Abstract
The matrix of dominant support parameters plays an important role in solving the normal and pseudo parameter reduction problems for soft sets. This article aims to make a fundamental investigation on the properties of matrix of dominant support parameters. Firstly, we obtain some basic structural and quantitative properties. Then we give some retrieving algorithms and filling algorithms for computing the initial soft sets and the matrix itself by using only part of the matrix. Next we propose some characterization theorems to check which kind of set-valued matrices can be induced by a soft set as its matrix of dominant support parameters. Finally, we make a comparison between the matrix of dominant support parameters and the soft discernibility matrix. It’s shown that the matrix of dominant support parameters has its own characteristic and can represent the soft discernibility matrix in a simple way. An alternative and simple procedure for computing the order relations with the matrix of dominant support parameters is brought in.
Highlights
The matrix of dominant support parameters for a soft set is different from the discernbility matrix of a general information system [50]
The main results of this paper (1) The fundamental structural and quantitative properties are investigated, and these properties can help us in having a better understanding of the matrix of dominant support parameters
With them we can judge which kind of set-valued matrices can be the matrices of dominant support parameters for certain soft sets or information systems
Summary
In 1999 Molodtsov initiated the theory of soft set, which represented a new mathematical tool for dealing with uncertainties and vagueness [1]. The matrix of dominant support parameters for a soft set is different from the discernbility matrix (or dominance relation) of a general (ordered) information system [50]. D. MAIN QUESTIONS TO BE INVESTIGATED The parameter reduction problems are quite different from that of information systems in rough set theory or that of formal concept analysis. MAIN QUESTIONS TO BE INVESTIGATED The parameter reduction problems are quite different from that of information systems in rough set theory or that of formal concept analysis It becomes an important task for researchers to learn and develop these important properties or characterizations for matrices of dominant support parameters. We come to a conclusion of this article and outlook for potential future work
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