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首页> 外文期刊>International Journal of Information Technology & Decision Making >YINYANG BIPOLAR FUZZY SETS AND FUZZY EQUILIBRIUM RELATIONS: FOR CLUSTERING, OPTIMIZATION, AND GLOBAL REGULATION
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YINYANG BIPOLAR FUZZY SETS AND FUZZY EQUILIBRIUM RELATIONS: FOR CLUSTERING, OPTIMIZATION, AND GLOBAL REGULATION

机译：阴阳双极性模糊集和模糊平衡关系：聚类，优化和全局调节

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摘要

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{sub}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 μ{sub}R:X => B{sub}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.
机译：基于双极点阵和L集的概念，提出了阴阳双极模糊集和模糊平衡关系，用于双极聚类，优化和全局调节。虽然将双极L集定义为双极平衡函数L，该函数将双极对象集X映射到任意双极晶格B上，如L：X => B，但这项工作着眼于单位正方形晶格B {sub} F = [ -1,0]×[0,1]。然后将双极集X中的强或弱双极模糊平衡关系定义为自反，对称和双极交互（或传递）模糊关系μ{sub} R：X => B {sub} F。提出了三种类型的双极α水平集用于双极去模糊和去极化。结果表明，模糊平衡关系是非线性双极泛化和/或多重相似关系的融合，它引起不相交的或联合的双极模糊子集，包括准联盟，冲突和和声集。然后，可以在不同的群集上利用均衡能量和稳定性分析来进行优化和全局调节。因此，这项工作为真相，模糊性和极性提供了统一的方法，并为基于认知图的可视化，优化，决策，全局调节和协调提供了一个整体理论。基本概念通过宏观经济学的模拟进行说明。

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