scholarly journals L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras

2019 ◽  
Vol 17 (1) ◽  
pp. 1538-1546
Author(s):  
Xin Zhou ◽  
Liangyun Chen ◽  
Yuan Chang
Keyword(s):  
Fuzzy Sets ◽  
Homomorphic Image ◽  
Quotient Algebra ◽  
Algebraic Properties ◽  
Novikov Algebras ◽  
Fuzzy Ideal

Abstract In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. We get a sufficient and neccessary condition such that an L-fuzzy subspace is an L-fuzzy ideal. Moreover, we show that the quotient algebra A/μ of the L-fuzzy ideal μ is isomorphic to the algebra A/Aμ of the non-fuzzy ideal Aμ. Finally, we discuss the algebraic properties of surjective homomorphic image and preimage of an L-fuzzy ideal.

Image development in the framework of ξ –complex fuzzy morphisms

2021 ◽  
pp. 1-13
Author(s):  
Aneeza Imtiaz ◽  
Umer Shuaib ◽  
Abdul Razaq ◽  
Muhammad Gulistan
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Fuzzy Sets ◽  
Unit Disk ◽  
Homomorphic Image ◽  
Significant Role ◽  
Original Form ◽  
Mathematical Tool ◽  
Fuzzy Subgroups ◽  
Fundamental Theorems

The study of complex fuzzy sets defined over the meet operator (ξ –CFS) is a useful mathematical tool in which range of degrees is extended from [0, 1] to complex plane with unit disk. These particular complex fuzzy sets plays a significant role in solving various decision making problems as these particular sets are powerful extensions of classical fuzzy sets. In this paper, we define ξ –CFS and propose the notion of complex fuzzy subgroups defined over ξ –CFS (ξ –CFSG) along with their various fundamental algebraic characteristics. We extend the study of this idea by defining the concepts of ξ –complex fuzzy homomorphism and ξ –complex fuzzy isomorphism between any two ξ –complex fuzzy subgroups and establish fundamental theorems of ξ –complex fuzzy morphisms. In addition, we effectively apply the idea of ξ –complex fuzzy homomorphism to refine the corrupted homomorphic image by eliminating its distortions in order to obtain its original form. Moreover, to view the true advantage of ξ –complex fuzzy homomorphism, we present a comparative analysis with the existing knowledge of complex fuzzy homomorphism which enables us to choose this particular approach to solve many decision-making problems.

scholarly journals Neutrosophic Quotient Algebra

2019 ◽  
pp. 83-89
Author(s):  
Binu R ◽  
Keyword(s):  
Quotient Algebra ◽  
Neutrosophic Set ◽  
Algebraic Structures ◽  
Algebra Isomorphism ◽  
Algebraic Properties ◽  
Definition Of

The algebraic properties of neutrosphic ideals over algebra, isomorphism properties of neutrosophic ideal and neutrosophic modules over algebra are discussed in this paper. Some of the charactrisations of Neutrosophic quotient algebra are derived and the role of algebraic structures is studied in the context of neutrosophic set. This paper expands the definition of quotient algebra within the context of neutrosophical set.

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.

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.

scholarly journals Fuzzy Normed Rings

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 515 ◽  
Author(s):  
Aykut Emniyet ◽  
Memet Şahin
Keyword(s):  
Prime Ideal ◽  
Fuzzy Sets ◽  
Maximal Ideal ◽  
Ring Homomorphism ◽  
Ring Theory ◽  
Basic Properties ◽  
Normed Ring ◽  
Normed Ideal ◽  
Algebraic Properties ◽  
Definition Of

In this paper, the concept of fuzzy normed ring is introduced and some basic properties related to it are established. Our definition of normed rings on fuzzy sets leads to a new structure, which we call a fuzzy normed ring. We define fuzzy normed ring homomorphism, fuzzy normed subring, fuzzy normed ideal, fuzzy normed prime ideal, and fuzzy normed maximal ideal of a normed ring, respectively. We show some algebraic properties of normed ring theory on fuzzy sets, prove theorems, and give relevant examples.

scholarly journals On Some Nonclassical Algebraic Properties of Interval-Valued Fuzzy Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaoyan Liu ◽  
Feng Feng ◽  
Hui Zhang
Keyword(s):  
Fuzzy Sets ◽  
Soft Computing ◽  
General Framework ◽  
Soft Sets ◽  
Computing Model ◽  
Special Cases ◽  
Algebraic Properties ◽  
Different Types ◽  
Fuzzy Soft Sets ◽  
Interval Valued

Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov’s soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold in the conventional sense, but hold in weaker forms characterized in terms of the relation=L. We obtain a number of algebraic inequalities of interval-valued fuzzy soft sets characterized by interval-valued fuzzy soft inclusions. We also establish the weak idempotent law and the weak absorptive law of interval-valued fuzzy soft sets using interval-valued fuzzy softJ-equal relations. It is revealed that the soft product operations∧and∨of interval-valued fuzzy soft sets do not always have similar algebraic properties. Moreover, we find that only distributive inequalities described by the interval-valued fuzzy softL-inclusions hold for interval-valued fuzzy soft sets.

scholarly journals Three Ways of Defining Owa Operator on the Set of All Normal Convex Fuzzy Sets

2017 ◽  
Vol 69 (1) ◽  
pp. 101-118
Author(s):  
Zdenko Takáč
Keyword(s):  
Fuzzy Sets ◽  
Linear Order ◽  
Recent Literature ◽  
Weighted Averaging ◽  
Owa Operator ◽  
Main Obstacle ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Algebraic Properties

Abstract We deal with an extension of ordered weighted averaging (OWA, for short) operators to the set of all normal convex fuzzy sets in [0, 1]. The main obstacle to achieve this goal is the non-existence of a linear order for fuzzy sets. Three ways of dealing with the lack of a linear order on some set and defining OWA operators on the set appeared in the recent literature. We adapt the three approaches for the set of all normal convex fuzzy sets in [0, 1] and study their properties. It is shown that each of the three approaches leads to operator with desired algebraic properties, and two of them are also linear.

scholarly journals Algebraic properties of fuzzy sets

1972 ◽  
Vol 40 (2) ◽  
pp. 373-386 ◽  
Author(s):  
A De Luca ◽  
S Termini
Keyword(s):  
Fuzzy Sets ◽  
Algebraic Properties

THE LOOMIS–SIKORSKI THEOREM FOR -ALGEBRAS

2018 ◽  
Vol 106 (2) ◽  
pp. 200-234 ◽  
Author(s):  
ANATOLIJ DVUREČENSKIJ ◽  
OMID ZAHIRI
Keyword(s):  
Fuzzy Sets ◽  
Homomorphic Image ◽  
The State ◽  
Topological Properties ◽  
Maximal Ideals ◽  
Mv Algebra ◽  
Algebraic Operations

An EMV-algebra resembles an MV-algebra in which a top element is not guaranteed. For$\unicode[STIX]{x1D70E}$-complete$EMV$-algebras, we prove an analogue of the Loomis–Sikorski theorem showing that every$\unicode[STIX]{x1D70E}$-complete$EMV$-algebra is a$\unicode[STIX]{x1D70E}$-homomorphic image of an$EMV$-tribe of fuzzy sets where all algebraic operations are defined by points. To prove it, some topological properties of the state-morphism space and the space of maximal ideals are established.

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