By W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral

ISBN-10: 1931233985

ISBN-13: 9781931233989

This publication provides a few new kinds of Fuzzy and Neutrosophic types that can learn difficulties in a progressive manner. the hot notions of bigraphs, bimatrices and their generalizations are used to construct those types so that it will be worthy to research time based difficulties or difficulties which want stage-by-stage comparability of greater than specialists. The types expressed right here will be regarded as generalizations of Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps.

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**Extra info for Applications of Bimatrices to Some Fuzzy and Neutrosophic Models**

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13: In a connected bigraph G = G1 ∪ G2 a bicut set is a set of edges (together with their end vertices) whose removal from G = G1 ∪ G2 leaves both the graphs G1 and G2 disconnected, provided removal of no proper subset of these edges disconnects G. Further we see the bicut set of a connected bigraph G = G1 ∪ G2 need not be unique. We can have more than one bicut set of a bigraph. We illustrate this by an example. 28. 28 G = G1 ∪ G2 = {v1, v2, v3, …, v6} ∪{ v'1, v'2, v'3, v'4}. 56 The graph of G1 and G2 are separately given by the following figures.

Clearly G = G1 ∪ G2 is not a complete bigraph. 15b of the edge glued bigraph of two complete graphs which is not complete. 15b 42 v'4 The edge v1, v2 of G1 is glued with the edge v'1, v'5 of G2. A bigraph can also be a bipartite bigraph. e. V G1C ( ) V G2C = V (G) and = V (G) and making two adjacent vertices u and v adjacent in GC if and only if they are non adjacent in G. 16a. 16b. 16b 43 We see if G is a disjoint bigraph so is its complement. 5: If G = G1 ∪ G2 be a disjoint bigraph such that G1 = G2C then G is a self complementary bigraph.

G1 × G2 ≠ G1 ∪ G2. For this is clear from the following example. 23. 23a. 23a Now we proceed on to define the notion of directed bigraph. 11: A directed bigraph G = G1 ∪ G2 is a pair of ordered triple {(V (G1), A (G1), I G1 ) , (V (G2), A (G2), I G2 )} where V (G1) and V (G2) are non empty proper sets of V (G) called the set of vertices of G = G1 ∪ G2. A(G1) and A (G2) is a set disjoint from V (G1) and V(G2) respectively called the set of arcs of G1 and G2 and I G1 and I G2 are incidence map that associates with each arc of G1 and G2 an ordered pair of vertices of G1 and G2 respectively.

### Applications of Bimatrices to Some Fuzzy and Neutrosophic Models by W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral

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