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.

Does Performing Other Audit Tasks Affect Going-Concern Judgments?

1999 ◽  
Vol 74 (4) ◽  
pp. 493-508 ◽  
Author(s):  
Stephen E. Rau ◽  
Donald V. Moser
Keyword(s):  
Information Processing ◽  
Review Process ◽  
Negative Information ◽  
The Other ◽  
Positive Information ◽  
Going Concern ◽  
Staff Members

This study examines whether personally performing other audit tasks can bias supervising seniors' going-concern judgments. During an audit, the senior performs some audit tasks him/herself and delegates other tasks to staff members. When personally performing an audit task, the senior would focus on the evidence related to that task. We predict that such evidence will have greater influence on the senior's subsequent going-concern judgment. The results of our experiment are consistent with our predictions. When provided with an identical set of information, seniors who performed another audit task for which the underlying facts of the case reflected positively (negatively) on the company's viability, subsequently made going-concern judgments that were relatively more positive (negative). Our results also demonstrate that the well-documented tendency of auditors to attend more to negative information does not always dominate auditors' information processing. Subjects who performed the task for which the underlying facts reflected positively on the company's viability directed their attention to such positive information and, consequently, both their memory and judgments were more positive than those of subjects in the other conditions. Recent findings indicating that biases in seniors' going-concern judgments may not be fully offset in the review process are discussed along with other potential implications of our results.

scholarly journals Modeling Imprecise and Bipolar Algebraic and Topological Relations using Morphological Dilations

2021 ◽  
Vol 5 (1) ◽  
pp. 1-20
Author(s):  
Isabelle Bloch
Keyword(s):  
Information Processing ◽  
Fuzzy Sets ◽  
Mathematical Morphology ◽  
Complete Lattice ◽  
Spatial Reasoning ◽  
Topological Relations ◽  
Preference Modeling ◽  
Logical Sense ◽  
Bipolar Fuzzy Sets ◽  
Core Features

Abstract In many domains of information processing, such as knowledge representation, preference modeling, argumentation, multi-criteria decision analysis, spatial reasoning, both vagueness, or imprecision, and bipolarity, encompassing positive and negative parts of information, are core features of the information to be modeled and processed. This led to the development of the concept of bipolar fuzzy sets, and of associated models and tools, such as fusion and aggregation, similarity and distances, mathematical morphology. Here we propose to extend these tools by defining algebraic and topological relations between bipolar fuzzy sets, including intersection, inclusion, adjacency and RCC relations widely used in mereotopology, based on bipolar connectives (in a logical sense) and on mathematical morphology operators. These definitions are shown to have the desired properties and to be consistent with existing definitions on sets and fuzzy sets, while providing an additional bipolar feature. The proposed relations can be used for instance for preference modeling or spatial reasoning. They apply more generally to any type of functions taking values in a poset or a complete lattice, such as L-fuzzy sets.

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.

Complex bipolar fuzzy sets: An application in a transport’s company

2020 ◽  
pp. 1-17
Author(s):  
Muhammad Gulistan ◽  
Naveed Yaqoob ◽  
Ahmed Elmoasry ◽  
Jawdat Alebraheem
Keyword(s):  
Fuzzy Sets ◽  
Membership Function ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Cartesian Product ◽  
Real Numbers ◽  
Wide Range ◽  
Fuzzy Aggregation ◽  
Bipolar Fuzzy Sets ◽  
Range Of Values

Zadeh’s fuzzy sets are very useful tool to handle imprecision and uncertainty, but they are unable to characterize the negative characteristics in a certain problem. This problem was solved by Zhang et al. as they introduced the concept of bipolar fuzzy sets. Thus, fuzzy set generalizes the classical set and bipolar fuzzy set generalize the fuzzy set. These theories are based on the set of real numbers. On the other hand, the set of complex numbers is the generalization of the set of real numbers so, complex fuzzy sets generalize the fuzzy sets, with wide range of values to handle the imprecision and uncertainty. So, in this article, we study complex bipolar fuzzy sets which is the generalization of bipolar fuzzy set and complex fuzzy set with wide range of values by adding positive membership function and negative membership function to unit circle in the complex plane, where one can handle vagueness in a much better way as compared to bipolar fuzzy sets. Thus this paper leads us towards a new direction of research, which has many applications in different directions. We develop the notions of union, intersection, complement, Cartesian product and De-Morgan’s Laws of complex bipolar fuzzy sets. Furthermore, we develop the complex bipolar fuzzy relations, fundamental operations on complex bipolar fuzzy matrices and some operators of complex bipolar fuzzy matrices. We also discuss the distance measure on complex bipolar fuzzy sets and complex bipolar fuzzy aggregation operators. Finally, we apply the developed approach to a numerical problem with the algorithm.

On 2-absorbing bipolar fuzzy ideals over LA -semigroups

2021 ◽  
Vol 41 (2) ◽  
pp. 3173-3181
Author(s):  
Pairote Yiarayong
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Bipolar Fuzzy Sets ◽  
The Relationship

The aim of this manuscript is to apply bipolar fuzzy sets for dealing with several kinds of theories in LA -semigroups. To begin with, we introduce the concept of 2-absorbing (quasi-2-absorbing) bipolar fuzzy ideals and strongly 2-absorbing (quasi-strongly 2-absorbing) bipolar fuzzy ideals in LA -semigroups, and investigate several related properties. In particular, we show that a bipolar fuzzy set A = ( μ A P , μ A N ) over an LA -semigroup S is weakly 2-absorbing if and only if [ B ⊙ C ] ⊙ D ⪯ A implies B ⊙ C ⪯ A or C ⊙ D ⪯ A or B ⊙ D ⪯ A for any bipolar fuzzy sets B = ( μ B P , μ B N ) , C = ( μ C P , μ C N ) and D = ( μ D P , μ D N ) . Also, we give some characterizations of quasi-strongly 2-absorbing bipolar fuzzy ideals over an LA -semigroup S by bipolar fuzzy points. In conclusion of this paper we prove that the relationship between quasi-strongly 2-absorbing bipolar fuzzy ideals over an LA -semigroup S and quasi-2-absorbing bipolar fuzzy ideals over S.

