Madhumangal Pal

Fuzzy k-competition graphs and p-competition fuzzy graphs

Fuzzy competition graph as a generalization of competition graph is introduced here. Two generalizations of fuzzy competition graph as fuzzy k-competition graphs and p-competition fuzzy graphs are also defined. These graphs are related to fuzzy digraphs. Fuzzy neighbourhood graphs, related to fuzzy graphs, are also defined here. Besides, some relations between fuzzy competition graphs and fuzzy neighbourhood graphs have been established. And finally, several results to find strong edges of the above mentioned graphs have also been established.

A study on bipolar fuzzy graphs

Recently, bipolar fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. In this paper, at first we define three new operations on bipolar fuzzy graphs, viz. direct product, semi strong product and strong product. Likewise, sufficient conditions for each one of them to be complete are given. Also, it is proved that any of the products of strong bipolar fuzzy graphs are strong bipolar fuzzy graphs.

Fuzzy Planar Graphs

Fuzzy planar graph is a very important subclass of fuzzy graph. In this paper, two types of edges are mentioned for fuzzy graphs: effective edges and considerable edges. In addition, a comparative study between Kuratowskis graphs and fuzzy planar graph is made. A new concept of a strong fuzzy planar graph is introduced. Some related results are established. These results have certain applications in subway tunnels, routes, oil/gas pipelines representation, etc. It is also shown that an image can be represented by a fuzzy planar graph, and contraction of such an image can be made with the help of a fuzzy planar graph.

Shortest Path Problem on a Network with Imprecise Edge Weight

A network with its arc lengths as imprecise number, instead of a real number, namely, interval number and triangular fuzzy number is considered here. Existing ideas on addition and comparison between two imprecise numbers of same type are introduced. To obtain a fuzzy shortest path from a source vertex to all other vertices, a common algorithm is developed which works well on both types of imprecise numbers under consideration. In the proposed algorithm, a decision-maker is to negotiate with the obtained fuzzy shortest paths according to his/her view only when the means are same but the widths are different of the obtained paths. Otherwise, a fuzzy optimal path is obtained to which the decision-maker always satisfies with different grades of satisfaction. All pairs fuzzy shortest paths can be found by repeated use of the proposed algorithm.

Bipolar Fuzzy Graphs with Categorical Properties

AbstractTheoretical concepts of graphs are highly utilized by computer science applications. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. In this paper, we discussed some properties of the µ–complement of bipolar fuzzy graphs. Self µ–complement bipolar fuzzy graphs and self weak µ–complement bipolar fuzzy graphs are defined and a necessary condition for a bipolar fuzzy graph to be self µ–complement is given. We defined busy vertices and free vertices in bipolar fuzzy graphs and studied their image under an isomorphism. Categorical properties of bipolar fuzzy graphs are discussed. Also, we investigated some properties of isomorphism on bipolar fuzzy graphs.

LINEAR PROGRAMMING TECHNIQUE TO SOLVE TWO PERSON MATRIX GAMES WITH INTERVAL PAY-OFFS

A fuzzy two person interval game problem is proposed and treated in this paper which is not easily tackled by the conventional methods. First, with respect to this pay-off values, a necessary and sufficient condition for the existence of a saddle point is proved. Based on interval value model, we are to find the value of interval game without saddle point. Finally, example is given to illustrate the procedure and to indicate the performance of the proposed method.

Interval-valued fuzzy planar graphs

In this paper, interval-valued fuzzy planar graphs are defined and several properties are studied. The interval-valued fuzzy graphs are more efficient than fuzzy graphs, since the degree of membership of vertices and edges lie within the interval [0, 1] instead at a point in fuzzy graphs. We also use the term ‘degree of planarity’ to measures the nature of planarity of an interval-valued fuzzy graph. The other relevant terms such as strong edges, interval-valued fuzzy faces, strong interval-valued fuzzy faces are defined here. The interval-valued fuzzy dual graph which is closely associated to the interval-valued fuzzy planar graph is defined. Several properties of interval-valued fuzzy dual graph are also studied. An example of interval-valued fuzzy planar graph is given.

Intuitionistic fuzzy optimization technique for Pareto optimal solution of manufacturing inventory models with shortages

This paper discusses a manufacturing inventory model with shortages where carrying cost, shortage cost, setup cost and demand quantity are considered as fuzzy numbers. The fuzzy parameters are transformed into corresponding interval numbers and then the interval objective function has been transformed into a classical multi-objective EPQ (economic production quantity) problem. To minimize the interval objective function, the order relation that represents the decision maker’s preference between interval objective functions has been defined by the right limit, left limit, center and half width of an interval. Finally, the transformed problem has been solved by intuitionistic fuzzy programming technique. The proposed method is illustrated with a numerical example and Pareto optimality test has been applied as well.

New concepts of fuzzy planar graphs

Fuzzy planar graph is an important subclass of fuzzy graph. Fuzzy planar graphs and its several properties are presented. A very close association of fuzzy planar graph is fuzzy dual graph. This is also defined and several properties of it are studied. Isomorphism on fuzzy graphs are well defined in literature. Isomorphic relation between fuzzy planar graph and its dual graph are established.

Two new operators on fuzzy matrices

The fuzzy matrices are successfully used when fuzzy uncertainty occurs in a problem. Fuzzy matrices become popular for last two decades. In this paper, two new binary fuzzy operators ⊕ and ⊙ are introduced for fuzzy matrices. Several properties on ⊕ and ⊙ are presented here. Also, some results on existing operators along with these new operators are presented.