# Representation of a Boolean algebra by its triangular norms.

Mathware and Soft Computing (1997)

- Volume: 4, Issue: 1, page 63-68
- ISSN: 1134-5632

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topRay, Suryansu. "Representation of a Boolean algebra by its triangular norms.." Mathware and Soft Computing 4.1 (1997): 63-68. <http://eudml.org/doc/39097>.

@article{Ray1997,

abstract = {Given a complete and atomic Boolean algebra B, there exists a family taugamma of triangular norms on B such that, under the partial ordering of triangular norms, taugamma is a Boolean algebra isomorphic to B, where gamma is the set of all atoms in B. In other words, as we have shown in this note, every complete and atomic Boolean algebra can be represented by its own triangular norms. What we have not shown in this paper is our belief that taugamma is not unique for B and that, for such a representation, B needs neither to be complete, nor to be atomic.},

author = {Ray, Suryansu},

journal = {Mathware and Soft Computing},

keywords = {Norma triangular; Algebras de Boole; Conjuntos difusos; complete Boolean algebra; fuzzy group; atomic Boolean algebra; triangular norms},

language = {eng},

number = {1},

pages = {63-68},

title = {Representation of a Boolean algebra by its triangular norms.},

url = {http://eudml.org/doc/39097},

volume = {4},

year = {1997},

}

TY - JOUR

AU - Ray, Suryansu

TI - Representation of a Boolean algebra by its triangular norms.

JO - Mathware and Soft Computing

PY - 1997

VL - 4

IS - 1

SP - 63

EP - 68

AB - Given a complete and atomic Boolean algebra B, there exists a family taugamma of triangular norms on B such that, under the partial ordering of triangular norms, taugamma is a Boolean algebra isomorphic to B, where gamma is the set of all atoms in B. In other words, as we have shown in this note, every complete and atomic Boolean algebra can be represented by its own triangular norms. What we have not shown in this paper is our belief that taugamma is not unique for B and that, for such a representation, B needs neither to be complete, nor to be atomic.

LA - eng

KW - Norma triangular; Algebras de Boole; Conjuntos difusos; complete Boolean algebra; fuzzy group; atomic Boolean algebra; triangular norms

UR - http://eudml.org/doc/39097

ER -

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