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.

scholarly journals On matrices whose real linear combinations are non-singular

1965 ◽  
Vol 16 (2) ◽  
pp. 318-318
Author(s):  
J. F. Adams ◽  
Peter D. Lax ◽  
Ralph S. Phillips
Keyword(s):  
Linear Combinations ◽  
Real Linear

On Matrices Whose Real Linear Combinations are Nonsingular

1965 ◽  
Vol 16 (2) ◽  
pp. 318 ◽  
Author(s):  
J. F. Adams ◽  
Peter D. Lax ◽  
Ralph S. Phillips
Keyword(s):  
Linear Combinations ◽  
Real Linear

scholarly journals Affine Independence in Vector Spaces

2010 ◽  
Vol 18 (1) ◽  
pp. 87-93 ◽  
Author(s):  
Karol Pąk
Keyword(s):  
Linear Space ◽  
Vector Spaces ◽  
Barycentric Coordinates ◽  
Independent Subset ◽  
Linear Combinations ◽  
Affine Hull ◽  
Real Linear Space ◽  
Real Linear ◽  
The Given

Affine Independence in Vector Spaces In this article we describe the notion of affinely independent subset of a real linear space. First we prove selected theorems concerning operations on linear combinations. Then we introduce affine independence and prove the equivalence of various definitions of this notion. We also introduce the notion of the affine hull, i.e. a subset generated by a set of vectors which is an intersection of all affine sets including the given set. Finally, we introduce and prove selected properties of the barycentric coordinates.

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.

scholarly journals Residual quotient fuzzy subset in near-rings

2006 ◽  
Vol 2006 ◽  
pp. 1-12
Author(s):  
P. Dheena ◽  
S. Coumaressane
Keyword(s):  
Fuzzy Subset ◽  
Fuzzy Subsets

For any fuzzy subsetsλandμ, we introduce the notion of residual quotient fuzzy subset (λ:μ) and we have characterized residual quotient fuzzy subset in near-rings.

A Fuzzy Logical Model of Computer-Assisted Medical Diagnosis

1980 ◽  
Vol 19 (03) ◽  
pp. 141-148 ◽  
Author(s):  
K.-P. Adlassnig
Keyword(s):  
Medical Diagnosis ◽  
Diagnostic System ◽  
Diagnostic Process ◽  
Computer Assisted ◽  
Fuzzy Relations ◽  
Fuzzy Subset ◽  
Symptom Pattern ◽  
A Value ◽  
Fuzzy Logical Model ◽  
Fuzzy Subsets

A model of a computer-assisted diagnostic system using fuzzy subsets has been developed. The physician documents symptom—diagnosis presence relationships and symptom—diagnosis conclusiveness relationships by means of labels of the fuzzy subsets never, almost never, very very seldom, very seldom, seldom, more or less seldom, not known, more or less often, often, very often, very very often, almost always, always. Symptoms are regarded as fuzzy subsets of reference sets. The reference set includes all values the symptom may assume. The degree of membership of a value in the fuzzy subset of a symptom is calculated when the patient’s symptom pattern is available. By means of compositions of fuzzy relations, four different diagnostic indications are determined for every diagnosis under consideration: presence indication, conclusiveness indication, non-presence indication and non-symptom presence indication. By performing the diagnostic process, the system provides the physician with proven diagnoses, excluded diagnoses and diagnostic hints, including reasons for the diagnoses displayed. Proposals for further investigations may also be requested.

A Fuzzy Logical Model of Computer-Assisted Medical Diagnosis

1980 ◽  
Vol 19 (03) ◽  
pp. 141-148
Author(s):  
K.-P. Adlassnig
Keyword(s):  
Medical Diagnosis ◽  
Diagnostic System ◽  
Diagnostic Process ◽  
Computer Assisted ◽  
Fuzzy Relations ◽  
Fuzzy Subset ◽  
Symptom Pattern ◽  
A Value ◽  
Fuzzy Logical Model ◽  
Fuzzy Subsets

A model of a computer-assisted diagnostic system using fuzzy subsets has been developed. The physician documents symptom—diagnosis presence relationships and symptom—diagnosis conclusiveness relationships by means of labels of the fuzzy subsets never, almost never, very very seldom, very seldom, seldom, more or less seldom, not known, more or less often, often, very often, very very often, almost always, always. Symptoms are regarded as fuzzy subsets of reference sets. The reference set includes all values the symptom may assume. The degree of membership of a value in the fuzzy subset of a symptom is calculated when the patient’s symptom pattern is available. By means of compositions of fuzzy relations, four different diagnostic indications are determined for every diagnosis under consideration: presence indication, conclusiveness indication, non-presence indication and non-symptom presence indication. By performing the diagnostic process, the system provides the physician with proven diagnoses, excluded diagnoses and diagnostic hints, including reasons for the diagnoses displayed. Proposals for further investigations may also be requested.

Correction to "On Matrices Whose Real Linear Combinations are Nonsingular"

1966 ◽  
Vol 17 (4) ◽  
pp. 945 ◽  
Author(s):  
J. F. Adams ◽  
Peter D. Lax ◽  
Ralph S. Phillips
Keyword(s):  
Linear Combinations ◽  
Real Linear

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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