Prem Kumar Singh

Three-way fuzzy concept lattice representation using neutrosophic set

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.

m-polar fuzzy graph representation of concept lattice

Abstract Recently, the calculus of fuzzy concept lattice is studied beyond the three-way fuzzy space ([0,1] 3 ) for precise representation of uncertainty and vagueness in the attributes. However, to dovetail the uncertainty in case of voxel, multi-index or multi-polar information the properties of lattice theory need to be explored in component wise m -polar fuzzy space ( [ 0 , 1 ] m ). In this case, another problem arises while finding some of the hidden or interested pattern from the given m -polar fuzzy context for the knowledge processing tasks. To conquer this problem, current paper generalizes the mathematical background of concept lattice with m -polar fuzzy sets and its graphical properties. To elicit this objective, two methods are introduced for providing a unified framework based on discovered m -polar formal fuzzy concepts and their projection.

Concept Learning Using Vague Concept Lattice

Recently, the theory of Formal Concept Analysis is extensively studied with bipolar fuzzy setting for adequate analysis of vagueness in fuzzy attributes via a defined sharp boundary. However, many real life data sets contain vague attributes (i.e. beautiful, bald, and tadpole) which cannot be defined through a sharp or restricted boundaries. To process these types of data sets the current paper focused on disparate representation of vagueness in attributes through its evidence to support and reject. To achieve this goal, a method is proposed to generate vague concept lattice with an illustrative example.

Similar Vague Concepts Selection Using Their Euclidean Distance at Different Granulation

Recently, the calculus of fuzzy concept lattice is extensively studied with interval-valued and bipolar fuzzy set for the precise representation of vagueness in cognitive concept learning. In this process, selecting some of the semantic similar (or interesting) vague concept at user required granulation is addressed as one of the major issues. To conquer this problem, current paper aims at analyzing the cognitive concept learning based on the properties of vague graph, concept lattice and granular computing within (m × m) computational time. To mimic with the cognitive computing and its contextual data sets, two methods are proposed for the precise representation of human cognition based on the evidence to accept or reject the attributes using the calculus of vague set. The hierarchical order visualization among the extracted cognitive vague concept is shown through calculus of concept lattice for adequate description of their textual syntax analysis. In addition, another method is proposed to improve the quality of sentic (or cognitive) reasoning using semantics relationship among the discovered vague concepts at user defined information granulation. The obtained results from the proposed methods approve that the vague concept lattice and its reduction at user defined granulation provides an alternative way to analyze the cognitive contextual data set with an improved description of vague attributes “tall” and “young.” Euclidean distance provides a way to select some of the interesting vague concepts based on their semantic similarity. The obtained results from both of the proposed methods correspond to each other which validate the results. This paper establishes that cognitive contextual data set can be processed through the calculus of vague concept lattice, and granular computing. This gives an alternative and compact visualization of discovered patterns from the cognitive data set when compared to its numerical representation. In this way, the proposed method provides an adequate analysis for cognitive concept learning when compared to any of the available approaches. In addition, the proposed method provides various ways to select some of the interesting cognitive vague concepts at user defined granulation for their Euclidean distance within (m × m) computational time. However, the proposed method is unable to measure the fluctuation in uncertainty for the cognitive context at given phase of time. In the future, the author will focus on conquering this research problem with an illustrative example.

Complex Fuzzy Concept Lattice

Recently, several properties of complex fuzzy sets are introduced to measure the changes in dynamic or periodic fuzzy attributes using its amplitude and phase terms. In this process, a problem is observed while discovering some of the meaningful information from the given complex data sets for the knowledge processing tasks. The reason is lack of researches on complex fuzzy matrix and its graphical properties. To fill this backdrop, the current paper introduces a method for mathematical analysis of complex fuzzy context using the properties of lower neighbors and

Three-way n-valued neutrosophic concept lattice at different granulation

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Concept lattice reduction using different subset of attributes as information granules

δ-equality. The current paper also describes the application of the complex fuzzy concept lattice with an illustrative example.

Complex vague set based concept lattice

This paper introduces a mathematical model for precise analysis of uncertainty and its fluctuation in the given interval-valued fuzzy attributes. In this regard, a method is introduced for drawing the interval-valued complex lattice and its navigation at user required complex granules with demonstration.