Telecommunication System Based on Fuzzy Graphs

Abstract

Telecommunication is one of the unavoidable utilities of daily life. Telecommunication service providers have data records of its users. These records are represented by crisp graphs. Certain parameters like center persons, churn prediction, etc. are more perfectly calculated if the data are represented by fuzzy graphs. In this paper, we have introduced a fuzzy telecommunication network (FTN) using fuzzy graph theory.Star persons and related terms are defined in this fuzzy telecommunication network.A small example is described to illustrate the network. Churn prediction is a big issue for telecom service providers. This study introduces churn prediction in the fuzzy telecommunication network. New idea on measurement of churn prediction is presented here.

Geodesic Iteration Number of g-contour of a Fuzzy Graph

“…Samanta and Pal in [20] suggested that a social network can be represented by a fuzzy graph, there by introducing the concept of fuzzy social network. A telecommunication network is a social network and the same authors in [21] discussed telecommunication network by using a fuzzy graph model. In this section, a method to represent the land line telecommunication network (LTN) by an undirected fuzzy graph is proposed by modifying the membership values of the links in the telecommunication network suggested by Samanta and Pal in [21].…”

“…A telecommunication network is a social network and the same authors in [21] discussed telecommunication network by using a fuzzy graph model. In this section, a method to represent the land line telecommunication network (LTN) by an undirected fuzzy graph is proposed by modifying the membership values of the links in the telecommunication network suggested by Samanta and Pal in [21]. The modifications include representation of telecommunication system by an undirected fuzzy graph G:(V, σ , µ) instead of the directed fuzzy graph G → (V, σ , μ → ) where the membership value μ → (a, b) of the link between two customers a and b depends on t, the outgoing call time of a to b, whereas in G, the membership value µ(a, b) depends on the variable t , the sum of out-going call durations of a to b and of b to a.…”

“…Before defining the membership values of the customers in V 1 , Samanta and Pal in [21] defined a co-related term 'recognition number' as follows. In every society, recognition of each person is measured by some members of the society.…”

“…Here, V 2 = {c n+1 , c n+2 , ... , c m } are the outside customers connected to the members of LTN. Before introducing the membership values of customers outside LTN, a co-related term 'satisfied time of calling' is defined as in [21]. If an outside customer of LTN calls certain amount of time to customers of LTN, then the outside customer is also valuable for LTN.…”

“…So strength between two customers depends on how much time they call to each other by phones per unit interval of time. Note that in [21], the telecommunication system is represented by a directed fuzzy graph G → = (V, σ , μ → ) where the membership value of a link between customers is given by μ → (c i ,…”