This method presented in the paper provides new insight into product sale risk analysis with a pictorial representation of its associated factors. Also, the concept of the PFHS graph with the help of the PFHS set is introduced with some operations like the cartesian product, composition, union, direct product, and lexicographic product. These structures work best for evaluating uncertainty using membership, non-membership, neutral, and multi-argument functions, making them ideal for Risk Evaluation studies. Picture Fuzzy Hypersoft set (PFHSs) is employed in this technique, a hybrid structure of Picture Fuzzy set and Hypersoft Set. This is achieved using novel Picture fuzzy Hypersoft Graphs. Considering this idea, this paper aims to evaluate the risk factor of investing in different nature of products in a supermarket for a better proportioning of investment based on the product's sales. A finely detailed evaluation of the risk factor can lead to better returns in terms of investment in a particular business. Risk evaluation has always been of great interest for individuals wanting to invest in various businesses, especially in the marketing and product sale centres. Finally, a real-world mobile network application that is directly related to the integrity of the mPFG concept has been discussed. Several facts about efficient mPFG have also been studied here along with details descriptions. A new type of mPFG called efficient mPFG which is directly related to dominating integrity concept has also been introduced. We also discussed the interrelation between them. Under isomorphism, their properties have also been studied. Different types of integrity on mPFG such as node integrity, dominating integrity, and edge integrity are discussed thoroughly along with some of its interesting facts have been introduced. We have thoroughly covered some of their related properties as well as a brand-new idea called dominating integrity on mPFG. In this article, we developed a brand-new idea known as node integrity on mPFG and went in-depth on a few of their related properties. As in the m-polar fuzzy environment, each node and edge has m components, so we have more flexibility to address the uncertainty rather than fuzzy as well as other uncertain environments. So, defining integrity in the mPF environment needs a new concept. However, in m-polar fuzzy graphs (mPFG), each node as well as edges has m components. However, the integrity concept for fuzzy graphs has only recently been defined and extensively researched. Integrity for crisp graph theory is a well-defined topic. In the end, an application of the degree of vertices in the cubic fuzzy graph structure is presented. It has been found that the condition of the membership function is effective in the quality of degree calculation. These degrees can be easily compared in the form of a cubic number expressed. In this regard, a comparative study between vertex regular and total vertex regular cubic fuzzy graph structure has been carried out and the necessary and sufficient conditions have been provided. In this context, the concepts of vertex regularity and total vertex regularity have been informed and some of its properties have been studied. The quality and method of determining the degree of vertices in this type of fuzzy graphs simultaneously supports fuzzy membership and interval-valued fuzzy membership, in addition to the multiplicity of relations, motivated us to conduct a study on the regularity of cubic fuzzy graph structures. The cubic fuzzy graph structure, as a combination of cubic fuzzy graphs and fuzzy graph structures, shows better capabilities in solving complex problems, especially in cases where there are multiple relationships.
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