies its corresponding twelve axioms although its subsethood or supsethood measure only hold one of the two boundary conditions. We further define five conditional granularity entropies and five conditional fineness entropies respectively, and each entropy only satisfies part of the boundary conditions but all the ten monotone conditions

A Logic Approach to Granular computing

This article was originally published by the International Journal of Cognitive Informatics and Natural IntelligenceGranular computing is an emerging field of study that attempts to formalize and explore methods and heuristics of human problem solving with multiple levels of granularity and abstraction. A fundamental issue of granular computing is the representation and utilization of granular structures. The main objective of this article is to examine a logic approach to address this issue. Following the classical interpretation of a concept as a pair of intension and extension, we interpret a granule as a pair of a set of objects and a logic formula describing the granule. The building blocks of granular structures are basic granules representing an elementary concept or a piece of knowledge. They are treated as atomic formulas of a logic language. Different types of granular structures can be constructed by using logic connectives. Within this logic framework, we show that rough set analysis (RSA) and formal concept analysis (FCA) can be interpreted uniformly. The two theories use multilevel granular structures but differ in their choices of definable granules and granular structures.NSERC Canada Discovery gran

In Search of Effective Granulization with DTRS for Ternary Classification

This article was originally published by the International Journal of Cognitive Informatics and Natural IntelligenceDecision-Theoretic Rough Set (DTRS) model provides a three-way decision approach to classification problems, which allows a classifier to make a deferment decision on suspicious examples, rather than being forced to make an immediate determination. The deferred cases must be reexamined by collecting further information. Although the formulation of DTRS is intuitively appealing, a fundamental question that remains is how to determine the class of the deferment examples. In this paper, the authors introduce an adaptive learning method that automatically deals with the deferred examples by searching for effective granulization. A decision tree is constructed for classification. At each level, the authors sequentially choose the attributes that provide the most effective granulization. A subtree is added recursively if the conditional probability lies in between of the two given thresholds. A branch reaches its leaf node when the conditional probability is above or equal to the first threshold, or is below or equal to the second threshold, or the granule meets certain conditions. This learning process is illustrated by an example.NSERC Alexander Graham Bell Canada Graduate Scholarship and NSERC Canada Discovery grant

Joint design-time and post-silicon optimization for digitally tuned analog circuits,” ICCAD

Abstract-Joint design time and post-silicon optimization for analog circuits has been an open problem in literature because of the complex nature of analog circuit modeling and optimization. In this paper we formulate the co-optimization problem for digitally tuned analog circuits to optimize the parametric yield, subject to power and area constraints. A general optimization framework combing the branch-andbound algorithm and gradient ascent method is proposed. We demonstrate our framework with two examples in high-speed serial link, the transmitter design and the phase-locked-loop (PLL) design. Simulation results show that compared with the design heuristic from analog designers' perspective, joint design-time and post-silicon optimization can improve the yield by up to 47% for transmitter design and up to 56% for PLL design under the same area and power constraints. To the best of the authors' knowledge, this is the first yield-driven analog circuit design technique that optimizes post-silicon tuning together with the design-time optimization

A Contrastive Corpus Study on Lexical Features of the English Translation of the Report of the 20th and 19th CPC National Congress

As the channel spreads the Chinese voice and promotes Chinese culture, the status of political document translation is self-evident with the deepening of global communication. Taking the English translation of the reports of the 20th and the 19th CPC National Congress as examples, this paper makes a contrastive study of their lexical features in a corpus-based way. With the assistance of corpus analysis software such as AntConc, TagAnt and WordSmith4.0, the author investigates TTR (type-token ratio), lexical density, average sentence length, high-frequency words, and keywords between two reports. It is found that the report of the 20th CPC Nation Congress has more diversified and native expressions with fewer words used, which provides a guiding significance for the English translation of political documents

Visualize and Learn Sorting Algorithms in Data Structure Subject in a Game-based Learning

The Data Structure subject is an essential Computer Science subject. Sorting algorithms are important topics in Data Structure where students are expected to learn how various sorting algorithms work and their time complexities. Some sorting algorithms may easily cause confusions to novice students, as they usually find it challenging to understand and memorize these algorithms. There is a need to find a means of technology enhanced learning to improve the learning process of students. Game based learning is a pedagogy where students learn through game playing. This mode of learning could effectively engage students to focus on the learning topics more efficiently. The study uses a sorting algorithm serious game to allow students to learn four types of sorting algorithms: Bubble sort, Selection sort, Insertion sort and Quick sort. The students would carry out self-directed learning lecture materials in the serious game, followed by refreshing their learning using a visualizer, and lastly reinforce their learning through playing a sorting serious game. Two groups of students participate in the experiment, a control group and an experiment group. The experiment group that sues the sorting algorithm games achieves better results, compared to the control group who learns without the serious game. Game-based learning provides a positive learning experience to the students that could improve the learning effectiveness. Coupled with technology such as VR headsets as a future upgrade, it would be a niche factor that would create an immersive learning experience to engage the students and enhance their learning in a virtual environment