Characterizations of Fuzzy Sublattices Based on Fuzzy Point

2020 ◽  
pp. 105-127
Author(s):  
Chiranjibe Jana ◽  
Faruk Karaaslan
Keyword(s):  
Fuzzy Set ◽  
Cartesian Product ◽  
Inverse Image ◽  
Fuzzy Point ◽  
Fuzzy Ideal ◽  
The Relationship

In a lattice 𝔏, the authors used the concept of belongingness and quasi-coincidence of fuzzy point to a fuzzy set, and by this notion, (∈,∈∨q)-fuzzy sublattice, (∈,∈∨q)-fuzzy ideal, cartesian product of (∈,∈∨q)-fuzzy sublattice, (∈,∈∨q)-fuzzy complemented sublattice, and cartesian product of (∈,∈∨q)-fuzzy complemented sublattice are introduced, and their properties are briefly studied. The relationship between fuzzy sublattice and (∈,∈∨q)-fuzzy sublattice, fuzzy ideal and (∈,∈∨q)-fuzzy ideal of L are established. The authors prove that the cartesian product of two (∈,∈∨q)-fuzzy ideals of a lattice is not necessarily a fuzzy ideal of a lattice. The theory of image and inverse image of an (∈,∈∨q)-fuzzy sublattice and (∈,∈∨q)-fuzzy ideal, an (∈,∈∨q)-fuzzy complemented sublattice, and (∈,∈∨q)-fuzzy complemented ideal of 𝔏 on the basis of homomorphism of lattices are also significantly established.

scholarly journals A p-Ideal in BCI-Algebras Based on Multipolar Intuitionistic Fuzzy Sets

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 993
Author(s):  
Jeong-Gon Lee ◽  
Mohammad Fozouni ◽  
Kul Hur ◽  
Young Bae Jun
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Finite Degree ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Ideal ◽  
The Relationship

In 2020, Kang, Song and Jun introduced the notion of multipolar intuitionistic fuzzy set with finite degree, which is a generalization of intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. In this paper, we used this notion to study p-ideals of BCI-algebras. The notion of k-polar intuitionistic fuzzy p-ideals in BCI-algebras is introduced, and several properties were investigated. An example to illustrate the k-polar intuitionistic fuzzy p-ideal is given. The relationship between k-polar intuitionistic fuzzy ideal and k-polar intuitionistic fuzzy p-ideal is displayed. A k-polar intuitionistic fuzzy p-ideal is found to be k-polar intuitionistic fuzzy ideal, and an example to show that the converse is not true is provided. The notions of p-ideals and k-polar ( ∈ , ∈ ) -fuzzy p-ideal in BCI-algebras are used to study the characterization of k-polar intuitionistic p-ideal. The concept of normal k-polar intuitionistic fuzzy p-ideal is introduced, and its characterization is discussed. The process of eliciting normal k-polar intuitionistic fuzzy p-ideal using k-polar intuitionistic fuzzy p-ideal is provided.

Regular (ϵ,ϵνqk) - Fuzzy Duo Ordered Semigroups

2013 ◽  
Vol 756-759 ◽  
pp. 3084-3088
Author(s):  
Qi Cheng ◽  
Feng Lian Yuan ◽  
Yun Qiang Yin ◽  
Qing Yan Chen
Keyword(s):  
Fuzzy Set ◽  
Ordered Semigroup ◽  
Ordered Semigroups ◽  
Fuzzy Point ◽  
Fuzzy Ideal ◽  
Characterization Theorems ◽  
The Ideal

In this paper, the ideal of quasi-coincidence of a fuzzy point with a fuzzy set is generalized and the concept of an - fuzzy ideal (bi-ideal, quasi-ideal) of an ordered semigroup is introduced. The the notion of - fuzzy duo ordered semigroups is introduced and some characterization theorems are presented in terms of - fuzzy ideals.

