Grouping fuzzy sets by similarity

a b s t r a c t The paper presents results on factorization of systems of fuzzy sets. The factorization consists in grouping those fuzzy sets which are pairwise similar at least to a prescribed degree a. An obstacle to such factorization, well known in fuzzy set theory, is the fact that ''being similar at least to degree a" is not an equivalence relation because, in general, it is not transitive. As a result, ordinary factorization using equivalence classes cannot be used. This obstacle can be overcome by considering maximal blocks of fuzzy sets which are pairwise similar at least to degree a. We show that one can introduce a natural complete lattice structure on the set of all such maximal blocks and study this lattice. This lattice plays the role of a factor structure for the original system of fuzzy sets. Particular examples of our approach include factorization of fuzzy concept lattices and factorization of residuated lattices

Clustering and its Application in Requirements Engineering

Large scale software systems challenge almost every activity in the software development life-cycle, including tasks related to eliciting, analyzing, and specifying requirements. Fortunately many of these complexities can be addressed through clustering the requirements in order to create abstractions that are meaningful to human stakeholders. For example, the requirements elicitation process can be supported through dynamically clustering incoming stakeholders’ requests into themes. Cross-cutting concerns, which have a significant impact on the architectural design, can be identified through the use of fuzzy clustering techniques and metrics designed to detect when a theme cross-cuts the dominant decomposition of the system. Finally, traceability techniques, required in critical software projects by many regulatory bodies, can be automated and enhanced by the use of cluster-based information retrieval methods. Unfortunately, despite a significant body of work describing document clustering techniques, there is almost no prior work which directly addresses the challenges, constraints, and nuances of requirements clustering. As a result, the effectiveness of software engineering tools and processes that depend on requirements clustering is severely limited. This report directly addresses the problem of clustering requirements through surveying standard clustering techniques and discussing their application to the requirements clustering process

FCAIR 2012 Formal Concept Analysis Meets Information Retrieval Workshop co-located with the 35th European Conference on Information Retrieval (ECIR 2013) March 24, 2013, Moscow, Russia

International audienceFormal Concept Analysis (FCA) is a mathematically well-founded theory aimed at data analysis and classifiation. The area came into being in the early 1980s and has since then spawned over 10000 scientific publications and a variety of practically deployed tools. FCA allows one to build from a data table with objects in rows and attributes in columns a taxonomic data structure called concept lattice, which can be used for many purposes, especially for Knowledge Discovery and Information Retrieval. The Formal Concept Analysis Meets Information Retrieval (FCAIR) workshop collocated with the 35th European Conference on Information Retrieval (ECIR 2013) was intended, on the one hand, to attract researchers from FCA community to a broad discussion of FCA-based research on information retrieval, and, on the other hand, to promote ideas, models, and methods of FCA in the community of Information Retrieval

Towards Ordinal Data Science

Order is one of the main instruments to measure the relationship between objects in (empirical) data. However, compared to methods that use numerical properties of objects, the amount of ordinal methods developed is rather small. One reason for this is the limited availability of computational resources in the last century that would have been required for ordinal computations. Another reason - particularly important for this line of research - is that order-based methods are often seen as too mathematically rigorous for applying them to real-world data. In this paper, we will therefore discuss different means for measuring and ‘calculating’ with ordinal structures - a specific class of directed graphs - and show how to infer knowledge from them. Our aim is to establish Ordinal Data Science as a fundamentally new research agenda. Besides cross-fertilization with other cornerstone machine learning and knowledge representation methods, a broad range of disciplines will benefit from this endeavor, including, psychology, sociology, economics, web science, knowledge engineering, scientometrics

On-Device Recommender Systems: A Comprehensive Survey

Recommender systems have been widely deployed in various real-world applications to help users identify content of interest from massive amounts of information. Traditional recommender systems work by collecting user-item interaction data in a cloud-based data center and training a centralized model to perform the recommendation service. However, such cloud-based recommender systems (CloudRSs) inevitably suffer from excessive resource consumption, response latency, as well as privacy and security risks concerning both data and models. Recently, driven by the advances in storage, communication, and computation capabilities of edge devices, there has been a shift of focus from CloudRSs to on-device recommender systems (DeviceRSs), which leverage the capabilities of edge devices to minimize centralized data storage requirements, reduce the response latency caused by communication overheads, and enhance user privacy and security by localizing data processing and model training. Despite the rapid rise of DeviceRSs, there is a clear absence of timely literature reviews that systematically introduce, categorize and contrast these methods. To bridge this gap, we aim to provide a comprehensive survey of DeviceRSs, covering three main aspects: (1) the deployment and inference of DeviceRSs (2) the training and update of DeviceRSs (3) the security and privacy of DeviceRSs. Furthermore, we provide a fine-grained and systematic taxonomy of the methods involved in each aspect, followed by a discussion regarding challenges and future research directions. This is the first comprehensive survey on DeviceRSs that covers a spectrum of tasks to fit various needs. We believe this survey will help readers effectively grasp the current research status in this field, equip them with relevant technical foundations, and stimulate new research ideas for developing DeviceRSs