B-spline curve interpolation model by using intuitionistic fuzzy approach

In this paper, B-spline curve interpolation model by using intuitionistic fuzzy set approach is introduced. Firstly, intuitionistic fuzzy control point relation is defined based on the intuitionistic fuzzy concept. Later, the intuitionistic fuzzy control point relation is blended with B-spline basis function. Through interpolation method, intuitionistic fuzzy B-spline curve model is visualized. Finally, some numerical examples and an algorithm to generate the desired curve is shown

B-spline curve interpolation model by using intuitionistic fuzzy approach

In this paper, B-spline curve interpolation model by using intuitionistic fuzzy set approach is introduced. Firstly, intuitionistic fuzzy control point relation is defined based on the intuitionistic fuzzy concept. Later, the intuitionistic fuzzy control point relation is blended with B-spline basis function. Through interpolation method, intuitionistic fuzzy B-spline curve model is visualized. Finally, some numerical examples and an algorithm to generate the desired curve is shown

Articles indexats publicats per autors de l'ETSAB

Aquest document recull els articles publicats per investigadors de l'ETSAB en revistes del Web of Science i de Scopus des de l'any 2000 fins el 2011.Preprin

Shape theory and mathematical design of a general geometric kernel through regular stratified objects

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This dissertation focuses on the mathematical design of a unified shape kernel for geometric computing, with possible applications to computer aided design (CAM) and manufacturing (CAM), solid geometric modelling, free-form modelling of curves and surfaces, feature-based modelling, finite element meshing, computer animation, etc. The generality of such a unified shape kernel grounds on a shape theory for objects in some Euclidean space. Shape does not mean herein only geometry as usual in geometric modelling, but has been extended to other contexts, e. g. topology, homotopy, convexity theory, etc. This shape theory has enabled to make a shape analysis of the current geometric kernels. Significant deficiencies have been then identified in how these geometric kernels represent shapes from different applications. This thesis concludes that it is possible to construct a general shape kernel capable of representing and manipulating general specifications of shape for objects even in higher-dimensional Euclidean spaces, regardless whether such objects are implicitly or parametrically defined, they have ‘incomplete boundaries’ or not, they are structured with more or less detail or subcomplexes, which design sequence has been followed in a modelling session, etc. For this end, the basic constituents of such a general geometric kernel, say a combinatorial data structure and respective Euler operators for n-dimensional regular stratified objects, have been introduced and discussed

Fuzzy Sets, Fuzzy Logic and Their Applications 2020

The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity

Scribe: A Clustering Approach To Semantic Information Retrieval

Information retrieval is the process of fulfilling a user?s need for information by locating items in a data collection that are similar to a complex query that is often posed in natural language. Latent Semantic Indexing (LSI) was the predominant technique employed at the National Institute of Standards and Technology?s Text Retrieval Conference for many years until limitations of its scalability to large data sets were discovered. This thesis describes SCRIBE, a modification of LSI with improved scalability. SCRIBE clusters its semantic index into discrete volumes described by high-dimensional extensions to computer graphics data structures. SCRIBE?s clustering strategy limits the number of items that must be searched and provides for sub-linear time complexity in the number of documents. Experimental results with a large, natural language document collection demonstrate that SCRIBE achieves retrieval accuracy similar to LSI but requires 1/10 the time

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Comparing Features of Three-Dimensional Object Models Using Registration Based on Surface Curvature Signatures

This dissertation presents a technique for comparing local shape properties for similar three-dimensional objects represented by meshes. Our novel shape representation, the curvature map, describes shape as a function of surface curvature in the region around a point. A multi-pass approach is applied to the curvature map to detect features at different scales. The feature detection step does not require user input or parameter tuning. We use features ordered by strength, the similarity of pairs of features, and pruning based on geometric consistency to efficiently determine key corresponding locations on the objects. For genus zero objects, the corresponding locations are used to generate a consistent spherical parameterization that defines the point-to-point correspondence used for the final shape comparison