Single-valued neutrosophic context analysis at distinct multi-granulation
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(2019) 38:80
Single-valued neutrosophic context analysis at distinct multi-granulation Prem Kumar Singh1 Received: 10 September 2018 / Revised: 13 March 2019 / Accepted: 18 March 2019 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019
Abstract In the current era, most of the researchers addressed an issue while dealing with uncertainty and indeterminacy that exists in fuzzy attributes. It becomes more complex when indeterminacy exists independently when compared to acceptation and rejection part. Due to which, some of the researchers tried to develop a three-way fuzzy concept lattice using neutrosophic set for characterization of uncertainty based on its acceptation, rejection, and uncertain parts, independently. In this process, a problem was addressed while processing the neutrosophic context based on user-required subset of attributes. It takes more time to extract interesting pattern from a given neutrosophic context having a large number of attributes. One of the solutions is to decompose the neutrosophic context via a defined multi-granulation for the truth, falsity and indeterminacy, membership values. To accomplish this task, a method is proposed in this paper using the computing paradigm of granular computing and applied lattice theory with an example. Keywords Formal concept analysis · Fuzzy concept lattice · Formal fuzzy concept · Three-way concept lattice · Neutrosophic set Mathematics Subject Classification 06Axx · 06Fxx · 08Cxx · 15Bxx · 68Wxx
1 Introduction The development of neutrosophic set1 given a mathematical way to characterize the indeterminacy in data with fuzzy attributes more independently rather than its acceptation and rejection part as discussed in Singh (2018e). This notable advantage of neutrosophic set theory (Smarandache 1999) molds the data analytics researchers in various applications as discussed (Broumi et al. 2018a, b). In this direction, one of the mathematical models 1 http://fs.unm.edu/FlorentinSmarandache.htm.
Communicated by Rosana Sueli da Motta Jafelice.
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Prem Kumar Singh [email protected]; [email protected] Amity Institute of Information Technology, Amity University, Sector–125, Noida, Uttar Pradesh 201313, India
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P. K. Singh
Table 1 Overview of potential findings on neutrosophic set for data analytics Methodology
Novelty
Pitfall
Ali and Smarandache (2017)
Complex neutrosophic set δ-equality method
No pattern given
Broumi and Smarandache (2014)
Neutrosophic complex set Graph method
No pattern given
Broumi et al. (2018a, b)
Neutrosophic set
Broumi et al. (2018b)
Complex neutrosophic set Similarity method
Granulation method
No pattern given
Djouadi (2011)
Possibility theory set
Djouadi and Prade (2011)
Possibility theory set
Fuzzy lattice theory
Granulation not discussed
Mao and Lin (2017)
Interval neutrosophic set
Graph method
Granulation not discussed
No granulation
Applied lattice theory Granulation not discussed
Mittal et al. (2017)
Neutrosophic lattice
Human cognition
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