Sovan Samanta

Tamralipta Mahavidyalaya · Mathematics

The computational data received from sensors are varying according to situation depending on data accuracy. So, for a particular time period, it is very tough to find the appropriate data for its certainty. In this paper, all received sensor data are to be assumed as fuzzy numbers and such assumption could be beneficial to improve the functionality...

Domination and competition have been there since the beginning of the Universe. Bigger stars dominate the smaller ones and draw them towards themselves. Domination and competition are such phenomenon which nothing in this universe can stay without. Stronger things and animals dominate the weaker ones. Again, when there are more than one strong domi...

The basic goal of this research is to find the shortest path of a semidirected graph and apply it to the road network system. In the field of graph theory, networks are described as directed graphs, undirected graphs, or a combination of both. However, in the modern era of computing, several networks, such as social media networks, granular network...

Sometimes a group of similar types of dimensions is also treated as nodes. However, these groups can be considered as bunch nodes which may contain several nodes. This paper also justifies the study on bunch graphs which introduced a concept of graphs, where bunch nodes are also allowed. The auto-encoder, a specific type of feedforward neural netwo...

Fuzzy sets have undergone several expansions and generalisations in the literature, including Atanasov's intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets, to name a few. They can be regarded as fuzzy multisets from a formal standpoint; nevertheless, their interpretation differs from the two other approaches to fuzzy multisets that...

In today's digital world, millions of individuals are linked to one another via the Internet and social media. This opens up new avenues for information exchange with others. Sentiment analysis (SA) has gotten a lot of attention during the last decade. We analyse the challenges of Sentiment Analysis (SA) in one of the Asian regional languages known...

A pandemic due to COVID19 is going on globally. Scientists are struggling to prevent it. Some common prevention measures include using musk, social distance, quarantine, etc. In this paper, we study some factors, namely outsiders' effect, life expectancy, population density, smoker percentage, and temperature in ninety-five affected countries and f...

Graph colouring enjoys many practical as well as theoretical uses. Graph colouring is still a very active subject of research. This article introduces a new concept of the chromatic number of the neutrosophic graph (NG). There is a discussion of the difference between the fuzzy colouring of the fuzzy graph (FG) and the NG. Finally, a real-life appl...

The concept of bipolar-valued fuzzy relationships and their role in modeling bipolar-valued fuzzy social networks (BVFSN) are discussed. The goal of this study is to represent the bipolarity and fuzziness that are always present in the relationship between actors. Ranking the most central actors to achieve maximum spreading ability has been a diffi...

Natural genetic material may shed light on gene expression mechanisms and aid in the detection of genetic disorders. Single Nucleotide Polymorphism (SNP), small insertions and deletions (indels), and major chromosomal anomalies are all chromosomal abnormality-related disorders. As a result, several methods have been applied to analyze DNA sequences...

The main objective of this paper is to find the duration of maximum time connectivity of sensor nodes under uncertainty utilizing the prespecified voltage/power of each sensor node. Wireless sensor networks (WSNs) are composed of nodes that transmit data between each other over routing. A variety of routing protocols and algorithms exist, each rela...

The major network design or data distributed problems may be described as constrained optimization problems. Constrained optimization problems include restrictions imposed by the system designers. These limitations are basically due to the system design’s physical limitations or functional requirements of the network system. Constrained optimizatio...

In this research work, we proposed a medical image analysis framework with two separate releases whether or not Synovial Sarcoma (SS) is the cell structure for cancer. Within this framework the histopathology images are decomposed into a third-level sub-band using a two-dimensional Discrete Wavelet Transform. Subsequently, the structure features (S...

In this article, we present the concept of Pythagorean fuzzy threshold graphs (FTGs) which are generalizations of intuitionistic FTGs. We show that Pythagorean FTGs do not contain Pythagorean fuzzy alternating (FA) 4 − cycle. Pythagorean FTGs can be constructed by consecutively adding an isolated node or a dominating node. We propose that Pythagore...

Aiming of this paper is to introduce large-scale group decision-making (LSGDM) into three-way decisions (3WDs) with decision-theoretic rough sets (DTRSs) and propose LSGDM based 3WDs under linguistic assessments. There are two parameters involved of the 3WDs with DTRSs such as conditional probability and loss functions. Here we mainly focus on the...

Data is always a crucial issue of concern especially during its prediction and computation in digital revolution. This paper exactly helps in providing efficient learning mechanism for accurate predictability and reducing redundant data communication. It also discusses the Bayesian analysis that finds the conditional probability of at least two par...