Atanassov’s interval-valued intuitionistic fuzzy set theory applied in KU-subalgebras

2019 ◽  
Vol 11 (02) ◽  
pp. 1950023 ◽  
Author(s):  
Tapan Senapati ◽  
K. P. Shum
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Set ◽  
Inverse Image ◽  
Fundamental Properties ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this paper, the notion of interval-valued intuitionistic fuzzy (IVIF) [Formula: see text]-subalgebras of [Formula: see text]-algebras are introduced and some fundamental properties are discussed. The image and the inverse image of IVIF [Formula: see text]-subalgebras are defined and how the image and the inverse image of IVIF [Formula: see text]-subalgebras in [Formula: see text]-algebras become IVIF [Formula: see text]-subalgebras are studied. Moreover, the cartesian product of IVIF [Formula: see text]-subalgebras are given.

A Hesitant Intuitionistic Fuzzy Set Approach to Study Ideals of Semirings

2021 ◽  
Vol 10 (3) ◽  
pp. 1-17
Author(s):  
Debabrata Mandal
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Set ◽  
Ideal Theory ◽  
Hesitant Fuzzy Set ◽  
Neutrosophic Set ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
The Ideal

The classical set theory was extended by the theory of fuzzy set and its several generalizations, for example, intuitionistic fuzzy set, interval valued fuzzy set, cubic set, hesitant fuzzy set, soft set, neutrosophic set, etc. In this paper, the author has combined the concepts of intuitionistic fuzzy set and hesitant fuzzy set to study the ideal theory of semirings. After the introduction and the priliminary of the paper, in Section 3, the author has defined hesitant intuitionistic fuzzy ideals and studied several properities of it using the basic operations intersection, homomorphism and cartesian product. In Section 4, the author has also defined hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals of a semiring and used these to find some characterizations of regular semiring. In that section, the author also has discussed some inter-relations between hesitant intuitionistic fuzzy ideals, hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals, and obtained some of their related properties.

scholarly journals Bipolar Fuzzy Implicative Ideals of BCK-Algebras

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
G. Muhiuddin ◽  
D. Al-Kadi
Keyword(s):  
Fuzzy Set ◽  
Extension Property ◽  
Fuzzy Ideal

The notion of bipolar fuzzy implicative ideals of a BCK-algebra is introduced, and several properties are investigated. The relation between a bipolar fuzzy ideal and a bipolar fuzzy implicative ideal is studied. Characterizations of a bipolar fuzzy implicative ideal are given. Conditions for a bipolar fuzzy set to be a bipolar fuzzy implicative ideal are provided. Extension property for a bipolar fuzzy implicative ideal is stated.

scholarly journals The Relationship between Environmental Uncertainty and Enterprise Performance. A Fuzzy-Set Analysis

2018 ◽  
Vol 1 (1) ◽  
pp. 809-816
Author(s):  
Anna Kwiotkowska ◽  
Magdalena Gębczyńska
Keyword(s):  
Comparative Analysis ◽  
Firm Performance ◽  
Fuzzy Set ◽  
Small And Medium Enterprises ◽  
Qualitative Comparative Analysis ◽  
Environmental Uncertainty ◽  
Business Environment ◽  
Market Demand ◽  
General Business ◽  
The Relationship

Abstract The purpose of this paper is to explore causal complexity in the relationship between environmental uncertainty and firm’s performance. Due to complexity in the external and internal environment, the relationship between environment and firm performance rests not only on a single attribute but on the interrelation and complementarities between multiple characteristics such as firm features and external factors. This study examines the influence of a firm’s specific characteristics and the dimensions of environmental uncertainty on the company’s performance. Fuzzy-set qualitative comparative analysis is used to analyze data collected via questionnaires from 58 Polish small and medium enterprises (SMEs). The results suggest that characteristics of the general business environment, as well as the firm-specific characteristics all matter to firm performance. In addition, our findings clearly demonstrate that the determination of high firm performance is underpinned by substantial interdependence among the selected conditions and complexity. Therefore, any particular condition may have a different or even opposite effect on the outcome depending on the presence or absence of other conditions. Based on this, we conclude that external environmental uncertainty characteristics, with the dimensions of competitive intensity, technological turbulence and market/demand turbulence, are not as important as the other conditions for high-performing firms. The study offers a new perspective on the relationship between environmental uncertainty and firm performance with its systematic comparative analysis of complex cases. It identifies different combinations of conditions (paths) leading to a high firm performance.

