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On strict lower and upper sections of weakly complete fuzzy pre-orders based on co-implication

机译:基于共蕴涵的弱完备模糊序的严格上下段

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摘要

Fono and Gwet [On strict lower and upper sections of fuzzy orderings, Fuzzy Sets and Systems 139 (2003) 583-599] introduced and studied strict lower section, strict upper section and strict order interval of a given weakly complete fuzzy pre-order R when the minimal regular fuzzy strict component of R is defined by the residual coimplicator of the Lukasiewicz t-conorm. And they gave an example of application of fuzzy strict lower sections in economics. In this paper, we generalize their framework for the minimal regular fuzzy strict component of R defined by the residual complicator of a continuous t-conorm. We show that fuzzy strict sections and fuzzy strict order intervals, defined in this general case, generate fuzzy topologies.
机译:Fono和Gwet [在模糊序的严格上下部分上,Fuzzy Sets and Systems 139(2003)583-599]引入并研究了给定弱完全模糊预序R的严格下半部分,严格上半部分和严格有序区间。当Lukasiewicz t-conorm的残差协整因子定义R的最小正则模糊严格分量时。并给出了模糊严格下节在经济学中的应用实例。在本文中,我们推广了它们的框架,该框架适用于由连续t-conorm的残差复杂因子定义的R的最小正则模糊严格分量。我们表明,在这种一般情况下定义的模糊严格部分和模糊严格顺序间隔会生成模糊拓扑。

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