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.

scholarly journals A characterization of regular, intra-regular, left quasi-regular and semisimple hypersemigroups in terms of fuzzy sets

2017 ◽  
Vol 26 (1) ◽  
pp. 46-56
Author(s):  
Niovi Kehayopulu
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Subset ◽  
Fuzzy Subsets

Abstract We prove that an hypersemigroup H is regular if and only, for any fuzzy subset f of H, we have f ≼ f ο 1 ο f and it is intra-regular if and only if, for any fuzzy subset f of H, we have f ≼1 ο f ο f ο 1. An hypersemigroup H is left (resp. right) quasi-regular if and only if, for any fuzzy subset f of H we have f ≼ 1 ο f ο 1 ο f (resp. f ≼ f ο 1 ο f ο 1) and it is semisimple if and only if, for any fuzzy subset f of H we have f ≼ 1 ο f ο 1 ο f ο 1. The characterization of regular and intra-regular hypersemigroups in terms of fuzzy subsets are very useful for applications.

A new approach for computing with fuzzy sets using interval analysis

2007 ◽  
Author(s):  
Arunas Mazeika ◽  
Luc Jaulin ◽  
Christophe Osswald
Keyword(s):  
Fuzzy Sets ◽  
Interval Analysis ◽  
New Approach

scholarly journals The Interaction between Fuzzy Subsets and Groupoids

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Seung Joon Shin ◽  
Hee Sik Kim ◽  
J. Neggers
Keyword(s):  
Binary System ◽  
Fuzzy Subset ◽  
Linear Combinations ◽  
Real Linear ◽  
Fuzzy Subsets

We discuss properties of a class of real-valued functions on a setX2constructed as finite (real) linear combinations of functions denoted asX,*;μ, whereX,*is a groupoid (binary system) andμis a fuzzy subset ofXand whereX,*;μx,y≔μx*y-minμx,μy. Many properties, for example,μbeing a fuzzy subgroupoid ofX,*, can be restated as some properties ofX,*;μ. Thus, the context provided opens up ways to consider well-known concepts in a new light, with new ways to prove known results as well as to provide new questions and new results. Among these are identifications of many subsemigroups and left ideals ofBinX;□for example.

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