Science vs. Sophistry—A historical debate on bipolar fuzzy sets and equilibrium-based mathematics for AI&QI

2021 ◽  
pp. 1-20
Author(s):  
Wen-Ran Zhang
Keyword(s):  
Fuzzy Sets ◽  
Logical Basis ◽  
The Road ◽  
Computing Machinery ◽  
Computing Paradigm ◽  
Socially Constructed ◽  
Mathematical Abstraction ◽  
Bipolar Fuzzy Sets ◽  
Scientific Advances

The road from bipolar fuzzy sets to equilibrium-based mathematical abstraction is surveyed. A continuing historical debate on bipolarity and isomorphism is outlined. Related literatures are critically reviewed to counter plagiarism, distortion, renaming, and sophistry. Based on the debate, the term “isomorphistry” is coined. It is concluded that if isomorphism is used correctly it can be helpful in mathematics. If abused it may become isomorphistry—a kind of historical, socially constructed, entrenched, and “noble” hypocrisy hindering major scientific advances. It is shown that isomorphistry can be motivated by “denying” the originality of bipolar fuzzy sets and aimed at “justifying” plagiarism and distortion. Thus, isomorphistry is sophistry on isomorphism . Some (-,+)-bipolar isomorphistry behaviors are critiqued. YinYang vs. YangYin are distinguished. The geometrical and logical basis of equilibrium-based AI&QI computing machinery is introduced as a new computing paradigm with logically definable causality for mind-body unity. A philosophical joke on sophistry is appended.

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 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.

Application of Bipolar Fuzzy Sets in Planar Graphs

2016 ◽  
Vol 3 (2) ◽  
pp. 773-785 ◽  
Author(s):  
Muhammad Akram ◽  
Sovan Samanta ◽  
Madhumangal Pal
Keyword(s):  
Fuzzy Sets ◽  
Planar Graphs ◽  
Bipolar Fuzzy Sets

scholarly journals SMART WARNING SYSTEM USING EDGE COMPUTING

2021 ◽  
Author(s):  
Devi R
Keyword(s):  
Mobile Phones ◽  
Warning System ◽  
Edge Computing ◽  
Road Accidents ◽  
Human Errors ◽  
The Road ◽  
Computing Paradigm ◽  
Road Users ◽  
The People ◽  
General Rules

<div>In recent years, the occurrence of road accidents increases drastically. There are many factors influencing the road accidents. Nowadays usage of mobile phones while driving is common but it leads to the distraction in driving and subsequently causes accidents. Though jurisdictions are made that usage of electronic devices such as mobile phones, tablets, laptops while driving are illegal, no one is aware of that. The drivers who use mobile gadgets while driving not only risk their lives but also the people around them. Most of the road users are well aware of the general rules and safety measures. However due to human errors, accidents occur. To overcome from the human errors this paper focuses on developing a security alert system for drivers using edge computing paradigm.</div>

scholarly journals SMART WARNING SYSTEM USING EDGE COMPUTING

2021 ◽  
Author(s):  
Devi R
Keyword(s):  
Mobile Phones ◽  
Warning System ◽  
Edge Computing ◽  
Road Accidents ◽  
Human Errors ◽  
The Road ◽  
Computing Paradigm ◽  
Road Users ◽  
The People ◽  
General Rules

<div>In recent years, the occurrence of road accidents increases drastically. There are many factors influencing the road accidents. Nowadays usage of mobile phones while driving is common but it leads to the distraction in driving and subsequently causes accidents. Though jurisdictions are made that usage of electronic devices such as mobile phones, tablets, laptops while driving are illegal, no one is aware of that. The drivers who use mobile gadgets while driving not only risk their lives but also the people around them. Most of the road users are well aware of the general rules and safety measures. However due to human errors, accidents occur. To overcome from the human errors this paper focuses on developing a security alert system for drivers using edge computing paradigm.</div>

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.

Bipolar Fuzzy Sets and Equilibrium Relations

2011 ◽  
pp. 129-158
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Clustering ◽  
Theoretical Basis ◽  
Cognitive Map ◽  
Global Regulation ◽  
Quantum Lattices ◽  
Bipolar Fuzzy Sets

Based on bipolar sets and quantum lattices, the concepts of bipolar fuzzy sets and equilibrium relations are presented in this chapter for bipolar fuzzy clustering, coordination, and global regulation. Related theorems are proved. Simulated application examples in multiagent macroeconomics are illustrated. Bipolar fuzzy sets and equilibrium relations provide a theoretical basis for cognitive-map-based bipolar decision, coordination, and global regulation.

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.

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