The theoretical concepts of graphs are highly utilized by computer science applications, social sciences, and medical sciences, especially in computer science for applications such as data mining, image segmentation, ...
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The theoretical concepts of graphs are highly utilized by computer science applications, social sciences, and medical sciences, especially in computer science for applications such as data mining, image segmentation, clustering, image capturing, and networking. Fuzzy graphs, bipolar fuzzy graphs and the recently developed m -polar fuzzy graphs are growing research topics because they are generalizations of graphs (crisp). In this paper, three new operations, i.e., direct product, semi-strong product and strong product, are defined on m -polar fuzzy graphs. It is proved that any of the products of m -polar fuzzy graphs are again an m -polar fuzzy graph. Sufficient conditions are established for each to be strong, and it is proved that the strong product of two complete m -polar fuzzy graphs is complete. If any of the products of two m -polar fuzzy graphs G 1 and G 2 are strong, then at least G 1 or G 2 must be strong. Moreover, the density of an m -polar fuzzy graph is defined, the notion of balanced m -polar fuzzy graph is studied, and necessary and sufficient conditions for the preceding products of two m -polar fuzzy balanced graphs to be balanced are established. Finally, the concept of product m -polar fuzzy graph is introduced, and it is shown that every product m -polar fuzzy graph is an m -polar fuzzy graph. Some operations, like union, direct product, and ring sum are defined to construct new product m -polar fuzzy graphs.
In many real world problems, data sometimes comes from n agents ( n ≥ 2), i.e., “multipolar information” exists. This information cannot be well-represented by means of fuzzy graphs or bipolar fuzzy grap...
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In many real world problems, data sometimes comes from n agents ( n ≥ 2), i.e., “multipolar information” exists. This information cannot be well-represented by means of fuzzy graphs or bipolar fuzzy graphs. Therefore, m -polar fuzzy set theory is applied to graphs to describe the relationships among several individuals. In this paper, some operations are defined to formulate these graphs. Some properties of strong m -polar fuzzy graphs, self-complementary m -polar fuzzy graphs and self-complementary strong m -polar fuzzy graphs are discussed.
In this paper, we define three operations on intuitionistic fuzzy graphs, viz. direct product, semi-strong product and strong product. In addition, we investigated many interesting results regarding the operations. Mo...
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In this paper, we define three operations on intuitionistic fuzzy graphs, viz. direct product, semi-strong product and strong product. In addition, we investigated many interesting results regarding the operations. Moreover, it is demonstrated that any of the products of strong intuitionistic fuzzy graphs are strong intuitionistic fuzzy graphs. Finally, we defined product intuitionistic fuzzy graphs and investigated many interesting results.
Theoretical concepts of graphs are highly utilized in applications of computer science especially in research area of computer science such as data mining, image segmentation, clustering, image capturing and networkin...
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Theoretical concepts of graphs are highly utilized in applications of computer science especially in research area of computer science such as data mining, image segmentation, clustering, image capturing and networking. An interval-valued fuzzy graph can be obtained from two given interval-valued fuzzy graphs using Cartesian product and composition. In this paper, we introduced the degree of an edge and total degree of an edge. Likewise, we established the degree of an edge in interval-valued fuzzy graphs formed by these operations in terms of the degree of edges in the given interval-valued fuzzy graphs in some particular cases.
In this paper, bipolar fuzzy planar graph is defined and studied several properties. The bipolar fuzzy planar graph is defined in a very interesting way. The parameter "degree of planarity" measures the plan...
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In this paper, a supplier selection model was developed for a retailer. Suppliers have different influence factors that have a risk of profit loss or less profit as well as a loss of goodwill to a retailer. Thus, a re...
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In this paper, a supplier selection model was developed for a retailer. Suppliers have different influence factors that have a risk of profit loss or less profit as well as a loss of goodwill to a retailer. Thus, a retailer must choose a supplier that can provide better profit and better goodwill. Different suppliers have different business policies. Here, different risk factors and their corresponding severity in profit loss and goodwill loss are considered as a fuzzy number. Next, the total risk in profit loss and goodwill loss is formulated. To select a supplier with the minimum risk, a balanced solution of the soft set theory was applied to a numerical example.
Recently, in Mathematical and Computational Applications Journal Chiu et al. [1] and Chen and Chiu [2] propose an inventory model based on EPQ with rework to determine the replenishment lot size and the number of ship...
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Recently, in Mathematical and Computational Applications Journal Chiu et al. [1] and Chen and Chiu [2] propose an inventory model based on EPQ with rework to determine the replenishment lot size and the number of shipments for a vendor-buyer integrated production-inventory system. They solve the inventory problem by considering both variables as continuous. However, the number of shipments must be considered as discrete variable. In this direction, this paper revisits and solves the inventory problem of [1-2] considering the decision variables according to their nature. Two easy and improved algorithms are proposed which simplify and complement the research works of [1-2].
The present article deals with a backorder Economic Order Quantity (EOQ) model for natural leisure/closing time system where the demand rate depends upon the total shortage period and the seasonal effect. A cost minim...
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The shortest-paths problem is an important problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in ...
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The shortest-paths problem is an important problem in graph theory and finds diverse applications in various fields. This is why shortest path algorithms have been designed more thoroughly than any other algorithm in graph theory. A large number of optimization problems are mathematically equivalent to the problem of finding shortest paths in a graph. The Shortest-path between a pair of vertices is defined as the path with shortest length between the pair of vertices. The shortest path from one node to another often gives the best way to route message between the nodes. This paper presents an O(n 2 ) time algorithm for solving all pairs shortest path problems on trapezoid graphs which are extensions of interval graphs and permutation graphs. The space complexity of this algorithm is of O(n 2 ). This problem has been solved by constructing n breadth-first search (BFS) trees with each of the n vertices as root. As the lower bound of time complexity for computing the all pairs shortest paths is known to be of O(n 2 ), this proposed algorithm is optimal.
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