Metrics of Symmetric Difference on Fuzzy Sets Based on R-implicators of the Usual Families of t-norms

Fotso, Siméon; Kamga, Romuald Thierry Dzati; Fono, Louis Aimé

doi:10.1007/978-3-319-66824-6_8

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2022

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“…The possibility theory [12,30] is presented as an alternative framework to represent uncertain information. Distance measures and metrics was used in [8,10,15,17,20,28,31] for decision making in several environments such as medical diagnosis and pattern recognition for example.…”

Section: Introductionmentioning

confidence: 99%

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

Kamga¹,

Engoulou²,

Fotso³

et al. 2022

NIFS

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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.

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