Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Smarandache, Florentín; Zhang, Xiaohong; Ali, Mumtaz

doi:10.3390/sym11020171

Cited by 10 publications

(12 citation statements)

References 57 publications

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“…With the help of several neutrosophic systems, the degree of falsehood function is reduced [40]. The algebraic properties of neutrosophic sets duplets, triplets and multisets are presented [41]. The existing statistical methods are not able to apply for reliable censored failure test.…”

Section: Related Workmentioning

confidence: 99%

Outlier detection in neutrosophic sets by using rough entropy based weighted density method

Sangeetha

Amalanathan

2020

CAAI trans. intell. technol.

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Neutrosophy is the study of neutralities, which is an extension of discussing the truth of opinions. Neutrosophic logic can be applied to any field, to provide the solution for indeterminacy problem. Many of the real-world data have a problem of inconsistency, indeterminacy and incompleteness. Fuzzy sets provide a solution for uncertainties, and intuitionistic fuzzy sets handle incomplete information, but both concepts failed to handle indeterminate information. To handle this complicated situation, researchers require a powerful mathematical tool, naming, neutrosophic sets, which is a generalised concept of fuzzy and intuitionistic fuzzy sets. Neutrosophic sets provide a solution for both incomplete and indeterminate information. It has mainly three degrees of membership such as truth, indeterminacy and falsity. Boolean values are obtained from the three degrees of membership by cut relation method. Data items which contrast from other objects by their qualities are outliers. The weighted density outlier detection method based on rough entropy calculates weights of each object and attribute. From the obtained weighted values, the threshold value is fixed to determine outliers. Experimental analysis of the proposed method has been carried out with neutrosophic movie dataset to detect outliers and also compared with existing methods to prove its performance.

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Section: Related Workmentioning

confidence: 99%

Outlier detection in neutrosophic sets by using rough entropy based weighted density method

Sangeetha

Amalanathan

2020

CAAI trans. intell. technol.

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“…In 2019 and 2020, within the field of neutrosophy, Smarandache [21,22,23] generalized the classical algebraic structures to neutroalgebraic structures (or neutroalgebras) whose operations and axioms are partially true, partially indeterminate, and partially false as extensions of partial algebra, and to antialgebraic structures (or antialgebras) {whose operations and axioms are totally false}. And in general, he extended any classical structure, in no matter what field of knowledge, to a neutrostructure and an antistructure.…”

Section: Introductionmentioning

confidence: 99%

On Neutro-LA-semihypergroups and Neutro-Hv-LA-semigroups

Mirvakili

Rezaei

Al-Shanqiti

et al. 2023

Preprint

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In this paper, we extend the notion of LA-semihypergroups (resp. Hv-LA-semigroups) to neutro-LA-semihypergroups (respectively, neutro-Hv-LA-semigroups). Anti-LA-semihypergroups (respectively, anti-Hv-LA-semigroups) are studied and investigated some of their properties. We show that these new concepts are di fferent from classical concepts by several examples. These are particular cases of the classical algebraic structures generalized to neutroalgebraic structures and antialgebraic structures (Smarandache, 2019). 2000 Mathematics subject classification: 20N20, 20N99.

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“…To grab this kind of problem, Haque et al. ( 2020 ) extended this concept into generalised spherical fuzzy number (GSFN) after some crucial structural modification on SFN which is the particular case of single-valued spherical neutrosophic numbers (Smarandache 2017 ). Till now, only a few works have been done in this GSFN field (Haque et al.…”

Section: Introductionmentioning

confidence: 99%

Selection of most effective COVID-19 virus protector using a novel MCGDM technique under linguistic generalised spherical fuzzy environment

2022

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In this article, we have introduced a new linguistic generalized spherical fuzzy set by combining the idea of generalized spherical fuzzy set and linguistic fuzzy set. Linguistic generalized spherical fuzzy set is described by linguistic positive, linguistic neutral and linguistic negative membership degrees with the condition that the square sum of its linguistic membership degrees is less than or equal to 3 which deal with the uncertain and imprecise information in decision making in a much more suitable way. We have discussed some basic operations of linguistic generalized spherical fuzzy sets and introduced new score and accuracy functions to compare any two linguistic generalized spherical fuzzy numbers. We have developed various types of aggregation operators based on the newly defined linguistic generalized spherical fuzzy set, which have been manifested to construct a new multi-criteria group decision-making technique. Numerical example has been presented to demonstrate the proposed model. Finally, sensitivity and comparative analysis is performed to show the reliability and efficiency of the new multi-criteria group decision-making technique.

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Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Cited by 10 publications

References 57 publications

Outlier detection in neutrosophic sets by using rough entropy based weighted density method

Outlier detection in neutrosophic sets by using rough entropy based weighted density method

On Neutro-LA-semihypergroups and Neutro-Hv-LA-semigroups

Selection of most effective COVID-19 virus protector using a novel MCGDM technique under linguistic generalised spherical fuzzy environment

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