Interval-valued intuitionistic fuzzy soft graphs with application

The concept of interval-valued intuitionistic fuzzy soft sets and fuzzy graphs structure together constitute a new structure called an interval-valued intuitionistic fuzzy soft graph. The definitions of interval-valued intuitionistic fuzzy soft subgraph and strong interval-valued intuitionistic fuzzy soft graph are introduced with suitable examples. The degree of the good influence of a parameter in a fuzzy network and there is no influence by an interval number in the same system. Similarly, the effectiveness and non-effectiveness of the other fuzzy system on other parameters is measured by the concept of soft graphs in this article. Also, several different types of operations, including Cartesian product, strong product and composition on interval-valued intuitionistic fuzzy soft graphs are presented. Some related properties of these operations are investigated. Finally, we give a real-life application of interval-valued intuitionistic fuzzy soft graphs on social media and find out the most affected person in social media.Publisher's Versio

Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference

A study on irregularity in vague graphs with application in social relations

Considering all physical, biological and social systems, fuzzy graph models serves the elemental processes of all natural and artificial structures. As the indeterminate information is an essential real-life problems, which are mostly uncertain, modelling those problems based on fuzzy graph is highly demanding for an expert. Vague graph can manage the uncertainty relevant to the inconsistent and indeterminate information of all real-world problems, in which fuzzy graphs possibly will not succeed into bringing about satisfactory results. Also, vague graphs are so useful tool to examine many issues such as networking, social systems, geometry, biology, clustering, and traffic plan. Hence, in this paper, we introduce strongly edge irregular vague graphs and strongly edge totally irregular vague graphs. A comparative study between strongly edge irregular vague graphs and strongly edge totally irregular vague graphs is done. Finally, we represent an applicationof irregular vague influence graph to show the importance of irregularity in vague graphs.Publisher's Versio

On the relation between the base of an EI algebra and word graphs

This paper is an attempt to investigate the possibilities to link algebraic fuzzy set theory with the theory of word graphs. In both theories concepts are studied and concepts can be set in correspondence. This enables to use algebraic results in the context of word graph theory

Intelligent active force control of a three-link manipulator using fuzzy logic

The paper presents a novel approach to estimate the inertia matrix of a robot arm using a fuzzy logic (FL) mechanism in order to trigger the active force control (AFC) strategy. A comprehensive study is performed on a rigid three-link manipulator subjected to a number of external disturbances. The robustness and effectiveness of the proposed control scheme are investigated considering the trajectory track performance of the robotic arm taking into account the application of external disturbances and that the arm is commanded to describe a reference trajectory given a number of initial and operating conditions. The results show that the FL mechanism used in the study successfully computes appropriate estimated inertia matrix value to execute the control action. The proposed scheme exhibits a high degree of robustness and accuracy as the track error is bounded within an acceptable range of value even under the influence of the introduced disturbances

Optimizing an Organized Modularity Measure for Topographic Graph Clustering: a Deterministic Annealing Approach

This paper proposes an organized generalization of Newman and Girvan's modularity measure for graph clustering. Optimized via a deterministic annealing scheme, this measure produces topologically ordered graph clusterings that lead to faithful and readable graph representations based on clustering induced graphs. Topographic graph clustering provides an alternative to more classical solutions in which a standard graph clustering method is applied to build a simpler graph that is then represented with a graph layout algorithm. A comparative study on four real world graphs ranging from 34 to 1 133 vertices shows the interest of the proposed approach with respect to classical solutions and to self-organizing maps for graphs