THE NECESSITY OF THE STRONG α-CUTS OF A FUZZY SET

2001 ◽  
Vol 09 (02) ◽  
pp. 249-262 ◽  
Author(s):  
INÉS COUSO ◽  
SUSANA MONTES ◽  
PEDRO GIL
Keyword(s):  
Fuzzy Set ◽  
Unknown Parameter ◽  
New Interpretation ◽  
The Relationship ◽  
Point Coverage

Some aspects of the relationship between Goodman and Nguyen's one-point coverage interpretation of a fuzzy set and Zadeh's possibilistic interpretation are discussed. As a result of this, we derive a new interpretation of the strong α-cut of a normalized fuzzy set, namely that of being the most precise set we are sure to contain an unknown parameter with probability greater than or equal to 1-α.

Fuzzy roughness via ideals

2020 ◽  
Vol 39 (5) ◽  
pp. 6869-6880
Author(s):  
S. H. Alsulami ◽  
Ismail Ibedou ◽  
S. E. Abbas
Keyword(s):  
Fuzzy Set ◽  
Closure Operator ◽  
Approximation Space ◽  
Approximation Spaces ◽  
Fuzzy Connectedness ◽  
Fuzzy Approximation ◽  
Separation Axioms ◽  
Fuzzy Ideal ◽  
Interior Operator

In this paper, we join the notion of fuzzy ideal to the notion of fuzzy approximation space to define the notion of fuzzy ideal approximation spaces. We introduce the fuzzy ideal approximation interior operator int Φ λ and the fuzzy ideal approximation closure operator cl Φ λ , and moreover, we define the fuzzy ideal approximation preinterior operator p int Φ λ and the fuzzy ideal approximation preclosure operator p cl Φ λ with respect to that fuzzy ideal defined on the fuzzy approximation space (X, R) associated with some fuzzy set λ ∈ IX. Also, we define fuzzy separation axioms, fuzzy connectedness and fuzzy compactness in fuzzy approximation spaces and in fuzzy ideal approximation spaces as well, and prove the implications in between.

Interval-Valued Fuzzy H-Ideals on ß-Algebra

2020 ◽  
pp. 244-274
Author(s):  
Prakasam Muralikrishna ◽  
Tapan Senapati ◽  
Perumal Hemavathi
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Cartesian Product ◽  
Algebraic Structures ◽  
Interval Valued

The notion of interval valued fuzzy set was first introduced by Zadeh as a generalization of fuzzy sets. Using interval valued fuzzy set, various algebraic structures and related topics were discussed. This chapter extends fuzzy H-ideal into interval valued fuzzy H-ideals of β-algebra and deals some related results. It also provides the study on homomorphic images of an interval valued fuzzy H-ideals of β-algebra and the idea of Cartesian product of interval valued fuzzy H-ideals of β-algebra.

scholarly journals Foldness of Bipolar Fuzzy Sets and Its Application in BCK/BCI-Algebras

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1036
Author(s):  
Young Bae Jun ◽  
Seok-Zun Song
Keyword(s):  
Information Processing ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Negative Information ◽  
Positive Information ◽  
Fuzzy Ideal ◽  
Recent Trends ◽  
Modern Information ◽  
Bipolar Fuzzy Sets

Recent trends in modern information processing have focused on polarizing information, and and bipolar fuzzy sets can be useful. Bipolar fuzzy sets are one of the important tools that can be used to distinguish between positive information and negative information. Positive information, for example, already observed or experienced, indicates what is guaranteed to be possible, and negative information indicates that it is impossible, prohibited, or certainly false. The purpose of this paper is to apply the bipolar fuzzy set to BCK/BCI-algebras. The notion of (translated) k-fold bipolar fuzzy sets is introduced, and its application in BCK/BCI-algebras is discussed. The concepts of k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal are introduced, and related properties are investigated. Characterizations of k-fold bipolar fuzzy subalgebra/ideal are considered, and relations between k-fold bipolar fuzzy subalgebra and k-fold bipolar fuzzy ideal are displayed. Extension of k-fold bipolar fuzzy subalgebra is discussed.

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