In this study, cluster hypergraphs are introduced to generalize the concept of hypergraphs, where cluster nodes are allowed. Few related terms and properties on cluster hypergraphs are discussed. Some operations, including the Cartesian product, union, intersection, etc., are studied. Different types of matrix representations and isomorphism are al...

In the real-world scenario, one has to find a dominating person in a social network, conferences, meetings or any group discussion. The fuzzy graph (network) is one of the most powerful tools to find the strongest influential person in a network. This paper aims to develop a concept of fuzzy graphs (FGs) in the setup of bipolar-valued hesitant fuzz...

We introduce bunch graphs to generalize the structure of graphs, where bunches (groups) are considered essential. The significance of a bunch (a node in a network) is to represent a group as a single entity. We find that simultaneous competition and collaboration are observed among individuals /groups working on a topic/project in the real world. T...

The prime objective of this paper is to introduce a new model of threshold graphs in the complex fuzzy environment that has the capability of handling two-dimensional vague data. The proposed model is called as complex fuzzy threshold graph (CFTG). We introduce certain concepts related to CFTGs including, complex fuzzy alternating 4-cycle, complex...

This article focuses on a group decision‐making (GDM) approach based on the multiplicative consistency of linguistic preference relation (LPR) with experts' self-confidence and self‐doubting (SC&SD) levels. To give their preferences, the experts use their knowledge of the experience according to their degree of SC&SD levels. First, we propose the c...

For the development of any organization, evaluation of performance is an important task. To analyze the performance, Das et al. introduced a ranking framework based on fuzzy logic. That framework compared the current NIRF system of Indian Institutions with the fuzzy logic-based Mamdani system, KSM index. In that study, uniform membership functions...

To represent qualitative aspect of uncertainty and imprecise information, linguistic preference relation (LPR) is a powerful tool for experts expressing their opinions in group decision-making (GDM) according to linguistic variables (LVs). Since for an LV, it generally means that membership degree is one, and non-membership and hesitation degrees o...

Chordal graphs are those graphs which have chords for each cycle of the length > 3. For large graphs/ networks, generally, the number of chords is less in number than the required number of chords to for a chordal graph. By definition, those graphs are not chordal. The algorithms and properties of chordal graphs do not apply to such cases. Also, th...

Graph colouring is the system of assigning a colour to each vertex of a graph. It is done in such a way that adjacent vertices do not have equal colour. It is fundamental in graph theory. It is often used to solve real-world problems like traffic light signalling, map colouring, scheduling, etc. Nowadays, social networks are prevalent systems in ou...

In the literature of graph theory, networks are represented as directed graphs or undirected graphs and a mixed of both combinations. In today’s era of computing, networks like brain and facebook that do not belong to any of the mentioned networks category and in fact, it belong to the combination of both networks which have connections as directed...

Usually, foods are packaged with some preservative and such chemicals in the form of organic and inorganic preservative are being used for packaging different types of food. But in India, companies are using inorganic preservatives mostly and these inorganic preservatives are very harmful to human’s body. In this paper, a new model is developed to...

Society may be assumed to be a combination of several small networks. Naturally, an individual from one network is connected to several other networks (associated networks). The concept of associated networks is introduced here in a fuzzy environment. Although individuals of a given (focal) network are more likely to interact with others in the net...

A complex fuzzy set (CFS) is a remarkable generalization of the fuzzy set in which membership function is restricted to take the values from the unit circle in the complex plane. A CFS is an efficient model to deal with uncertainties of human judgement in more comprehensive and logical way due to the presence of phase term. In this research article...

In the recent phenomenon of social networks, both online and offline, two nodes may be connected, but they may not follow each other. Thus there are two separate links to be given to capture the notion. Directed links are given if the nodes follow each other, and undirected links represent the regular connections (without following). Thus, this net...

This book provides an extensive set of tools for applying fuzzy mathematics and graph theory to real-life problems. Balancing the basics and latest developments in fuzzy graph theory, this book starts with existing fundamental theories such as connectivity, isomorphism, products of fuzzy graphs, and different types of paths and arcs in fuzzy graphs...

Like crisp graphs, fuzzy graphs (FGs) also have useful many applications. But, a very few number of applications of FGs are available in the literature. In this chapter, some applications of FGs are incorporated. The main use of fuzzy graph theory is to represent the network with ambiguity. An ecological problem is modeled as a fuzzy digraph and

Graph coloring is a very important problem in graph theory. It has many applications to solve real life problem, viz. scheduling, registrar allocation, traffic light signaling, city planning, frequency assignment, and many more. This chapter gives new concepts on coloring of fuzzy graph (FG). Mainly, there are two types of colorings, vertex/node co...

