0–1 Linear programming methods for optimal normal and pseudo parameter reductions of soft sets

Han, Banghe; Li, Yongming; Geng, Shengling

doi:10.1016/j.asoc.2016.08.052

Cited by 28 publications

(26 citation statements)

References 38 publications

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“…According to [42], we have the following concepts about parameter reduction of soft sets. Note that we do not require the minimality condition for normal parameter reductions as defined in [33].…”

Section: Algorithms For Normal Parameter Reduction Problemsmentioning

confidence: 99%

“…(iii) For the normal parameter reduction problems, the linear programming method in [42] can be combined with the integer partition method proposed in this paper. On the one hand, the linear constraints in the linear programming method can constrain the occurrence times of partition factors or the combination of multiple partition factors in the process of integer partition, so the solving process can be simplified.…”

Section: Future Workmentioning

confidence: 99%

“…On the one hand, the linear constraints in the linear programming method can constrain the occurrence times of partition factors or the combination of multiple partition factors in the process of integer partition, so the solving process can be simplified. On the other hand, the combination of k|U | constraints and the existing linear constraints in [42] can be used to mine normal parameter reductions with relevant features.…”

Section: Future Workmentioning

confidence: 99%

See 2 more Smart Citations

An Offline and Online Algorithm for All Minimal k|U| Parameter Subsets of a Soft Set Based on Integer Partition

Geng

Han

et al. 2020

IEEE Access

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This paper investigates k|U | parameter subsets of a soft set matrix whose column sums are integral multiples of |U | (i.e., the number of objects in the soft set domain U). This kind of parameter subset represents an important data structure. Particularly, as a necessary condition, it has been shown to be useful in the parameter reduction problems of soft sets. This paper focuses on the minimal k|U | parameter subsets, whose any proper subset cannot be a k|U | parameter subset. An offline and online algorithm for minimal k|U| parameter subsets is proposed. Its basic function is based on integer partition in an offline way. When soft set data come online, the algorithm only needs to filter the factorization results according to the related constraints within the input soft set. We also bring in combinatorial formulas for computing the number of k|U | parameter subsets and the approximate number of minimal k|U | parameter subsets. As an application of k|U | parameter subsets, the method of integer partition is also extended for normal parameter reduction problems of soft sets. The experimental results show that the proposed method does result in better performance.

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Section: Algorithms For Normal Parameter Reduction Problemsmentioning

confidence: 99%

Section: Future Workmentioning

confidence: 99%

Section: Future Workmentioning

confidence: 99%

See 1 more Smart Citation

An Offline and Online Algorithm for All Minimal k|U| Parameter Subsets of a Soft Set Based on Integer Partition

Geng

Han

et al. 2020

IEEE Access

Self Cite

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“…Kong et al [18] constructed a mathematical model about normal parameter reduction in soft set, and used particle swarm algorithm to solve the reduction. Han et al pointed out some inappropriate notes and gave explicit model in [19], and defined the matrix of dominant support parameters and proposed approaches for dealing with the reduction problems of normal and pseudo parameter by transforming them into a series of equivalent 0-1 linear programming models [20]. Xie [21] investigated the soft sets parameter reduction in light of the attribute reduction which is applied widely in information systems.…”

Section: Introductionmentioning

confidence: 99%

New Normal Parameter Reduction Method in Fuzzy Soft Set Theory

Kong

Wang

et al. 2019

IEEE Access

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Soft set theory is a good tool to deal with uncertain problems. The study of reduction problem is an important part of soft set theory. Different decision-making criteria lead to different reduction methods. In this paper, the problem of parameter reduction of soft sets is studied based on the score decision criteria. Four cases of dispensable sets are discussed in parameter reduction. Then, a newly parameter reduction method is proposed. Finally, a comparison is shown between the new proposed parameter reduction method and the previous parameter reduction method based on the choice value decision criteria, and remarks are given.

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“…Regarding decisionmaking methods with help of rough set theory, some scholars established new method and techniques (the reader is addressed to Sun et al 2017a, c). In the past two decades, progress has been made in the investigation of soft sets and especially regarding the corresponding applications, such as decision making (briefly, DM) (Alcantud 2016a;Sun and Ma 2014;Zhan et al 2017b;Zhan and Zhu 2017), data mining (Herawan and Deris 2011), linear programs (Han et al 2017), medical diagnosis (Alcantud and Santos-García 2017), measurement theory (Feng et al 2010a), forecasting (Xiao et al 2009), information process (Xiao et al 2013;Zhang et al 2014), and so on. In recent years, some researchers compared the relationships among rough sets and fuzzy sets, for example, see (Alcantud 2016b;Ali 2011;Ali and Shabir 2014;Li and Xie 2014).…”

Section: Introductionmentioning

confidence: 99%

Covering-based soft fuzzy rough theory and its application to multiple criteria decision making

Zhan

Sun

2019

Comp. Appl. Math.

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Covering-based rough set model is a vital topic as a generalization of rough sets which is a tool for AI and data mining. For the purpose, we establish two classes of hybrid uncertain systems: soft rough fuzzy-covering models and soft fuzzy rough covering models by means of (fuzzy) soft neighborhoods. By means of fuzzy soft measure degrees, we deduce αsoft rough fuzzy coverings, D-soft rough fuzzy coverings, α-soft fuzzy rough coverings, and D-soft fuzzy rough coverings by these two hybrid uncertain systems, respectively. The relationships among the proposed covering-based rough set models are given. Based on the theoretical discussion for the combination of covering fuzzy rough sets and soft sets, we set forth a new method to multiple criteria decision-making problem. By comparative analysis, we obtain that the optimal results are the same between the aggregation operator method and our proposed method, which means that our method is reasonable and effective. Keywords (Fuzzy) rough covering • (Fuzzy) soft neighborhood • (Fuzzy) soft measure degree • Soft rough fuzzy covering • Soft fuzzy rough covering • Multiple criteria decision making Mathematics Subject Classification 68T30 • 68T10 • 90B50 B Jianming Zhan

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0–1 Linear programming methods for optimal normal and pseudo parameter reductions of soft sets

Cited by 28 publications

References 38 publications

An Offline and Online Algorithm for All Minimal k|U| Parameter Subsets of a Soft Set Based on Integer Partition

An Offline and Online Algorithm for All Minimal k|U| Parameter Subsets of a Soft Set Based on Integer Partition

New Normal Parameter Reduction Method in Fuzzy Soft Set Theory

Covering-based soft fuzzy rough theory and its application to multiple criteria decision making

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