YINYANG BIPOLAR FUZZY SETS AND FUZZY EQUILIBRIUM RELATIONS: FOR CLUSTERING, OPTIMIZATION, AND GLOBAL REGULATION

2006 ◽  
Vol 05 (01) ◽  
pp. 19-46 ◽  
Author(s):  
WEN-RAN ZHANG
Keyword(s):  
Fuzzy Sets ◽  
Square Lattice ◽  
Equilibrium Relation ◽  
Global Regulation ◽  
Similarity Relations ◽  
Equilibrium Function ◽  
Clustering Optimization ◽  
Holistic Theory ◽  
Α Level ◽  
Bipolar Fuzzy Sets

Based on the notions of bipolar lattices and L-sets, YinYang bipolar fuzzy sets and fuzzy equilibrium relations are presented for bipolar clustering, optimization, and global regulation. While a bipolar L-set is defined as a bipolar equilibrium function L that maps a bipolar object set X over an arbitrary bipolar lattice B as L:X ⇒ B, this work focuses on the unit square lattice B F = [-1, 0] × [0, 1]. A strong or weak bipolar fuzzy equilibrium relation in a bipolar set X is then defined as a reflexive, symmetric, and bipolar interactive (or transitive) fuzzy relation μR: X ⇒ B F . Three types of bipolar α-level sets are presented for bipolar defuzzification and depolarization. It is shown that a fuzzy equilibrium relation is a non-linear bipolar generalization and/or fusion of multiple similarity relations, which induces disjoint or joint bipolar fuzzy subsets including quasi-coalition, conflict, and harmony sets. Equilibrium energy and stability analysis can then be utilized on different clusters for optimization and global regulation purposes. Thus, this work provides a unified approach to truth, fuzziness, and polarity and leads to a holistic theory for cognitive-map-based visualization, optimization, decision, global regulation, and coordination. Basic concepts are illustrated with a simulation in macroeconomics.

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.

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

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.

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