Golumbic and Trenk first introduced tolerance graph [7] to generalize some well-known applications of interval graphs. In a tolerance graph, every vertex is represented by an interval and a tolerance such that an edge occurs if and only if the overlap of corresponding intervals is at least as large as the tolerance associated with one of the vertic...

It is well known that in fuzzy set only one characteristic of an element is considered called membership value, i.e. the degree of belongingness (or degree of acceptance) of an element in the set. But, the counter complement part, i.e. the degree of non-belongingness (or degree of rejection) is not considered, though this case occurs naturally in a...

In this chapter, we discuss about planarity and isomorphism in FGs. The first four sections deal with fuzzy planar graph (FPG) and fuzzy dual graph, whereas the last section deals with isomorphism. Having started with work of Abdul Jabbar et al. [1], the first work on the planarity of FGs, it becomes an interesting as well as a highly researched ar...

The journey of graph theory started with famous Königsberg seven bridges problem and its negative resolution by Leonhard Euler in 1736. So, it is an old subject, even it is very new due to its wide applications in modeling of modern society. The graphs are being used as mathematical tools for modeling a huge number of real world problems. Graphs ca...

In 1968, Cohen [4] first introduced competition graph while working on a problem in ecology. Competition graph (CompG) is one kind of intersection graph and it is originally used for modeling ecological problems. Though this graph can be used to model various types of problems in the real world, Cohen used the crisp competition graph to model the e...

In 1847, Kirchhoff developed the theory of trees, to solve a system of simultaneous linear equations. Also, in 1857, Cayley worked on this theory and enumerated the isomers of saturated hydrocarbons \(C_nH_{2n+2}\) for different values of n. Nowadays, trees are frequently used to construct the directory of a computer, searching of files and folders...

Fuzzy graph is a generalization of crisp graph which investigates uncertainty in various types of networks. To deal with multiple information precisely, graphical models can be applied. To discuss the multipolar nature of objects, the theory of fuzzy graphs have been extended to m-polar fuzzy graphs.

In 1973, Chvatal and Hammer [2] introduced threshold graphs and applied them in set packing problems. This particular class of graphs has many applications in several applied areas such as computer science, scheduling theory, psychology, etc. These graphs are also used in control theory, particularly to control the flow of information between proce...

The computation of link prediction is one of the most important tasks on a social network. Several methods are available in the literature to predict links in networks and RSM index is one of them. The RSM index is applicable in the fuzzy environment and it does not incorporate the notion of falsity and indecency parameters which occur frequently i...

The graph theory is being used for representation in networks and chemical atomic structures very frequently. However, these days, uncertainties are imposed on such networks. Isomorphism in generalized fuzzy graphs has been introduced here to capture the similarity of uncertainties in different networks. Homomorphism, weak isomorphism, co-weak isom...

Coloring of graph theory is widely used in different fields like the map coloring, traffic light problems, etc. Hypergraphs are an extension of graph theory where edges contain single or multiple vertices. This study analyzes cluster hypergraphs where cluster vertices too contain simple vertices. Coloring of cluster networks where composite/cluster...

Distance is an important parameter in any networks/ graphs. The idea of strong sum distance in the fuzzy graph was introduced by Tom and Sunitha (2015). A generalization of fuzzy graph called neutrosophic graph is more realistic to handle imprecise data. In this study, the weight of an edge of a neutrosophic graph is defined and hence defined su...

Distance is an important parameter in any networks/ graphs. The idea of strong sum distance in the fuzzy graph was introduced by Tom and Sunitha (2015). A generalization of fuzzy graph called neutrosophic graph is more realistic to handle imprecise data. In this study, the weight of an edge of a neutrosophic graph is defined and hence defined su...

In the existing definition of a neutrosophic planar graph, there is a limitation. In that definition, the value of falsity in degree of planarity is 1, even then the crisp underline graph is planar. This limitation is removed in the proposed definition. In this study, an advanced concept of the neutrosophic planar graphs is given and investigated t...

Social networks are represented using graph theory. In this case, individuals in a social network are assumed as nodes. Sometimes institutions or groups are also assumed as nodes. Institutions and such groups are assumed as cluster nodes that contain individuals or simple nodes. Hypergraphs have hyperedges that include more than one node. In this s...

