New Parameter Reduction of Soft Sets

Several algorithms exist to address the issues concerning parameter reduction of soft sets. The most recent concept of Normal Parameter Reduction (NPR) is introduced, which overcomes the problem of suboptimal choice and added parameter set of soft sets. However, the algorithm involves a great amount of computation. In this thesis, a New Efficient Normal Parameter Reduction algorithm (NENPR) of soft sets is proposed based on the new theorems, which have been proved and presented. The proposed technique can be carried out without parameter important degree and decision partition. As a result, it can involve relatively less computation, compared with the algorithm of NPR. The experimental results are analyzed and comparisons are done with three real-life datasets and ten synthetic generated datasets. The computational complexity is described in terms of the number of entry access, the number of parameter importance degree access and oriented-parameter access, and the number of candidate parameter reduction set. From these experimental results, some conclusions can be drawn that NENPR improves the number of entry access, the number of parameter importance degree access and oriented-parameter access, the number of candidate parameter reduction set and the executing time of NPR averagely up to 95.21%, 52.45%, 53.58% and 60.02% through three real-life datasets and ten synthetic generated datasets, respectively. Sum up, NENPR provides the better solutions for capturing the normal parameter reduction compared with NPR. An interval-valued fuzzy soft set is a special case of a soft set by combining the interval-valued fuzzy set and soft set. However, up to the present, the previous work has not involved parameter reduction of the interval-valued fuzzy soft sets. In this thesis, four new parameter reductions of the interval-valued fuzzy soft sets are proposed: Optimal Choice Considered Parameter Reduction (OCCPR), Invariable Rank of Decision Choice Considered Parameter Reduction (IRDCCPR), Standard Parameter Reduction (SPR) and Approximate Standard Parameter Reduction (ASPR). The related heuristic algorithms are given. In order to show the high efficiency of the proposed four algorithms, comparisons and analysis for decision making between OCCPR, IRDCCPR, ASPR, SPR and directly Interval-Valued Fuzzy Soft Sets based Fuzzy Decision Making algorithm (IVFSS-FDM) with three real-life datasets and ten synthetic generated datasets are made. Average percent of improvement of four proposed algorithms compared with IVFSS-FDM on the executing time concerning all of datasets are 80.28%, 56.37%, 47.44%, 10%, respectively. From these experimental results, conclusions can be drawn that our four proposed algorithms have much higher efficiency compared with directly IVFSS-FDM for decision making and four approaches have the respective merits and demerits. Therefore these proposed methods can be applied into the different situations