Sometimes information in a network model is based on multi-agent, multi-attribute, multi-object, multi-polar information or uncertainty rather than a single bit. An m-polar fuzzy model is useful for such network models which gives more and more precision, flexibility, and comparability to the system as compared to the classical, fuzzy and bipolar fuzzy models. In this research article, we introduce the notion of m-polar fuzzy graph structure and present various operations, including Cartesian product, strong product, cross product, lexicographic product, composition, union and join of m-polar fuzzy graph structures. We illustrate these operations by several examples. We also investigate some of their related properties.
Graph theory have applications in many areas of computer science including data mining, image segmentation, clustering, image capturing, networking. A graph structure, introduced by Sampathkumar (2006), is a generalization of undirected graph which is quite useful in studying some structures including graphs, signed graphs, graphs in which every edge is labeled or colored. A graph structure helps to study the various relations and the corresponding edges simultaneously. A fuzzy set (Zadeh 1965) is an important mathematical structure to represent a collection of objects whose boundary is vague. Fuzzy models are becoming useful because of their aim in reducing the differences between the traditional models used in engineering and science. Nowadays fuzzy sets are playing a substantial role in chemistry, economics, computer science, engineering, medicine and decision making problems. In 1998, Zhang (1998) generalized the idea of a fuzzy set and gave the concept of bipolar fuzzy set on a given set X as a map which associates each element of X to a real number in the interval [−1, 1]. In 2014, Chen et al. (2014) introduced the idea of m-polar fuzzy sets as an extension of bipolar fuzzy sets and showed that bipolar fuzzy sets and 2-polar fuzzy sets are cryptomorphic mathematical notions and that we can obtain concisely one from the corresponding one in Chen et al. (2014).
Publisher : Springer
By : Muhammad Akram , Rabia Akmal and Noura Alshehri
File Information: English Language/ 19 Page / size: 1,169 KB
سال : 2016
ناشر : Springer
کاری از : Muhammad Akram , Rabia Akmal and Noura Alshehri
اطلاعات فایل : زبان انگلیسی / 19 صفحه / حجم : KB 1,169
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