Decision-theoretic rough set approach for fuzzy decisions based on fuzzy probability measure and decision making

Dai, Jianhua; Zheng, Guojie; Hu, Qinghua; Liu, Maofu; Su, Huashi

doi:10.3233/ifs-162200

Cited by 10 publications

(3 citation statements)

References 42 publications

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“…If we want to obtain an optimal separation threshold for passive shadowed sets, we can only modify line 16 in Algorithm 1 as follows: (9) In this case, the minimum optimal solution point in Q A ( ) will be achieved, which minimizes the optimization objective function and derives the minimal positive region and negative region at the same time.…”

Section: Shadowed Setsmentioning

confidence: 99%

“…Two important paradigms of granular computing, rough sets and fuzzy sets, to a significant extent, were developed separately. There is extensive literature on integrating and combining them . Shadowed sets, proposed by Pedrycz, are considered a bridge between rough sets and fuzzy sets and are an emerging aspect of granular computing .…”

Section: Introductionmentioning

confidence: 99%

“…There is extensive literature on integrating and combining them. [8][9][10][11] Shadowed sets, proposed by Pedrycz,12 are considered a bridge between rough sets and fuzzy sets and are an emerging aspect of granular computing. 13,14 The concepts of positive region, negative region, and boundary region from the rough set theory correspond to three logical values-0, 1, and [0, 1]-in shadowed sets, which are often induced from a given fuzzy set.…”

Section: Introductionmentioning

confidence: 99%

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Constrained shadowed sets and fast optimization algorithm

et al. 2019

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Shadowed sets provide a meaningful description of information granules by abstracting the corresponding fuzzy sets into three categories: full acceptance, full rejection, and uncertain (represented by shadows). One of the main motivating points to derive shadowed sets from fuzzy sets is the determination and explanation of the separation thresholds based on a specific optimization mechanism. The available optimization objective functions are mainly discussed on semantic interpretations and their mathematical properties; constructive algorithms for optimal solutions have rarely been reported. In this paper, the continuous and convex properties of Pedrycz's optimization objective function to construct shadowed sets, as well as the existence and uniqueness of solution points, are analyzed in detail. It is demonstrated that different approximation region partitions would be generated even under the same optimization model, which requires further criteria to make the constructed shadowed sets well‐defined. To address this limitation, the notions of passive and active constrained shadowed sets are introduced. A fast algorithm to obtain the proposed constrained shadowed sets is also designed based on the analyzed mathematical properties. Its performance is then illustrated by some typical fuzzy sets and some real data from the UCI repository.

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Section: Shadowed Setsmentioning

confidence: 99%