Introduction to neutrosophy and neutrosophic environment

Smarandache, Florentín; Singh, Prem Kumar; Rao, V.V. Bapeswara; Yang, Hai-Long; Pătrașcu, Ion; Elhassouny, Azeddine

doi:10.1016/b978-0-12-818148-5.00001-1

Cited by 158 publications

(219 citation statements)

References 19 publications

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“…Each member x in A is described by three real subsets named as T , I and F in [0, 1]. Element x in A is expressed as x ( t , i , f ) which can be interpreted as it is t % true, i % indeterminacy, and f % false [ 33 ]. This interpretation depends on the application.…”

Section: Review Of Neutrosophic Set and Graph Cutmentioning

confidence: 99%

“…Neutrosophy is a branch of philosophy which studies the nature and scope of the neutralities and their interactions which is the basis of neutrosophic (NS) logic and NS set [ 33 ]. This theory was applied for image segmentation first by Guo et al [ 34 ] and has subsequently been successfully used for other image processing applications [ 35 – 41 ].…”

Section: Introductionmentioning

confidence: 99%

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Fully-automated segmentation of fluid regions in exudative age-related macular degeneration subjects: Kernel graph cut in neutrosophic domain

Rashno¹,

Nazari²,

Koozekanani³

et al. 2017

PLoS ONE

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A fully-automated method based on graph shortest path, graph cut and neutrosophic (NS) sets is presented for fluid segmentation in OCT volumes for exudative age related macular degeneration (EAMD) subjects. The proposed method includes three main steps: 1) The inner limiting membrane (ILM) and the retinal pigment epithelium (RPE) layers are segmented using proposed methods based on graph shortest path in NS domain. A flattened RPE boundary is calculated such that all three types of fluid regions, intra-retinal, sub-retinal and sub-RPE, are located above it. 2) Seed points for fluid (object) and tissue (background) are initialized for graph cut by the proposed automated method. 3) A new cost function is proposed in kernel space, and is minimized with max-flow/min-cut algorithms, leading to a binary segmentation. Important properties of the proposed steps are proven and quantitative performance of each step is analyzed separately. The proposed method is evaluated using a publicly available dataset referred as Optima and a local dataset from the UMN clinic. For fluid segmentation in 2D individual slices, the proposed method outperforms the previously proposed methods by 18%, 21% with respect to the dice coefficient and sensitivity, respectively, on the Optima dataset, and by 16%, 11% and 12% with respect to the dice coefficient, sensitivity and precision, respectively, on the local UMN dataset. Finally, for 3D fluid volume segmentation, the proposed method achieves true positive rate (TPR) and false positive rate (FPR) of 90% and 0.74%, respectively, with a correlation of 95% between automated and expert manual segmentations using linear regression analysis.

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Section: Review Of Neutrosophic Set and Graph Cutmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fully-automated segmentation of fluid regions in exudative age-related macular degeneration subjects: Kernel graph cut in neutrosophic domain

Rashno¹,

Nazari²,

Koozekanani³

et al. 2017

PLoS ONE

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“…In indeterminate and inconsistent environment, neutrosophic sets [ 28 , 29 ] are described independently by the truth, falsity, and indeterminacy membership degrees, but the aforementioned Z-numbers cannot depict them. Then, neutrosophic sets have been applied in various areas, such as image processing [ 30 ], decision making [ 31 – 34 ], medical diagnosis [ 35 – 37 ], and mechanical fault diagnosis [ 38 ].…”

Section: Introductionmentioning

confidence: 99%

Some aggregation operators of neutrosophic Z-numbers and their multicriteria decision making method

Rui

et al. 2020

Complex Intell. Syst.

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As the generalization of the classical fuzzy number, the concept of Z-number introduced by Zadeh indicates more ability to depict the human knowledge and judgments of both restraint and reliability as an order pair of fuzzy numbers. In indeterminacy and inconsistent environment, a neutrosophic set is described by the truth, falsity, and indeterminacy degrees, but they lack measures related to reliability. To describe the hybrid information of combining the truth, falsity and indeterminacy degrees with their corresponding reliability degrees, this paper first proposes the concept of a neutrosophic Z-number (NZN) set, which is a new framework of neutrosophic values combined with the neutrosophic measures of reliability, as the generalization of the Z-number and the neutrosophic set. Then, we define the operations of neutrosophic Z-numbers (NZNs) and a score function for ranking NZNs. Next, we present NZN weighted arithmetic averaging (NZNWAA) and NZN weighted geometric averaging (NZNWGA) operators to aggregate NZN information and investigate their properties. Regarding the NZNWAA and NZNWGA operators and the score function, a multicriteria decision making (MDM) approach is developed in the NZN environment. Finally, an illustrative example about the selection problem of business partners is given to demonstrate the applicability and effectiveness of the developed MDM approach in NZN setting.

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“…Malik and Riaz [32,33] studied action of modular group on real quadratic fields. Soft sets, neutrosophic set and rough sets with decision making problems have studied by many researchers [34][35][36][37][38][39][40]. We define SR-topology on soft rough set in the form of the pair τ SR = (τ SR , τ SR ), where τ SR is the lower SR-topology and τ SR is the upper SR-topology on set Y.…”

Section: Introductionmentioning

confidence: 99%

On Soft Rough Topology with Multi-Attribute Group Decision Making

et al. 2019

Self Cite

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Rough set approaches encounter uncertainty by means of boundary regions instead of membership values. In this paper, we develop the topological structure on soft rough set ( SR -set) by using pairwise SR -approximations. We define SR -open set, SR -closed sets, SR -closure, SR -interior, SR -neighborhood, SR -bases, product topology on SR -sets, continuous mapping, and compactness in soft rough topological space ( SRTS ). The developments of the theory on SR -set and SR -topology exhibit not only an important theoretical value but also represent significant applications of SR -sets. We applied an algorithm based on SR -set to multi-attribute group decision making (MAGDM) to deal with uncertainty.

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Introduction to neutrosophy and neutrosophic environment

Cited by 158 publications

References 19 publications

Fully-automated segmentation of fluid regions in exudative age-related macular degeneration subjects: Kernel graph cut in neutrosophic domain

Fully-automated segmentation of fluid regions in exudative age-related macular degeneration subjects: Kernel graph cut in neutrosophic domain

Some aggregation operators of neutrosophic Z-numbers and their multicriteria decision making method

On Soft Rough Topology with Multi-Attribute Group Decision Making

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