The generalized version of Jun's cubic sets in semigroups

Khan, M. Rashid; Jun, Young Bae; Gulistan, Muhammad; Yaqoob, Naveed

doi:10.3233/ifs-141377

Cited by 43 publications

(12 citation statements)

References 32 publications

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“…Definition 4 [33], [34]: LetÃ 1 = T 1 , I 1 , F 1 andÃ 2 = T 2 , I 2 , F 2 be two single valued neutrosophic number. Then, the operations for NNs are defined as below;…”

Section: Preliminariesmentioning

confidence: 99%

Novel Neutrosophic Cubic Graphs Structures With Application in Decision Making Problems

et al. 2019

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Graphs allow us to study the different patterns of inside the data by making a mental image. The aim of this paper is to develop a neutrosophic cubic graph structure, which is the extension of neutrosophic cubic graphs. As neutrosophic cubic graphs are defined for one set of edges between vertices, while neutrosophic cubic graphs structures are defined for more than one set of edges. Further, we defined some basic operations, such as Cartesian product, composition, union, join, cross product, strong product, and lexicographic product of two neutrosophic cubic graph structures. Several types of other interesting properties of neutrosophic cubic graph structures are discussed in this paper. Finally, a decisionmaking algorithm based on the idea of neutrosophic cubic graph structures is constructed. The proposed decision-making algorithm is applied in a decision-making problem to check the validity.

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“…Definition 4 [33], [34]: LetÃ 1 = T 1 , I 1 , F 1 andÃ 2 = T 2 , I 2 , F 2 be two single valued neutrosophic number. Then, the operations for NNs are defined as below;…”

Section: Preliminariesmentioning

confidence: 99%

Novel Neutrosophic Cubic Graphs Structures With Application in Decision Making Problems

et al. 2019

Self Cite

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“…Moreover, they defined and studied some basic operations and their properties. Later on, a number of research papers have been devoted to the study of cubic set theory on various aspects in several algebraic structures (see for e.g., [24][25][26][27][28][29][30][31][32][33][34][35]). Now, in the real life, some phenomena can be modeled with fuzzy graph concepts and some with interval-valued graph concepts.…”

Section: Introductionmentioning

confidence: 99%

Cubic Graphs and Their Application to a Traffic Flow Problem

Muhiuddin¹,

Takallo²,

Jun³

et al. 2020

IJCIS

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A graph structure is a useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we introduce the concept of cubic graph, which is different from the notion of cubic graph in S. Rashid, N. Yaqoob, M. Akram, M. Gulistan, Cubic graphs with application, Int. J. Anal. Appl. 16 (2018), 733-750, and investigate some of their interesting properties. Then we define the notions of cubic path, cubic cycle, cubic diameter, strength of cubic graph, complete cubic graph, strong cubic graph and illustrate these notions by several examples. We prove that any cubic bridge is strong and we investigate equivalent condition for cubic cutvertex. Finally, we use the concept of cubic graphs in traffic flows to get the least time to reach the destination.

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“…The hybrid platform provided by a cubic set has the main advantage since it contains more information than a fuzzy set and an interval-valued fuzzy set. By using this concept, different problems arising in several areas can be solved by means of cubic sets as in the works of Rashid et al [ 20 ], Ma et al [ 21 ], Khan et al [ 22 ], Jun et al [ 23 , 24 ], Gulistan et al [ 25 ], Khaleed et al [ 26 ], Fu et al [ 27 ] and Ashraf et al [ 28 ].…”

Section: Introductionmentioning

confidence: 99%

Cubic Vague Set and its Application in Decision Making

Alhazaymeh

Al-Qudah

Hassan

et al. 2020

Entropy

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From the hybrid nature of cubic sets, we develop a new generalized hybrid structure of cubic sets known as cubic vague sets (CVSs). We also define the concept of internal cubic vague sets (ICVSs) and external cubic vague sets (ECVSs) with examples and discuss their interesting properties, including ICVSs and ECVSs under both P and R-Order. Moreover, we prove that the R and R-intersection of ICVSs (or ECVSs) need not be an ICVS (or ECVS). We also derive the different conditions for P-union (P-intersection, R and R-intersection) operations of both ICVSs (ECVSs) to become an ICVS (ECVS). Finally, we introduce a decision-making based on the proposed similarity measure of the CVSs domain and a numerical example is given to elucidate that the proposed similarity measure of CVSs is an important concept for measuring entropy in the information/data. It will be shown that the cubic vague set has the novelty to accurately represent and model two-dimensional information for real-life phenomena that are periodic in nature.

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The generalized version of Jun's cubic sets in semigroups

Cited by 43 publications

References 32 publications

Novel Neutrosophic Cubic Graphs Structures With Application in Decision Making Problems

Novel Neutrosophic Cubic Graphs Structures With Application in Decision Making Problems

Cubic Graphs and Their Application to a Traffic Flow Problem

Cubic Vague Set and its Application in Decision Making

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