# Searching degrees of self-contradiction in Atanassov's fuzzy sets.

Elena E. Castiñeira; Susana Cubillo; Carmen Torres

Mathware and Soft Computing (2006)

- Volume: 13, Issue: 3, page 139-156
- ISSN: 1134-5632

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topCastiñeira, Elena E., Cubillo, Susana, and Torres, Carmen. "Searching degrees of self-contradiction in Atanassov's fuzzy sets.." Mathware and Soft Computing 13.3 (2006): 139-156. <http://eudml.org/doc/41878>.

@article{Castiñeira2006,

abstract = {In [11] and [12] Trillas et al. introduced the study of contradiction in the framework of Fuzzy Logic because of the significance to avoid contradictory outputs in the processes of inference. Later, the study of contradiction in the framework of intuitionistic or Atanassov s fuzzy sets was initiated in [6] and [5]. The aim of this work is to go into the problem of measuring the self-contradiction in the case of intuitionistc fuzzy sets, since it is interesting to know not only if a set is contradictory, but also the extend to which this property holds. The study of self-contradiction is tackled from two different aspects: the self-contradiction with respect to a specific intuitionistic fuzzy negation, and the self-contradition without depending on any negation. To the purpose of measuring the contradiction degrees, in both cases, some functions based on a previous geometrical study are defined. Also, some properties of these functions are shown as well as some particular relations among them.},

author = {Castiñeira, Elena E., Cubillo, Susana, Torres, Carmen},

journal = {Mathware and Soft Computing},

keywords = {Lógica difusa; Lógica intuicionista; intuitionistic fuzzy set},

language = {eng},

number = {3},

pages = {139-156},

title = {Searching degrees of self-contradiction in Atanassov's fuzzy sets.},

url = {http://eudml.org/doc/41878},

volume = {13},

year = {2006},

}

TY - JOUR

AU - Castiñeira, Elena E.

AU - Cubillo, Susana

AU - Torres, Carmen

TI - Searching degrees of self-contradiction in Atanassov's fuzzy sets.

JO - Mathware and Soft Computing

PY - 2006

VL - 13

IS - 3

SP - 139

EP - 156

AB - In [11] and [12] Trillas et al. introduced the study of contradiction in the framework of Fuzzy Logic because of the significance to avoid contradictory outputs in the processes of inference. Later, the study of contradiction in the framework of intuitionistic or Atanassov s fuzzy sets was initiated in [6] and [5]. The aim of this work is to go into the problem of measuring the self-contradiction in the case of intuitionistc fuzzy sets, since it is interesting to know not only if a set is contradictory, but also the extend to which this property holds. The study of self-contradiction is tackled from two different aspects: the self-contradiction with respect to a specific intuitionistic fuzzy negation, and the self-contradition without depending on any negation. To the purpose of measuring the contradiction degrees, in both cases, some functions based on a previous geometrical study are defined. Also, some properties of these functions are shown as well as some particular relations among them.

LA - eng

KW - Lógica difusa; Lógica intuicionista; intuitionistic fuzzy set

UR - http://eudml.org/doc/41878

ER -

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