On conjunctive complex fuzzification of Lagrange's theorem of ξ−CFSG

The application of a complex fuzzy logic system based on a linear conjunctive operator represents a significant advancement in the field of data analysis and modeling, particularly for studying physical scenarios with multiple options. This approach is highly effective in situations where the data involved is complex, imprecise and uncertain. The linear conjunctive operator is a key component of the fuzzy logic system used in this method. This operator allows for the combination of multiple input variables in a systematic way, generating a rule base that captures the behavior of the system being studied. The effectiveness of this method is particularly notable in the study of phenomena in the actual world that exhibit periodic behavior. The foremost aim of this paper is to contribute to the field of fuzzy algebra by introducing and exploring new concepts and their properties in the context of conjunctive complex fuzzy environment. In this paper, the conjunctive complex fuzzy order of an element belonging to a conjunctive complex fuzzy subgroup of a finite group is introduced. Several algebraic properties of this concept are established and a formula is developed to calculate the conjunctive complex fuzzy order of any of its powers in this study. Moreover, an important condition is investigated that determines the relationship between the membership values of any two elements and the membership value of the identity element in the conjunctive complex fuzzy subgroup of a group. In addition, the concepts of the conjunctive complex fuzzy order and index of a conjunctive complex fuzzy subgroup of a group are also presented in this article and their various fundamental algebraic attributes are explored structural. Finally, the conjunctive complex fuzzification of Lagrange's theorem for conjunctive complex fuzzy subgroups of a group is demonstrated

Toward knowledge-based automatic 3D spatial topological modeling from LiDAR point clouds for urban areas

Le traitement d'un très grand nombre de données LiDAR demeure très coûteux et nécessite des approches de modélisation 3D automatisée. De plus, les nuages de points incomplets causés par l'occlusion et la densité ainsi que les incertitudes liées au traitement des données LiDAR compliquent la création automatique de modèles 3D enrichis sémantiquement. Ce travail de recherche vise à développer de nouvelles solutions pour la création automatique de modèles géométriques 3D complets avec des étiquettes sémantiques à partir de nuages de points incomplets. Un cadre intégrant la connaissance des objets à la modélisation 3D est proposé pour améliorer la complétude des modèles géométriques 3D en utilisant un raisonnement qualitatif basé sur les informations sémantiques des objets et de leurs composants, leurs relations géométriques et spatiales. De plus, nous visons à tirer parti de la connaissance qualitative des objets en reconnaissance automatique des objets et à la création de modèles géométriques 3D complets à partir de nuages de points incomplets. Pour atteindre cet objectif, plusieurs solutions sont proposées pour la segmentation automatique, l'identification des relations topologiques entre les composants de l'objet, la reconnaissance des caractéristiques et la création de modèles géométriques 3D complets. (1) Des solutions d'apprentissage automatique ont été proposées pour la segmentation sémantique automatique et la segmentation de type CAO afin de segmenter des objets aux structures complexes. (2) Nous avons proposé un algorithme pour identifier efficacement les relations topologiques entre les composants d'objet extraits des nuages de points afin d'assembler un modèle de Représentation Frontière. (3) L'intégration des connaissances sur les objets et la reconnaissance des caractéristiques a été développée pour inférer automatiquement les étiquettes sémantiques des objets et de leurs composants. Afin de traiter les informations incertitudes, une solution de raisonnement automatique incertain, basée sur des règles représentant la connaissance, a été développée pour reconnaître les composants du bâtiment à partir d'informations incertaines extraites des nuages de points. (4) Une méthode heuristique pour la création de modèles géométriques 3D complets a été conçue en utilisant les connaissances relatives aux bâtiments, les informations géométriques et topologiques des composants du bâtiment et les informations sémantiques obtenues à partir de la reconnaissance des caractéristiques. Enfin, le cadre proposé pour améliorer la modélisation 3D automatique à partir de nuages de points de zones urbaines a été validé par une étude de cas visant à créer un modèle de bâtiment 3D complet. L'expérimentation démontre que l'intégration des connaissances dans les étapes de la modélisation 3D est efficace pour créer un modèle de construction complet à partir de nuages de points incomplets.The processing of a very large set of LiDAR data is very costly and necessitates automatic 3D modeling approaches. In addition, incomplete point clouds caused by occlusion and uneven density and the uncertainties in the processing of LiDAR data make it difficult to automatic creation of semantically enriched 3D models. This research work aims at developing new solutions for the automatic creation of complete 3D geometric models with semantic labels from incomplete point clouds. A framework integrating knowledge about objects in urban scenes into 3D modeling is proposed for improving the completeness of 3D geometric models using qualitative reasoning based on semantic information of objects and their components, their geometric and spatial relations. Moreover, we aim at taking advantage of the qualitative knowledge of objects in automatic feature recognition and further in the creation of complete 3D geometric models from incomplete point clouds. To achieve this goal, several algorithms are proposed for automatic segmentation, the identification of the topological relations between object components, feature recognition and the creation of complete 3D geometric models. (1) Machine learning solutions have been proposed for automatic semantic segmentation and CAD-like segmentation to segment objects with complex structures. (2) We proposed an algorithm to efficiently identify topological relationships between object components extracted from point clouds to assemble a Boundary Representation model. (3) The integration of object knowledge and feature recognition has been developed to automatically obtain semantic labels of objects and their components. In order to deal with uncertain information, a rule-based automatic uncertain reasoning solution was developed to recognize building components from uncertain information extracted from point clouds. (4) A heuristic method for creating complete 3D geometric models was designed using building knowledge, geometric and topological relations of building components, and semantic information obtained from feature recognition. Finally, the proposed framework for improving automatic 3D modeling from point clouds of urban areas has been validated by a case study aimed at creating a complete 3D building model. Experiments demonstrate that the integration of knowledge into the steps of 3D modeling is effective in creating a complete building model from incomplete point clouds