Ranking of educational institutions in a state (or country or world) is an essential task for the overall development of the institution as well as human life. There are many conventional methods to find the rank of an institution. However, these methods do not display the correct ranking because of calculating the imprecise data of input parameter...

Personifying the most critical node in a network has a crucial task in the network analysis, and it has enormous applications in everyday life. Centrality measures are commonly used to find influential nodes. In this article, a new centrality measure named complete neighborhood centrality is introduced. At last, an application is discussed.

Personifying the most critical node in a network has a crucial task in the network analysis, and it has enormous applications in everyday life. Centrality measures are commonly used to find influential nodes. In this article, a new centrality measure named complete neighbourhood centrality is introduced. At last, an application is discussed.

In this research work, the notion of complex Pythagorean fuzzy planar graph (CPFPG), an extension of Pythagorean fuzzy planar graph, is presented to study the planarity. The planarity of these graphs is based on the extended range of degree from real to complex plane with unit circle. Here, the ideas of complex Pythagorean fuzzy multigraphs (CPFMGs...

In this paper, we introduce a new type of fuzzy set, called Pythagorean linguistic sets (PLSs), to address the preferred and nonpreferred degrees of linguistic variables. Moreover, it allows decision-makers to offer effectively handle uncertain information more flexible than intuitionistic linguistic sets (ILSs) when one compares two alternatives i...

The generalized neutrosophic graph is a generalization of the neutrosophic graph that represents a system perfectly. In this study, the concept of a neutrosophic digraph, generalized neutrosophic digraph and out-neighbourhood of a vertex of a generalized neutrosophic digraph is studied. The generalized neutrosophic competition graph and matrix repr...

Research in applications of Mathematics has experienced explosive growth in the last few decades. This book finds the relationship between the real world and mathematics. The mathematics is already there in nature in the form of symmetry and sequences. Many medical therapies use Kinds of music/songs recently. The mathematics is behind the wavelengt...

Colouring of graphs is being used in several representations of real world systems like map colouring, traffic signalling, etc. This study introduces the edge colouring of fuzzy graphs. The chromatic index and the strong chromatic index are defined and related properties are investigated. In addition, job oriented web sites, traffic light problems...

Based on the rules of the Federal Communications Commission (FCC) of the United States, there is a problem when FM radio stations are situated nearby and transmit on channels when they are satisfactorily far separated. The difficulty of taking an optimal assignment of channels for a particular set of radio stations according to some given limitatio...

In the world of mathematics and computer science, technological advancements are constantly being researched and applied to ongoing issues. Setbacks in social networking, engineering, and automation are themes that affect everyday life, and researchers have been looking for new techniques in which to solve these challenges. Graph theory is a widely...

Social network is the perfect place for connecting people. The social network is a social structure formed by a set of nodes (persons, organizations, etc.) and a set of links (connection between nodes). People feel very comfortable to share news and information through a social network. This chapter measures the influential persons in different typ...

Prediction of links/ connections in social networks is useful for increasing business in the area of telecom and social media. All types of social networking organization are trying to increase their nodes, i.e. the number of members. So the calculation of link prediction is the most important task because this calculation will help how to increase...

Nowadays the popularity of packaging food is growing in human life very speed- ily. The central reasons for the human to choose packaging food are because it is convenient, quickly prepared, inexpensive, and it has an attractive look. Also, it is covered by a container or package. Therefore, packaging food becomes an integral part of the food produ...

Fuzzy graphs are the backbone of many real networks. But, due to some restriction on edges, fuzzy graphs are limited to represent for some networks. In this study, generalized fuzzy graphs and generalized directed fuzzy graphs are discussed to avoid such restrictions. A pipeline network is expressed as a generalized directed fuzzy graph. In the pip...

Abstract. Graph theory includes two unavoidable graphs, namely Euler graphs and Hamiltonian graphs. In this study, generalized fuzzy Euler graphs (GFEGs) and generalized fuzzy Hamiltonian graphs (GFHGs) are defined to express uncertain system like routes, networks. Here, even degree of all vertices of a graph does not guarantee that the graph is GF...

Generalized fuzzy graphs are perfect to represent any system like networks, images, scheduling, etc. compared to fuzzy graphs. This study introduces the concept of a generalized fuzzy neighbourhood of a vertex and generalized fuzzy graphs. Also, an associated graph, called minimal graphs of competition graphs are defined. These graphs will represen...