Abstract
It is the case that, in certain applications of fuzzy graphs, a t-norm, instead of a minimum, is more suitable. This requires the development of a new theory of fuzzy graphs involving an arbitrary t-norm in the basic definition of a fuzzy graph. There is very little known about this type of fuzzy graph. The purpose of this paper is to further develop this type of fuzzy graph. We concentrate on the relatively new concept of fuzzy incidence graphs.
Highlights
It is well known that Zadeh is the originator of fuzzy logic [1] and that Rosenfeld [2] and Yeh andBang [3] are the founders of fuzzy graph theory.It is the case that in certain applications of fuzzy graphs, a t-norm, instead of a minimum, is more suitable
This requires the development of a new theory of fuzzy graphs involving an arbitrary t-norm in the basic definition of a fuzzy graph
We concentrate on the relatively new concept of fuzzy incidence graphs [5,6,7]. It is the goal of this paper to develop results that allow for the use of this new theory by the new concept of fuzzy incidence graphs
Summary
It is well known that Zadeh is the originator of fuzzy logic [1] and that Rosenfeld [2] and Yeh and. In relation to illegal immigration, it was shown in [9,10] that the combining of government response measures and vulnerability measures was more suitably accomplished using certain t-norms and t-conorms rather than using minimum and maximum, respectively This was determined to be the case in the combining measures of human trafficking flows from one country to another [8,13]. We show that, if a minimum is replaced by an arbitrary t-norm in the definition of a fuzzy incidence graph, certain basic results hold while others do not.
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