Bipolar complex fuzzy credibility aggregation operators and their application in decision making problem

A bipolar complex fuzzy credibility set (BCFCS) is a new approach in computational intelligence and decision-making under uncertainty. Bipolar complex fuzzy credibility (BCFC) information has been employed as a strategy for dealing with confusing and unreliable situations that arise in everyday life. In this paper, we used the concept of aggregation operators to diagnose the well-known averaging and geometric aggregation operators, as well as evaluate some properties and related results. Using described operators, an algorithm for multiple criteria group decision making is proposed. Then, a numerical example of a case study of Hospital selection is discussed. Lastly, the comparative analysis of suggested operators with existing operators are also given to discuss the rationality, efficiency and applicability of these operators

Features and Algorithms for Visual Parsing of Handwritten Mathematical Expressions

Math expressions are an essential part of scientific documents. Handwritten math expressions recognition can benefit human-computer interaction especially in the education domain and is a critical part of document recognition and analysis. Parsing the spatial arrangement of symbols is an essential part of math expression recognition. A variety of parsing techniques have been developed during the past three decades, and fall into two groups. The first group is graph-based parsing. It selects a path or sub-graph which obeys some rule to form a possible interpretation for the given expression. The second group is grammar driven parsing. Grammars and related parameters are defined manually for different tasks. The time complexity of these two groups parsing is high, and they often impose some strict constraints to reduce the computation. The aim of this thesis is working towards building a straightforward and effective parser with as few constraints as possible. First, we propose using a line of sight graph for representing the layout of strokes and symbols in math expressions. It achieves higher F-score than other graph representations and reduces search space for parsing. Second, we modify the shape context feature with Parzen window density estimation. This feature set works well for symbol segmentation, symbol classification and symbol layout analysis. We get a higher symbol segmentation F-score than other systems on CROHME 2014 dataset. Finally, we develop a Maximum Spanning Tree (MST) based parser using Edmonds\u27 algorithm, which extracts an MST from the directed line of sight graph in two passes: first symbols are segmented, and then symbols and spatial relationship are labeled. The time complexity of our MST-based parsing is lower than the time complexity of CYK parsing with context-free grammars. Also, our MST-based parsing obtains higher structure rate and expression rate than CYK parsing when symbol segmentation is accurate. Correct structure means we get the structure of the symbol layout tree correct, even though the label of the edge in the symbol layout tree might be wrong. The performance of our math expression recognition system with MST-based parsing is competitive on CROHME 2012 and 2014 datasets. For future work, how to incorporate symbol classifier result and correct segmentation error in MST-based parsing needs more research

Fuzzy Sets, Fuzzy Logic and Their Applications

The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches