Prediction on nature of cancer by fuzzy graphoidal covering number using artificial neural network.

Predicting the chances of various types of cancers for different organs in the human body is a typical decision-making process in medicine and health. The signaling pathways have played a vital role in increasing or decreasing the possibility of the deadliest disease, cancer. To combine the pathways concept and ambiguity in the prediction techniques of such diseases, we have used the proposed research on fuzzy graphoidal covers of fuzzy graphs in this paper. Determining a path with uncertainty and shortest length is a challenging topic of graph theory, and a collection of such shortest paths maintaining specific conditions is defined as a fuzzy graphoidal cover for a fuzzy graph. Also, we have defined fuzzy graphoidal covering number as a new parameter, reflecting the measure of coverage by fuzzy graphoidal covering set in a system. Afterwards, some important characterizations of the fuzzy graphoidal covering number are established with justified proof. Also, specific limit values of this number are provided for particular cases. Then, we developed an efficient algorithm for finding the defined covering set with its space and time complexity. The findings of this proposed study have been composed with an artificial neural network to model a strong tool for resolving an essential issue of medical sciences, the prediction of cancer type in the human body. We have analyzed two types of neural networks such as one one-dimensional and two-dimensional specification, for clarity of the obtained results. Also, we have found out the most possible cancer type is breast cancer from the data of our considered case study as a concluding statement for any decision-maker in the field of health sciences. Finally, sensitivity analysis and comparative study have been done to show the stability of our proposed work.

Solution of road network problem with the help of m-polar fuzzy graph using isometric and antipodal concept.

The isometry in crisp graph theory is a well-known fact. But, isometry under a fuzzy environment was developed recently and studied many facts. In a m-polar fuzzy graph, we have to think m components for each node and edge. Since, in our consideration, we consider m components for each nodes as well as edges, therefore we can not handle this type of situation using fuzzy model as their is a single components for this concept. Again, we can not apply bipolar or intuitionistic fuzzy graph model as each edges or nodes have just two components. Thus, these mPFG models give more efficient fuzziness results than other fuzzy model. Also, it is very interesting to develop and analyze such types of mPFGs with examples and related theorems. Considering all those things together, we have presented isometry under a m-polar fuzzy environment. In this paper, we have discussed the isometric m-polar fuzzy graph along with many exciting facts about it. Metric space properties have also been implemented on m-polar fuzzy isometric graph. We also have initiated a generalized fuzzy graph, namely antipodal m-polar fuzzy graphs, along with several issues. The degree of it is also presented along with edge regularity properties. We also give a relation between m-polar fuzzy antipodal graphs and their underlying crisp graphs. Its properties have also been discussed on m-polar fuzzy odd as well as even cycles, complete graphs, etc. Finally, a real-life application on a road network system in a m-polar fuzzy environment using the [Formula: see text]-distance concept is also presented.

Further development of F-index for fuzzy graph and its application in Indian railway crime.

From the mid-nineteenth century, the railway network has been the most important mode of conveying people and goods in India. 22.15 million passengers used this network and 3.32 million metric tons of goods were also shipped daily from 2019 to 2020. The national rail network comprised 126,366 km of track over a route of 67,368 km and 7,325 stations. It is the fourth-largest national railway network globally after the United States, Russia and China. But with the passage, they pose a threat to the general public while travelling, being the instances of crimes rising fourfold in rails. The ongoing railway crime has become a cause of concern for the common passenger now. In this article, F-index for fuzzy graphs is used to analyze the railway crimes in India and compared with three other topological indices. F-index for fuzzy graphs and the first Zagreb index for fuzzy graphs provide similar results whereas F-index for fuzzy graphs provides better realistic results than F-index for crisp graphs and first Zagreb index for crisp graphs to detect the crime in Indian railway. Also, this index is studied for several operations such as Cartesian product, composition, union and join of two fuzzy graphs. Some interesting relations of F-index are established during fuzzy graph transformations. Using those transformation, it is shown that n-vertex star has maximum F-index among the n-vertex trees. Also, maximal n-vertex unicyclic fuzzy graph having r cycle is determined with respect to F-index.

Fuzzy covering problem of fuzzy graphs and its application to investigate the Indian economy in new normal.

In this paper, new concepts of covering of fuzzy graphs are introduced. The definitions of fuzzy covering maps and fuzzy covering graphs of fuzzy graphs are given. Some special types of fuzzy covering graphs are discussed. Some important theorems to find out the fuzzy covering maps as well as fuzzy covering graphs for different types of fuzzy graphs are described. On the basis of the present situation during the current pandemic COVID-19, the world economic status is highly disruptive and deeply affected by the lock-down process. So, this topic is catching the eye for being an application part of this paper. Also, there are globally seventeen goals to sustain our development, which contain the eighth goal 'Decent Work and Economic Growth' having effect on the economy of the world. For this reason, the eighth sustainable development goal is combined with the economic impact of the pandemic for the discussion in the application part. Then some strategies are made to overcome this condition in a better way and perform all the steps to get a better situation in near future.

