Properties of interval valued intuitionistic (S,T) – Fuzzy graphs

Pacific Science Review A: Natural Science and Engineering Pub Date : 2016-01-01 DOI:10.1016/j.psra.2016.06.003

Hossein Rashmanlou , R.A. Borzooei , Sovan Samanta , Madhumangal Pal

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引用次数: 21

Abstract

The basis of the concept of interval valued intuitionistic fuzzy sets was introduced by K. Atanassov. Interval valued intuitionistic models provide more precision, flexibility, and compatibility to a system than do classic fuzzy models. In this paper, three new types of product operations (direct product, lexicographic product, and strong product) of interval valued intuitionistic (S,T)–fuzzy graphs are defined. One of the most studied classes of fuzzy graphs are regular fuzzy graphs, which appear in many contexts. For example, r-regular fuzzy graphs with connectivity and edge-connectivity equal to r play a key role in designing reliable communication networks. Hence, we introduced the concepts of regular and totally regular interval valued intuitionistic (S,T)–fuzzy graphs. Likewise, we defined busy vertices and free vertices in interval valued intuitionistic (S,T)–fuzzy graphs and studied their images under an isomorphism, which are highly important in fuzzy social networks.

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区间值直觉(S,T) -模糊图的性质

区间值直觉模糊集概念的基础由K. Atanassov提出。区间值直觉模型为系统提供了比经典模糊模型更高的精度、灵活性和兼容性。本文定义了区间值直觉(S,T) -模糊图的三种新的积运算(直接积、字典积和强积)。模糊图中研究最多的一类是规则模糊图，它出现在很多情况下。例如，连通性和边连通性等于r的r正则模糊图在设计可靠的通信网络中起着关键作用。因此，我们引入了正则和全正则区间值直觉(S,T)模糊图的概念。同样，我们定义了区间值直觉(S,T)模糊图中的忙点和自由点，并在同构条件下研究了它们的图像，这在模糊社交网络中非常重要。

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Pacific Science Review A: Natural Science and Engineering

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