On 2-absorbing bipolar fuzzy ideals over LA -semigroups

2021 ◽  
pp. 1-9
Author(s):  
Pairote Yiarayong
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Bipolar Fuzzy Sets ◽  
The Relationship

The aim of this manuscript is to apply bipolar fuzzy sets for dealing with several kinds of theories in LA -semigroups. To begin with, we introduce the concept of 2-absorbing (quasi-2-absorbing) bipolar fuzzy ideals and strongly 2-absorbing (quasi-strongly 2-absorbing) bipolar fuzzy ideals in LA -semigroups, and investigate several related properties. In particular, we show that a bipolar fuzzy set A = ( μ A P , μ A N ) over an LA -semigroup S is weakly 2-absorbing if and only if [ B ⊙ C ] ⊙ D ⪯ A implies B ⊙ C ⪯ A or C ⊙ D ⪯ A or B ⊙ D ⪯ A for any bipolar fuzzy sets B = ( μ B P , μ B N ) , C = ( μ C P , μ C N ) and D = ( μ D P , μ D N ) . Also, we give some characterizations of quasi-strongly 2-absorbing bipolar fuzzy ideals over an LA -semigroup S by bipolar fuzzy points. In conclusion of this paper we prove that the relationship between quasi-strongly 2-absorbing bipolar fuzzy ideals over an LA -semigroup S and quasi-2-absorbing bipolar fuzzy ideals over S.

Interval-Valued Doubt Fuzzy Ideals in BCK-Algebras

2019 ◽  
Vol 8 (4) ◽  
pp. 101-121
Author(s):  
Tripti Bej ◽  
Madhumangal Pal
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Common Features ◽  
Fuzzy Ideal ◽  
Interval Valued

Nearly forty years ago, interval-valued fuzzy sets were propounded by Zadeh as the normal ramification of fuzzy sets. This article focuses on the basics of a theory for such an interval-valued fuzzy set becoming interval-valued doubt fuzzy subalgebra and an interval-valued doubt fuzzy ideal of BCK-algebras. Also, the authors discuss fuzzy translation, fuzzy multiplication of an interval-valued doubt fuzzy subalgebra/ideal of a BCK-algebra. Besides this, the authors have attempted to substantiate a few common features relating them. At the same time, some properties of interval-valued doubt fuzzy ideals under homomorphism are investigated and the product of interval-valued doubt fuzzy ideals in BCK-algebras is also established.

scholarly journals m-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Juanjuan Chen ◽  
Shenggang Li ◽  
Shengquan Ma ◽  
Xueping Wang
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Real World ◽  
Ordinal Number ◽  
Information Uncertainty ◽  
Multi Index ◽  
Limit Process ◽  
Multi Agent ◽  
Bipolar Fuzzy Sets ◽  
Real World Problems

Recently, bipolar fuzzy sets have been studied and applied a bit enthusiastically and a bit increasingly. In this paper we prove that bipolar fuzzy sets and0,12-sets (which have been deeply studied) are actually cryptomorphic mathematical notions. Since researches or modelings on real world problems often involve multi-agent, multi-attribute, multi-object, multi-index, multi-polar information, uncertainty, or/and limit process, we put forward (or highlight) the notion ofm-polar fuzzy set (actually,0,1m-set which can be seen as a generalization of bipolar fuzzy set, wheremis an arbitrary ordinal number) and illustrate how many concepts have been defined based on bipolar fuzzy sets and many results which are related to these concepts can be generalized to the case ofm-polar fuzzy sets. We also give examples to show how to applym-polar fuzzy sets in real world problems.

scholarly journals Bad World: The Negativity Bias in International Politics

2019 ◽  
Vol 43 (3) ◽  
pp. 96-140 ◽  
Author(s):  
Dominic D.P. Johnson ◽  
Dominic Tierney
Keyword(s):  
International Relations ◽  
Fundamental Principle ◽  
Human Mind ◽  
Negative Information ◽  
Theory And Practice ◽  
Negativity Bias ◽  
Positive Information ◽  
Psychological Phenomena ◽  
Wide Range ◽  
New Research

A major puzzle in international relations is why states privilege negative over positive information. States tend to inflate threats, exhibit loss aversion, and learn more from failures than from successes. Rationalist accounts fail to explain this phenomenon, because systematically overweighting bad over good may in fact undermine state interests. New research in psychology, however, offers an explanation. The “negativity bias” has emerged as a fundamental principle of the human mind, in which people's response to positive and negative information is asymmetric. Negative factors have greater effects than positive factors across a wide range of psychological phenomena, including cognition, motivation, emotion, information processing, decision-making, learning, and memory. Put simply, bad is stronger than good. Scholars have long pointed to the role of positive biases, such as overconfidence, in causing war, but negative biases are actually more pervasive and may represent a core explanation for patterns of conflict. Positive and negative dispositions apply in different contexts. People privilege negative information about the external environment and other actors, but positive information about themselves. The coexistence of biases can increase the potential for conflict. Decisionmakers simultaneously exaggerate the severity of threats and exhibit overconfidence about their capacity to deal with them. Overall, the negativity bias is a potent force in human judgment and decisionmaking, with important implications for international relations theory and practice.

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.

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