A novel concept of domination in m-polar interval-valued fuzzy graph and its application.

The concept of domination is one of the most significant topics in graph theory to handle unpredictable phenomena. In this study, an unprecedented idea of domination is introduced in m-polar interval-valued fuzzy graph (m-PIVFG). Domination number (DN), isolated vertex, total dominating set, independent set of domination on m-PIVFG are discussed. Some algebraic properties of domination on m-PIVFG are investigated. Weak domination, strong domination, split and non-split domination, cototal and global dominating sets on m-PIVFG are investigated with some fundamental hypotheses and models. We explore the concept of domination in m-PIVFG by solving a case study of locating new facilities to handle a catastrophe reaction activity due to the "COVID-19 pandemic" in West Bengal, India. Ultimately, conclusions and avenues of future scopes are placed at the end of this study.

Multi-attribute decision making method using advanced Pythagorean fuzzy weighted geometric operator and their applications for real estate company selection.

In this paper, a novel multi-attribute decision-making method using Advanced Pythagorean fuzzy weighted geometric operator in a Pythagorean fuzzy environment is developed. Pythagorean fuzzy aggregation operators have drawbacks that they give indeterminate results in some special cases when membership value or non-membership value gets 0 value or 1 value and the weight vector is of type ( 1 , 0 ) T or ( 0 , 1 ) T . The Advanced Pythagorean fuzzy geometric operator, the proposed operator can overcome the drawbacks. In some situations, for example, where the sum of squares of membership degree and non-membership degree gets unit value of a Pythagorean fuzzy number, multi-attribute decision making (MADM) methods using some existing aggregation operators give unreasonable ranking orders (ROs) of alternatives or can't discriminate the ROs of alternatives. But the present MADM method can get over the drawbacks of the existing MADM methods. The present MADM method is devoted to eliminate the drawbacks of the existing MADM methods and to select the best real estate company for investment.

Completeness and regularity of generalized fuzzy graphs.

Fuzzy graphs are the backbone of many real systems like networks, image, scheduling, etc. But, due to some restriction on edges, fuzzy graphs are limited to represent for some systems. Generalized fuzzy graphs are appropriate to avoid such restrictions. In this study generalized fuzzy graphs are introduced. In this study, matrix representation of generalized fuzzy graphs is described. Completeness and regularity are two important parameters of graph theory. Here, regular and complete generalized fuzzy graphs are introduced. Some properties of them are discussed. After that, effective regular graphs are exemplified.

Interval-valued fuzzy [Formula: see text]-tolerance competition graphs.

This paper develops an interval-valued fuzzy [Formula: see text]-tolerance competition graphs which is the extension of basic fuzzy graphs and [Formula: see text] is any real valued function. Interval-valued fuzzy [Formula: see text]-tolerance competition graph is constructed by taking all the fuzzy sets of a fuzzy [Formula: see text]-tolerance competition graph as interval-valued fuzzy sets. Product of two IVFPTCGs and relations between them are defined. Here, some hereditary properties of products of interval-valued fuzzy [Formula: see text]-tolerance competition graphs are represented. Application of interval-valued fuzzy competition graph in image matching is given to illustrate the model.

A study on vague graphs.

The main purpose of this paper is to introduce the notion of vague h-morphism on vague graphs and regular vague graphs. The action of vague h-morphism on vague strong regular graphs are studied. Some elegant results on weak and co weak isomorphism are derived. Also, [Formula: see text]-complement of highly irregular vague graphs are defined.

Some isomorphic properties of m-polar fuzzy graphs with applications.

The theory of graphs are very useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we present a frame work to handle m-polar fuzzy information by combining the theory of m-polar fuzzy sets with graphs. We introduce the notion of weak self complement m-polar fuzzy graphs and establish a necessary condition for m-polar fuzzy graph to be weak self complement. Some properties of self complement and weak self complement m-polar fuzzy graphs are discussed. The order, size, busy vertices and free vertices of an m-polar fuzzy graphs are also defined and proved that isomorphic m-polar fuzzy graphs have same order, size and degree. Also, we have presented some results of busy vertices in isomorphic and weak isomorphic m-polar fuzzy graphs. Finally, a relative study of complement and operations on m-polar fuzzy graphs have been made. Applications of m-polar fuzzy graph are also given at the end.