Abstract
Due to the presence of two opposite directional thinking in relationships between countries and communication systems, the systems may not always be balanced. Therefore, the perfectness between countries relations are highly important. It comes from how much they were connected to each other for communication. In this study, first perfectly regular bipolar fuzzy graph is introduced and examined the regularity of nodes. Then, the relationship between the adjacent nodes and their regularity are visualized as a perfectly edge-regular bipolar fuzzy graphs. The totally accurate communication between all connected nodes is explained by introducing completely open neighborhood degree and completely closed neighborhood degree of nodes and edges in a bipolar fuzzy graph. Some algorithms and flowcharts of the proposed methods are given. Finally, two applications of these cogitation are exhibited in two bipolar fuzzy fields. The first one is in international relationships between some countries during cold-war era and the second one is in decision-making between teachers–students communication system for the improvement of teaching.
Highlights
Research backgroundIn daily life of humanity, decision structure is build upon the human thinking potency
If the nodes as well as edges in a graph become uncertain [33], fuzzy graph theory [26] gives us more accuracy for decision-making in some real problems
Due to the existence of bipolar judgemental thinking, the bipolar fuzzy sets and relations play a major role in extensive number of real-life bipolar fuzzy fields including qualitative model, cognitive mapping, cooperation, clustering, analysis of multi-agent data mining, strategic decision in international relationship, neurological modeling, analysis of diagnose of major depressive, granular computing, etc
Summary
In daily life of humanity, decision structure is build upon the human thinking potency. Graph theory plays an essential part to maintain the relationship and communication in various types of connected fields including computer network, artificial intelligence, decision-making, engineering science, signal processing, pattern recognition, image segmentation, and medical science. If the nodes as well as edges in a graph become uncertain [33], fuzzy graph theory [26] gives us more accuracy for decision-making in some real problems. If there is another opposite character for the nodes and edges whose membership values lie in [−1, 0], these types situations cannot be handled by means of fuzzy graphs. Bipolar fuzzy graphs (BFGs) [5,31] gives the two opposite side information about the nodes and edges. We cannot order the nodes and edges in this case
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