Cylindrical neutrosophic single‐valued number and its application in networking problem, multi‐criterion group decision‐making problem and graph theory

Chakraborty, Avishek; Mondal, Sankar Prasad; Alam, Shariful; Mahata, Animesh

doi:10.1049/trit.2019.0083

“…Another study suggested arithmetic and geometric operations under pentagonal neutrosophic numbers along with the application based on MCGDM in mobile communication [9]. The neutrosophic numbers are gaining much interest of the researchers as time passes, for instance, an MCGDM scheme was proposed under the cylindrical neutrosophic domain [10].…”

Section: Introductionmentioning

confidence: 99%

Neutrosophic ratio-type estimators for estimating the population mean

Tahir

¹

,

Khan

²

,

Aslam

³

et al. 2021

Complex Intell. Syst.

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All researches, under classical statistics, are based on determinate, crisp data to estimate the mean of the population when auxiliary information is available. Such estimates often are biased. The goal is to find the best estimates for the unknown value of the population mean with minimum mean square error (MSE). The neutrosophic statistics, generalization of classical statistics tackles vague, indeterminate, uncertain information. Thus, for the first time under neutrosophic statistics, to overcome the issues of estimation of the population mean of neutrosophic data, we have developed the neutrosophic ratio-type estimators for estimating the mean of the finite population utilizing auxiliary information. The neutrosophic observation is of the form $${Z}_{N}={Z}_{L}+{Z}_{U}{I}_{N}\, {\rm where}\, {I}_{N}\in \left[{I}_{L}, {I}_{U}\right], {Z}_{N}\in [{Z}_{l}, {Z}_{u}]$$ Z N = Z L + Z U I N where I N ∈ I L , I U , Z N ∈ [ Z l , Z u ] . The proposed estimators are very helpful to compute results when dealing with ambiguous, vague, and neutrosophic-type data. The results of these estimators are not single-valued but provide an interval form in which our population parameter may have more chance to lie. It increases the efficiency of the estimators, since we have an estimated interval that contains the unknown value of the population mean provided a minimum MSE. The efficiency of the proposed neutrosophic ratio-type estimators is also discussed using neutrosophic data of temperature and also by using simulation. A comparison is also conducted to illustrate the usefulness of Neutrosophic Ratio-type estimators over the classical estimators.

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“…Recently, researchers have introduced pentagonal [4], hexagonal [5], heptagonal [6] fuzzy numbers and its application in different fields. Wang et al manifested the conception of single-valued neutrosophic set (SVNS) [7] and interval neutrosophic set (INS) [8] which are subclasses of NSs and many other recent works [9][10][11][12] have improved and bring innovation into the NS hypothesis. Liu and Yuan [13] proposed the idea of triangular intuitionistic fuzzy set (TIFN) which is a combination of triangular fuzzy number and intuitionistic fuzzy number.…”

Section: Introductionmentioning

confidence: 99%

A novel logarithmic operational law and aggregation operators for trapezoidal neutrosophic number with MCGDM skill to determine most harmful virus

Haque

¹

,

Chakraborty

²

,

Mondal

³

et al. 2021

Appl Intell

Self Cite

14

0

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In the current era, the theory of vagueness and multi-criteria group decision making (MCGDM) techniques are extensively applied by the researchers in disjunctive fields like recruitment policies, financial investment, design of the complex circuit, clinical diagnosis of disease, material management, etc. Recently, trapezoidal neutrosophic number (TNN) draws a major awareness to the researchers as it plays an essential role to grab the vagueness and uncertainty of daily life problems. In this article, we have focused, derived and established new logarithmic operational laws of trapezoidal neutrosophic number (TNN) where the logarithmic base μ is a positive real number. Here, logarithmic trapezoidal neutrosophic weighted arithmetic aggregation (L arm ) operator and logarithmic trapezoidal neutrosophic weighted geometric aggregation (L geo ) operator have been introduced using the logarithmic operational law. Furthermore, a new MCGDM approach is being demonstrated with the help of logarithmic operational law and aggregation operators, which has been successfully deployed to solve numerical problems. We have shown the stability and reliability of the proposed technique through sensitivity analysis. Finally, a comparative analysis has been presented to legitimize the rationality and efficiency of our proposed technique with the existing methods.

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“…23–26 Neutrosophic number was further extended to cylindrical neutrosophic number and used in solving networking and minimal spanning tree problems. 27 The concept of fuzzy polygroups was generalised further to single-valued neutrosophic polygroups and its sets. 28 For better modelling of real-life applications, the crisp, fuzzy, intuitionistic fuzzy and neutrosophic sets were further generalised into plithogenic sets.…”

Section: Introductionmentioning

confidence: 99%

Safety modelling of marine systems using neutrosophic logic

Pai

¹

,

Gaonkar

²

2020

Proceedings of the Institution of Mechanical Engineers, Part M:

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Precisely assessing risk associated with critical and complex engineering systems operating in an environment with high amount of uncertainty is extremely difficult. Taking proper decisions to reduce risk level depends on how accurately the risks associated with the system are assessed. Risk assessment and safety modelling of complex systems were studied using various tools such as crisp sets, Bayesian belief network, fuzzy sets, classical logic and fuzzy logic. Neutrosophic set which is an extension of fuzzy set represents the real world better than fuzzy set due to the inclusion of the hesitancy component in the set. This research focuses on developing a neutrosophic logic–based model employing neutrosophic IF-THEN rules using linear trapezoidal neutrosophic number and analytical hierarchy process for qualitative and subjective analysis of human knowledge. The model is validated using an illustrative example for safety analysis of marine system.

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Cylindrical neutrosophic single‐valued number and its application in networking problem, multi‐criterion group decision‐making problem and graph theory

Cited by 36 publications

References 56 publications

Neutrosophic ratio-type estimators for estimating the population mean

Neutrosophic ratio-type estimators for estimating the population mean

A novel logarithmic operational law and aggregation operators for trapezoidal neutrosophic number with MCGDM skill to determine most harmful virus

Safety modelling of marine systems using neutrosophic logic

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