Papers by Keyword: Set Theory

Abstract: Based on research performed by the author, a universal formal definition of the concept of Intelligent Buildings in terms of theoretical cybernetics, set theory, system analysis, functional analysis (measure theory, function theory) and mathematical logic is proposed for the first time. The definition includes the absolute and design levels of abstraction as well as the abstract definition of the Building Intelligence Quotient (BIQ) which can be extended to any aspect of the building sector such as applied theory, structural design practice and construction management practice. Relevant formal fundamentals of the proposed definitions are presented, and the prospects for the development of designated areas by means of technical regulation of these areas are discussed.

Abstract: Measurement error is traditionally represented with probability distributions. Although probabilistic representations of measurement error have been successfully employed in many analyses, such representations have been criticized for requiring more refined knowledge with respect to the existing error than that is really present. As a result, this paper proposes a general framework and process for estimating the measurement error based on evidence theory. In this research cumulative belief functions (CBFs) and cumulative plausibility functions (CPFs) are used to estimate measurement error. The estimation includes two steps:(1) modeling the parameters by means of a random set, and discrediting the random set to focal elements in finite numbers; (2)summarizing the propagation error. An example is demonstrated the estimation process.

Abstract: This paper puts across the various approaches and methods that have been proposed in the context of Fuzzy Mathematical Morphology. The underlying principles of Dilation & Erosion, the structuring elements used in various techniques, the unique variations put forth by researchers, new applications in spatial relationships, decision making, segmentation of medical images have been discussed.