Topological and Algebraic Structures of the Space of Atanassov's
Intuitionistic Fuzzy Values
- URL: http://arxiv.org/abs/2111.12677v1
- Date: Wed, 17 Nov 2021 06:43:02 GMT
- Title: Topological and Algebraic Structures of the Space of Atanassov's
Intuitionistic Fuzzy Values
- Authors: Xinxing Wu, Tao Wang, Peide Liu, Gul Deniz Cayli, Xu Zhang
- Abstract summary: We show that the space of intuitionistic fuzzy values (IFVs) with the linear order based on a score function and an accuracy function has the same algebraic structure as the one induced by the linear order based on a similarity function and an accuracy function.
By introducing a new operator for IFVs via the linear order based on a score function and an accuracy function, we present that such an operator is a strong negation on IFVs.
- Score: 8.518591988944358
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We demonstrate that the space of intuitionistic fuzzy values (IFVs) with the
linear order based on a score function and an accuracy function has the same
algebraic structure as the one induced by the linear order based on a
similarity function and an accuracy function. By introducing a new operator for
IFVs via the linear order based on a score function and an accuracy function,
we present that such an operator is a strong negation on IFVs. Moreover, we
propose that the space of IFVs is a complete lattice and a Kleene algebra with
the new operator. We also observe that the topological space of IFVs with the
order topology induced by the above two linear orders is not separable and
metrizable but compact and connected. From exactly new perspectives, our
results partially answer three open problems posed by Atanassov [Intuitionistic
Fuzzy Sets: Theory and Applications, Springer, 1999] and [On Intuitionistic
Fuzzy Sets Theory, Springer, 2012]. Furthermore, we construct an isomorphism
between the spaces of IFVs and q-rung orthopedic fuzzy values (q-ROFVs) under
the corresponding linear orders. Meanwhile, we introduce the concept of the
admissible similarity measures with particular orders for IFSs, extending the
previous definition of the similarity measure for IFSs, and construct an
admissible similarity measure with the linear order based on a score function
and an accuracy function, which is effectively applied to a pattern recognition
problem about the classification of building materials.
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