“…It elaborates Manka’s proof of the fixed-point property of arcwise connected hereditarily unicoherent continua, based on the connection he observed between set theory and fixed-point theory via a certain partial order. …”
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“…The book covers a range of topics, from the very foundations (numbers, set theory) to basic abstract algebra (groups, rings, fields), driven throughout by the need to understand concrete equations and problems, such as determining which numbers are sums of squares. …”
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“…RESULTS: p3d is an object oriented Python module that adds a simple yet powerful interface to the Python interpreter to process and analyse three dimensional protein structure files (PDB files). p3d's strength arises from the combination of a) very fast spatial access to the structural data due to the implementation of a binary space partitioning (BSP) tree, b) set theory and c) functions that allow to combine a and b and that use human readable language in the search queries rather than complex computer language. …”
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“…Our approach is not based on explicit intergroup conflict, but instead uses evolutionary set theory. People can move between sets. Successful sets attract members, and successful strategies gain imitators. …”
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“…Our methods allow learning of a simple, consistent, and reliable multiclass theory by combining the rules of the multiple one-versus-rest theories into one rule list or rule set theory. Empirical evaluation over a number of data sets shows that our proposed methods produce coherent and accurate rule models from the rules learned by the ILP system of Aleph.…”
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“…This study suggests potential application areas and new research trends concerning rough set theory.…”
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“…To better simulate human subjectivity and ambiguity for understanding scene images, the current study proposes an emotional semantic annotation method for scene images based on fuzzy set theory. A fuzzy membership degree was calculated to describe the emotional degree of a scene image and was implemented using the Adaboost algorithm and a back-propagation (BP) neural network. …”
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“…To realize the significance of the unified dataset, we adopted a well-known rough set theory based rules creation process to create rules from the unified dataset. …”
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“…Uncertainty measures are important for knowledge discovery and data mining. Rough set theory (RST) is an important tool for measuring and processing uncertain information. …”
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“…To overcome drawbacks from the lack of exact probability data for the basic events, fuzzy set theory is employed and the probability data of each basic event is treated as intuitionistic trapezoidal fuzzy numbers. …”
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“…This includes the definition of alternative integrity concepts for space and time based on set theory and interval mathematics, establishing new types of maps that report on the trustworthiness of the represented information, as well as taking advantage of collaboration by improved filters incorporating person and object tracking. …”
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“…This paper proposes an information fusion method in which rough set theory (RST) is combined with an improved Dempster–Shafer (DS) evidence theory to identify various system operation states. …”
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“…This work is motivated by the fact that while dissimilarity measures have been surveyed in the fields of evidence theory and fuzzy set theory, no comprehensive survey is yet available for fuzzy evidence theory. …”
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“…Throughout the paper we work within constructive set theory.…”
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“…Cohen’s first model is a model of Zermelo–Fraenkel set theory in which there is a Dedekind-finite set of real numbers, and it is perhaps the most famous model where the Axiom of Choice fails. …”
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“…However, this hierarchical framework must consider unnecessary attributes and the interrelationships between the aspects and the criteria. Hence, fuzzy set theory is used for screening out the unnecessary attributes, a decision-making and trial evaluation laboratory (DEMATEL) is proposed to manage the complex interrelationships among the aspects and attributes, and interpretive structural modeling (ISM) is used to divide the hierarchy and finally construct a hierarchical framework. …”
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“…Fuzzy set theory and its extended form have been widely used in multiple-attribute group decision-making (MAGDM) problems, among which the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) got a lot of attention for its ability of capturing information denoted by interval values. …”
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“…To address this problem, we offer a fresh insight into rough set theory from the perspective of a positive approximation set. …”
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“…In this paper, we focus on the main concepts of rough set theory induced from the idea of neighborhoods. First, we put forward new types of maximal neighborhoods (briefly, [Formula: see text] -neighborhoods) and explore master properties. …”
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“…The rankings were constructed through the proposed weighting factor based on the concept of decision reducts—a feature reduction mechanism embedded in the rough set theory. Classical rough sets operate only in discrete input space by indiscernibility relation. …”
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