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Issue:On some classes of Tchebychev distance based on intuitionistic fuzzy cardinality and intuitionistic fuzzy statistical description

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Title of paper: On some classes of Tchebychev distance based on intuitionistic fuzzy cardinality and intuitionistic fuzzy statistical description
Author(s):
Romuald Thierry Dzati Kamga
Department of Mathematics, URFD MIBA, CRFD-STG, University of Yaounde I, Cameroon, P.O.BOX. 812 Yaounde, Cameroon
romualdkamga1@yahoo.fr
Bertrand Mbama Engoulou
Laboratory of Mathematics and Department of Mathematics and Computer Science, Faculty of Sciences, University of Douala, Cameroon
mbama0479@yahoo.fr
Siméon Fotso
Department of Mathematics, Higher Teacher’s Training College, University of Yaounde I ´, P.O.BOX. 47 Yaounde, Cameroon
simeonfotso@yahoo.fr
Louis Aimé Fono
Laboratory of Mathematics and Department of Mathematics and Computer Science, Faculty of Sciences, University of Douala, Cameroon
lfono2000@yahoo.fr
Presented at: 25th ICIFS, Sofia, 9—10 September 2022
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 3, pages 238–258
DOI: https://doi.org/10.7546/nifs.2022.28.3.238-258
Download:  PDF (298  Kb, File info)
Abstract: The Tchebychev distance on fuzzy sets (FSs) has been proposed to construct a measure of proximity between two modalities in a two-dimensional statistical description. The parameterized symmetric difference operations and cardinality for intuitionistic fuzzy sets (IFSs) has been proposed. This paper extends to intuitionistic fuzzy set the Tchebychev distance and possibility measure on fuzzy sets. More precisely, we firstly use the parameterized symmetric difference operations and the cardinality on IFSs to propose a Tchebychev distance measure for IFSs. From these, we then deduce two examples of metrics. Secondly, we introduce an intuitionistic fuzzy mapping that preserves the properties of the fuzzy mapping. We use this mapping to propose a Tchebychev possibility measure based on IF-cardinality. This leads to define a proximity measure between two modalities of a given character in a two-dimensional intuitionistic fuzzy statistical description.
Keywords: Intuitionistic fuzzy set, Distance measure, Metrics, Possibility measure, Intuitionistic fuzzy mapping, Intuitionistic fuzzy statistical description.
AMS Classification: 03F55
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