Cubic relations

Kim, Jun Hui; Lee, None Jeonggon; Hur, Kyeong; Lim, Pyung Ki

doi:10.30948/afmi.2020.19.1.21

Cited by 12 publications

(8 citation statements)

References 0 publications

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“…For the definitions of the order and the equality of two interval numbers, and the infimum and the supremum of any interval numbers, refer to [13,14]. Definition 2 ([2,15]).…”

Section: Preliminariesmentioning

confidence: 99%

Octahedron Subgroups and Subrings

2020

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In this paper, we define the notions of i-octahedron groupoid and i-OLI [resp., i-ORI and i-OI], and study some of their properties and give some examples. Also we deal with some properties for the image and the preimage of i-octahedron groupoids [resp., i-OLI, i-ORI and i-OI] under a groupoid homomorphism. Next, we introduce the concepts of i-octahedron subgroup and normal subgroup of a group and investigate some of their properties. In particular, we obtain a characterization of an i-octahedron subgroup of a group. Finally, we define an i-octahedron subring [resp., i-OLI, i-ORI and i-OI] of a ring and find some of their properties. In particular, we obtain two characterizations of i-OLI [resp., i-ORI and i-OI] of a ring and a skew field, respectively.

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“…For the definitions of the order and the equality of two interval numbers, and the infimum and the supremum of any interval numbers, refer to [13,14]. Definition 2 ([2,15]).…”

Section: Preliminariesmentioning

confidence: 99%

Octahedron Subgroups and Subrings

2020

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“…In 2012, the concept of cubic fuzzy sets (CFSs) which combines IVFS and FS to provide a more general way of handling uncertainty, was introduced by Jun et al [ 35 ]. They also defined some basic properties and operations enabling the use of CFSs in decision making to solve problems involving uncertain data.…”

Section: Introductionmentioning

confidence: 99%

Application of connectivity index of cubic fuzzy graphs for identification of danger zones of tsunami threat

Shi,

Kosari,

Hameed

et al. 2024

PLoS ONE

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Fuzzy graphs are very important when we are trying to understand and study complex systems with uncertain and not exact information. Among different types of fuzzy graphs, cubic fuzzy graphs are special due to their ability to represent the membership degree of both vertices and edges using intervals and fuzzy numbers, respectively. To figure out how things are connected in cubic fuzzy graphs, we need to know about cubic α−strong, cubic β−strong and cubic δ−weak edges. These concepts better help in making decisions, solving problems and analyzing things like transportation, social networks and communication systems. The applicability of connectivity and comprehension of cubic fuzzy graphs have urged us to discuss connectivity in the domain of cubic fuzzy graphs. In this paper, the terms partial cubic α−strong and partial cubic δ−weak edges are introduced for cubic fuzzy graphs. The bounds and exact expression of connectivity index for several cubic fuzzy graphs are estimated. The average connectivity index for cubic fuzzy graphs is also defined and some results pertaining to these concepts are proved in this paper. The results demonstrate that removing some vertices or edges may cause a change in the value of connectivity index or average connectivity index, but the change will not necessarily be related to both values. This paper also defines the concepts of partial cubic connectivity enhancing node and partial cubic connectivity reducing node and some related results are proved. Furthermore, the concepts of cubic α−strong, cubic β− strong, cubic δ−weak edge, partial cubic α−strong and partial cubic δ−weak edges are utilized to identify areas most affected by a tsunami resulting from an earthquake. Finally, the research findings are compared with the existing methods to demonstrate their suitability and creativity.

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“…All of them not only raise the significant uncertainties, but they are also unable to handle circumstances in which the decision-making process must take into account the degree of deception that corresponds to the real value, which applies over an interval. The concept of cubic FS (CFS) was introduced by Jun et al [23] to emphasize and characterize uncertainties more accurately. The analysis has been expanded to include the degree of agreement or disagreement corresponding to the truth interval.…”

Section: Introductionmentioning

confidence: 99%

MAGDM for selecting machine learning techniques: A novel approach utilizing the 2-tuple linguistic cubic q-rung orthopair fuzzy set

Naz

Akram

Sagheer

et al. 2023

Preprint

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Machine learning is a powerful technology for both current and future information management and it is already being used in a variety of domains. The use of machine learning in cyber security is still in its early stages, emphasizing the significant gap between research and practice. The q-rung orthopair fuzzy set (q-ROFS) has been demonstrated to be a valuable tool in describing decision-makers (DMs) assessment values in multi-attribute group decision-making (MAGDM). In this paper, we introduce a new tool called the 2-tuple linguistic cubic q-rung orthopair fuzzy set (2TLCq-ROFS) based on the combination of q-ROFS with interval-valued q-ROFS under the 2-tuple linguistic scenario in order to capture DMs assessment information in the complex MAGDM problems in a more efficient way. We investigate machine learning based MAGDM problems in cyber security in which the DM’s preference information is expressed as the 2TLCq-ROF numbers (2TLCqROFNs). Based on the combination of power average and power geometric operators with Muirhead mean, we propose a family of new aggregation operators including: the 2TLCq-ROF power Muirhead mean (2TLCq-ROFPMM), the 2TLCq-ROF dual power Muirhead mean (2TLCq-ROFDPMM), the 2TLCq-ROF weighted power Muirhead mean (2TLCq-ROFWPMM), and the 2TLCq-ROF weighted dual power Muirhead mean (2TLCq-ROFWDPMM) operators under the 2TLCq-ROF environment, which are more precise than the current aggregation operators and take into account the interconnection of the 2TLCq-ROFNs. Then, a versatile 2TLCq-ROF MAGDM approach is established and a case study on the evaluation of machine learning techniques in cyber security is given to show the method’s effectiveness and validity. Moreover, a parameter analysis is carried out to analyze the influence of parameters on ranking results. The comparative analysis further confirms the effectiveness and feasibility of the proposed approach to show why DMs should select our suggested strategy over several others. In the end, some conclusions of this paper are determined and future directions are demonstrated.

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Cubic relations

Cited by 12 publications

References 0 publications

Octahedron Subgroups and Subrings

Octahedron Subgroups and Subrings

Application of connectivity index of cubic fuzzy graphs for identification of danger zones of tsunami threat

MAGDM for selecting machine learning techniques: A novel approach utilizing the 2-tuple linguistic cubic q-rung orthopair fuzzy set

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