Possibility Distributions Generated by Intuitionistic $$\textsf {L}$$-Fuzzy Sets

2021 ◽  
pp. 149-163
Author(s):  
Stefania Boffa ◽  
Davide Ciucci
Keyword(s):  
Fuzzy Sets ◽  
Possibility Distributions

POSSIBILISTIC NORMALISATION AND REASONING UNDER PARTIAL INCONSISTENCY

2001 ◽  
Vol 09 (04) ◽  
pp. 413-436 ◽  
Author(s):  
JONATHAN LAWRY
Keyword(s):  
Fuzzy Sets ◽  
Possibility Distribution ◽  
Interval Approach ◽  
Possibility Distributions ◽  
Inconsistent Knowledge ◽  
Definition Of

The problem of normalisation of non-normalised fuzzy sets/possibility distributions is considered. A definition of a valid normalised possibility distribution is given at the mass assignment level and a characterisation of this definition at the distribution level is proposed. A number of possible normalisations are considered these being related to certain epistemic principles. Finally an interval approach to reasoning with partially inconsistent knowledge is introduced.

Normalizing Possibility Distributions Using t-Norms

2003 ◽  
Vol 11 (03) ◽  
pp. 343-360
Author(s):  
J. Recasens ◽  
J. Lawry
Keyword(s):  
Fuzzy Sets ◽  
Normalization Method ◽  
Fuzzy Subset ◽  
View Point ◽  
New Approach ◽  
Possibility Distributions ◽  
Fuzzy Subsets

A new approach to normalizing fuzzy sets is introduced where it is assumed that the normalization method is compatible with a given t-norm. In this context it is proved that the most usual ways to normalize fuzzy subsets correspond to the most common t-norms. For a given fuzzy subset μ, the corresponding normalized fuzzy subset [Formula: see text] can be viewed as the distribution of μ conditioned on the (degree of) existence of its elements with maximal membership. From this view point we investigate the less specific normal fuzzy subset of X among the most similar fuzzy subsets to μ and the normal fuzzy subset generating the same fuzzy T-preorder as μ.

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