Three-way fuzzy concept lattice representation using neutrosophic set

Abstract

Recently, three-way concept lattice is studied to handle the uncertainty and incompleteness in the given attribute set based on acceptation, rejection, and uncertain regions. This paper aimed at analyzing the uncertainty and incompleteness in the given fuzzy attribute set characterized by truth-membership, indeterminacy-membership, and falsity membership functions of a defined single-valued neutrosophic set. For this purpose a method is proposed to generate the component wise three-way formal fuzzy concept and their hierarchical order visualization in the fuzzy concept lattice using the properties of neutrosophic graph, neutrosophic lattice, and Gödel residuated lattice with an illustrative example.

Complex neutrosophic concept lattice and its applications to air quality analysis

“…Recently, the calculus of complex vague set concept lattice [25] and its properties [26][27][28]34,35] is introduced for measuring the changes in uncertainty using amplitude and phase term of a complex set. It has given a new mathematical way to characterize the uncertainty and vagueness in attributes more understandable manner when compared to approaches available in unipolar fuzzy space [11,16,23,24] .…”

“…The reason is that the calculus of complex set [12,13] and concept lattice theory [15,24] provides a wellestablished mathematical framework to measure the human cognitive thought [14] . To measure the fluctuation in uncertainty exists in fuzzy attributes the calculus of complex fuzzy sets [12,13] become more helpful in its precise representation using amplitude and phase term in bipolar [22][23][24][25] or three-way space [26,27] for multi-decision process [28] . In this process, an important problem was addressed while handling the three-way fuzzy attributes [26][27][28] that how to measure their changes at given phase of time.…”

“…To measure the fluctuation in uncertainty exists in fuzzy attributes the calculus of complex fuzzy sets [12,13] become more helpful in its precise representation using amplitude and phase term in bipolar [22][23][24][25] or three-way space [26,27] for multi-decision process [28] . In this process, an important problem was addressed while handling the three-way fuzzy attributes [26][27][28] that how to measure their changes at given phase of time. To achieve this goal, properties of complex neutrosophic sets [3][4][5] and its graphs [10] are introduced for handling multi-decision attributes [9,25,28,33] .…”

“…This extensive version of complex fuzzy set [1,2,29,30] and its properties in the neutrosophic or three-way polar space [31][32][33] given a new orientation to analyze the data sets E-mail addresses: premsingh.csjm@gmail.com , premsingh.csjm@yahoo.com based on applied abstract algebra [1,2,15,21,[37][38][39] . Towards this extension recently, Singh [26][27][28] introduces properties of neutrosophic [26,27] and complex vague set [25] based concept lattice for precise approximation of computational linguistics exists in threeway decision space [47,48] . In this process a problem is addressed while handling the changes in three-way fuzzy attributes based on its truth, indeterminacy and falsity membership-values [3][4][5]10] .…”

“…To achieve this goal, the current paper focuses on depth analysis of complex neutrosophic context and its graphical structure visualization based on applied abstract algebra. Recently, some of the researchers started analyzing the indeterminacy based on their partial ordering [17][18][19][20] graphical visualization [26][27][28] to approximate it more prominently via three-way decision space [40][41][42] . All of these approaches fail in precise measurement of periodic changes in three-way or neutrosophic fuzzy attributes.…”