• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.827-842
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• 2014

In this paper, we introduce the notion of Cayley intuitionistic fuzzy graphs and investigate some of their properties. We present some interesting properties of intuitionistic fuzzy graphs in terms of algebraic structures. We discuss connectedness in Cayley intuitionistic fuzzy graphs. We also describe different types of ${\alpha}$-connectedness in Cayley intuitionistic fuzzy graphs.

• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.95-111
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• 2017

Recently, interval-valued fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they allowed the degree of membership of a vertex to an edge to be represented by interval values in [0.1] rather than the crisp values between 0 and 1. In this paper, we introduce the concepts of regular and totally regular interval-valued fuzzy graphs and discusses some properties of the ${\mu}$-complement of interval-valued fuzzy graph. Self ${\mu}$-complementary interval-valued fuzzy graphs and self-weak ${\mu}$-complementary interval-valued fuzzy graphs are defined and a necessary condition for an interval valued fuzzy graph to be self ${\mu}$-complementary is discussed. We define busy vertices and free vertices in interval valued fuzzy graph and study their image under an isomorphism.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.1043-1052
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• 2022

Our goal in this paper is to propose the advancement proposed by Alsina, Klement and other researchers in the area of fuzzy logic applied to the area of fuzzy graph theory. We introduce the notion of complete Hamacher fuzzy graphs and the notion of balanced Hamacher fuzzy graphs and discuss their properties. Moreover, several operations on these fuzzy graphs are explored via the complete notion.

• Journal of applied mathematics & informatics
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• 제41권5호
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• pp.1145-1153
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• 2023

The notion of maximal product of two fuzzy graphs was introduced by Radha and Arumugam in 2015 and the notion of balanced fuzzy graph was introduced by Al-Hawary in 2011. In this paper, we give a modification of the maximal product definition, which we call maximal strong product. We also introduce the relatively new notion of maximal-balanced fuzzy graphs. We give necessary and sufficient conditions for the maximal strong product of two balanced (resp., maximal-balanced) fuzzy graphs to be balanced (resp., maximal-balanced) and we prove that these two independent notions are preserved under isomorphism.

• Annals of Fuzzy Mathematics and Informatics
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• 제16권3호
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• pp.363-371
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• 2018

The main objective of this paper is to connect fuzzy theory, graph theory and fuzzy graph theory with algebraic structure. We introduce the notion of fuzzy graph of semigroup, the notion of fuzzy ideal graph of semigroup as a generalization of fuzzy ideal of semigroup, intuitionistic fuzzy ideal of semigroup, fuzzy graph and graph, the notion of isomorphism of fuzzy graphs of semigroups and regular fuzzy graph of semigroup and we study some of their properties.

• Korean Journal of Mathematics
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• 제31권4호
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• pp.485-494
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• 2023

The degree of hesitancy of a vertex in a hesitancy fuzzy graph depends on the degree of membership and non-membership of the vertex. We define a new class of hesitancy fuzzy graph, the intuitionistic hesitancy fuzzy graph in which the degree of hesitancy of a vertex is independent of the degree of its membership and non-membership. We introduce the idea of β-product of a pair of hesitancy fuzzy graphs and intuitionistic hesitancy fuzzy graphs and prove certain results based on this product.

• Journal of applied mathematics & informatics
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• 제42권1호
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• pp.123-137
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• 2024

In this paper, Power fuzzy graphs is newly introduced by allotting fuzzy values on power graphs in such a way that the newly added edges, has the edge membership values between a closed interval which depends on vertex membership values and the length of the added edges. Power fuzzy subgraphs and total power fuzzy graphs are newly defined with properties and some special cases. It is observed that every power fuzzy graph is a fuzzy graph but the converse need not be true. Edges that are incident to vertices with the least vertex membership values are retained in the least power fuzzy subgraph. Further, the application of these concepts in real life time has been presented and discussed using power fuzzy graph model.

• 대한수학회논문집
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• 제32권4호
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• pp.1077-1097
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• 2017

In this research article, we introduce certain concepts, including domination, total domination, strong domination, weak domination, edge domination and total edge domination in m-polar fuzzy graphs. We describe these concepts by several examples. We investigate some related properties of certain dominations in m-polar fuzzy graphs. We also present a decision making method based on domination in m-polar fuzzy graphs.

• 대한수학회논문집
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• 제21권3호
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• pp.587-593
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• 2006

The notion of intuitionistic fuzzy graphs is introduced. We show how to associate an intuitionistic fuzzy sub(semi)group with an intuitionistic fuzzy graph in a natural way.

• 디지털융복합연구
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• 제11권11호
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• pp.409-414
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• 2013

Naive Bayesian classifiers 네이브 베이지안 분류기는 샘플 데이터로부터 쉽게 구현될 수 있는 강력하고도 많이 사용되는 형식의 분류기다. 그러나 강한 조건부 독립성으로 인하여 효율이 저하되는 분류 결과를 초래한다. 일반적으로 네이브 베이지안 분류기는 연속성을 가진 특징 데이터의 우도를 처리하기 위해 가우시안 분산을 사용한다. 속성들의 확률밀도는 항상 가우시안 분산에 적합한 것만은 아니다. 또 다른 형식의 분류기는 지도학습을 통해 퍼지 규칙과 퍼지집합을 학습할 수 있는 퍼지신경망이다. 퍼지신경망과 네이브 베이지안 분류기간에는 구조적 유사성을 가지고 있기 때문에 퍼지신경망으로 학습된 분산 그래프를 네이브 베이지안 분류기에 적용하고자 하는 방안이 본 연구의 목적이다. 따라서 네이브 베이지안 분류기에 가우시안 분산 그래프를 사용한 결과와 퍼지 분산 그래프를 사용한 결과를 비교하였다. 이를 위해 leukemia와 colon의 DNA 마이크로어레이 데이터를 적용하여 분류하였다. 네이브 베이지안 분류기에 퍼지 분산 그래프를 사용한 결과 가우시안 분산 그래프를 사용한 결과보다 더 신뢰성이 있음을 보여주었다.