The determining of alpha value for alpha-cut operation by using triangular polygon centroid

Fuzzy geometric modeling is a model that incorporates two major fields: fuzzy set theory and also geometric modeling. This idea is utilized in fuzzy set theory to define uncertainty data using the definitions of a fuzzy number. This method is then used for geometric modeling to generate a curve or surface using any parametric function such as Spline, Bezier, and B-spline. These two primary areas can be combined since they share similar features of defining and modeling a set of data points. Several steps have to be completed to produce the crisp fuzzy output, including defining, fuzzification, and defuzzification. The triangular polygon centroid will be used to determine the alpha value of the fuzzification process (alpha-cut operation)

Application Of Fuzzy Mathematics Methods To Processing Geometric Parameters Of Degradation Of Building Structures

The aim of research is formalization of the expert experience, which is used in processing geometric parameters of building structure degradation, using fuzzy mathematics. Materials that are used to specify fuzzy models are contained in expert assessments and scientific and technical reports on the technical condition of buildings. The information contained in the reports and assessments is presented in text form and is accompanied by a large number of photographs and diagrams. Model specification methods, based on the analysis of such information on the technical state of structures with damages and defects of various types, primarily lead to difficulties associated with the presentation of knowledge and require the formalization of expert knowledge and experience in the form of fuzzy rules. Approbation and adaptation of the rules is carried out in the process of further research taking into account the influence of random loads and fields. The scientific novelty of the work is expanding of the knowledge base due to the geometric parameters of structural degradation, on the basis of which a fuzzy conclusion about their technical state in the systems of fuzzy product rules at different stages of the object's life cycle is realized. The results of the work are presented in the form of a formalized description of the geometric parameters of degradation. The knowledge presented in the work is intended for the development of technical documentation that is used at the pre-project stage of building reconstruction, but the gained experience is the source of information on the basis of which a constructive solution is selected in the design process of analogical objects. In addition, the knowledge gained from the analysis of expert assessments of the state of various designs is necessary for development of automated expert evaluation processing systems. The use of such evaluation systems will significantly reduce the risks of the human factor associated with the errors in the specification of models for predicting the processes of structural failure at various stages of ensuring the reliability and safety of buildings

Geometric and form feature recognition tools applied to a design for assembly methodology

The paper presents geometric tools for an automated Design for Assembly (DFA) assessment system. For each component in an assembly a two step features search is performed: firstly (using the minimal bounding box) mass, dimensions and symmetries are identified allowing the part to be classified, according to DFA convention, as either rotational or prismatic; secondly form features are extracted allowing an effective method of mechanised orientation to be determined. Together these algorithms support the fuzzy decision support system, of an assembly-orientated CAD system known as FuzzyDFA

Quantitative analysis of properties and spatial relations of fuzzy image regions

Properties of objects and spatial relations between objects play an important role in rule-based approaches for high-level vision. The partial presence or absence of such properties and relationships can supply both positive and negative evidence for region labeling hypotheses. Similarly, fuzzy labeling of a region can generate new hypotheses pertaining to the properties of the region, its relation to the neighboring regions, and finally, the labels of the neighboring regions. In this paper, we present a unified methodology to characterize properties and spatial relationships of object regions in a digital image. The proposed methods can be used to arrive at more meaningful decisions about the contents of the scene

Fuzzy clustering with volume prototypes and adaptive cluster merging

Two extensions to the objective function-based fuzzy clustering are proposed. First, the (point) prototypes are extended to hypervolumes, whose size can be fixed or can be determined automatically from the data being clustered. It is shown that clustering with hypervolume prototypes can be formulated as the minimization of an objective function. Second, a heuristic cluster merging step is introduced where the similarity among the clusters is assessed during optimization. Starting with an overestimation of the number of clusters in the data, similar clusters are merged in order to obtain a suitable partitioning. An adaptive threshold for merging is proposed. The extensions proposed are applied to Gustafson–Kessel and fuzzy c-means algorithms, and the resulting extended algorithm is given. The properties of the new algorithm are illustrated by various examples

Intelligent computational sketching support for conceptual design

Sketches, with their flexibility and suggestiveness, are in many ways ideal for expressing emerging design concepts. This can be seen from the fact that the process of representing early designs by free-hand drawings was used as far back as in the early 15th century [1]. On the other hand, CAD systems have become widely accepted as an essential design tool in recent years, not least because they provide a base on which design analysis can be carried out. Efficient transfer of sketches into a CAD representation, therefore, is a powerful addition to the designers' armoury.It has been pointed out by many that a pen-on-paper system is the best tool for sketching. One of the crucial requirements of a computer aided sketching system is its ability to recognise and interpret the elements of sketches. 'Sketch recognition', as it has come to be known, has been widely studied by people working in such fields: as artificial intelligence to human-computer interaction and robotic vision. Despite the continuing efforts to solve the problem of appropriate conceptual design modelling, it is difficult to achieve completely accurate recognition of sketches because usually sketches implicate vague information, and the idiosyncratic expression and understanding differ from each designer