Fuzzy Hypergraphs

Graph theory has found many application area in science, engineering, and mathematics. In order to expand the application base, the notion of a graph was generalized to that of a hypergraph, that is, a set X of vertices together with a collection of subsets of X. In this chapter, we fuzzify the notation of a hypergraph and state some possible applications. In this article, we apply the concept of bipolar fuzzy sets to hypergraphs and investigate some basic theorems and some properties of bipolar fuzzy hypergraphs. Some basic concepts of bipolar fuzzy set are defined. It is shown that any bipolar fuzzy graph can be expressed as the bipolar fuzzy intersection graphs of some bipolar fuzzy sets

Clique graphs and Helly graphs

AbstractAmong the graphs for which the system of cliques has the Helly property those are characterized which are clique-convergent to the one-vertex graph. These graphs, also known as the so-called absolute retracts of reflexive graphs, are the line graphs of conformal Helly hypergraphs possessing a certain elimination scheme. From particular classes of such hypergraphs one can readily construct various classes G of graphs such that each member of G has its clique graph in G and is itself the clique graph of some other member of G. Examples include the classes of strongly chordal graphs and Ptolemaic graphs, respectively

The State-of-the-Art of Set Visualization

Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non-trivial problem due to the large number of possible relations between them. We provide a systematic overview of state-of-the-art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net

Controlling Complexity in Spatial Modelling

The present complexity approach is based on two assumptions: A1: measurability of deviations of outcomes with respect to reference values; A2 : extension of A1 to multi-set analysis. Complexity is then defined in terms of multi-set deviation compared to single-set ones; an interpretation is given in terms of information costs; examples show the relevance of the interpretation. As a useful by-product the explicit solution of the quadratic part of the discrete logistic ? one of the examples ? is derived; a set of pij-numbers is introduced, and a workable method for generating them exposed. Extensions are considered, in particular controllability. A further application is then proposed, namely to hypergraph conflict analysis, in particular conflict resolution. Many decisional conflicts at the spatial level can be axiomatised in this form; it is shown how the use of particular structures ? in the mathematical sense of that word ? of the problem allows of reducing greatly the degree of complexity of the problem, and hence the difficulty of finding a solution.Chaos, complexity, conflict, dynamics, hypergraphs, information

Constant single valued neutrosophic graphs with applications

In this paper, we introduced a new concept of single valued neutrosophic graph (SVNG) known as constant single valued neutrosophic graph (CSVNG). Basically, SVNG is a generalization of intuitionistic fuzzy graph (IFG). More specifically, we described and explored somegraph theoretic ideas related to the introduced concepts of CSVNG. An application of CSVNG in a Wi-Fi network system is discussed and a comparison of CSVNG with constant IFG is established showing the worth of the proposed work. Further, several terms like constant function and totally constant function are investigated in the frame-work of CSVNG and their characteristics are studied

Novel System and Method For Telephone Network Planing Based on Neutrosophic Graph

Telephony is gaining momentum in the daily lives of individuals and in the activities of all companies. With the great trend towards telephony networks, whether analogue or digital known as Voice over IP (VoIP), the number of calls an individual can receive becomes considerably high. However, effective management of incoming calls to subscribers becomes a necessity. Recently, much attention has been paid towards applications of single-valued neutrosophic graphs in various research fields. One of the suitable reason is it provides a generalized representation of fuzzy graphs (FGs) for dealing with human nature more effectively when compared to existing models i.e. intuitionistic fuzzy graphs (IFGs), inter-valued fuzzy graphs (IVFGs) and bipolar-valued fuzzy graphs (BPVFGs) etc. In this paper we focused on precise analysis of useful information extracted by calls received, not received due to some reasons using the properties of SVNGs. Hence the proposed method introduced one of the first kind of mathematical model for precise analysis of instantaneous traffic beyond the Erlang unit. To achieve this goal an algorithm is proposed for a neutrosophic mobile network model (NMNM) based on a hypothetical data set. In addition, the drawback and further improvement of proposed method with a mathematical proposition is established for it precise applications

Answering Spatial Multiple-Set Intersection Queries Using 2-3 Cuckoo Hash-Filters

We show how to answer spatial multiple-set intersection queries in O(n(log w)/w + kt) expected time, where n is the total size of the t sets involved in the query, w is the number of bits in a memory word, k is the output size, and c is any fixed constant. This improves the asymptotic performance over previous solutions and is based on an interesting data structure, known as 2-3 cuckoo hash-filters. Our results apply in the word-RAM model (or practical RAM model), which allows for constant-time bit-parallel operations, such as bitwise AND, OR, NOT, and MSB (most-significant 1-bit), as exist in modern CPUs and GPUs. Our solutions apply to any multiple-set intersection queries in spatial data sets that can be reduced to one-dimensional range queries, such as spatial join queries for one-dimensional points or sets of points stored along space-filling curves, which are used in GIS applications.Comment: Full version of paper from 2017 ACM SIGSPATIAL International Conference on Advances in Geographic Information System