Parameter Reduction Of Soft Sets Research Articles

Soft Set-based Parameter Reduction Algorithm Through a Discernibility Matrix and the Hybrid Approach for the Risk-Factor Prediction of Cardiovascular Diseases by Various Machine Learning Techniques

Parameter reduction without performance degradation is a promising task in decision-making problems. For instance, a great challenge exists in constructing cost functions in gaming theory. Nevertheless, soft set theory handles all its drawbacks conveniently through a new tool for the choice function mathematically. In this paper, we propose an algorithm (SSPRDM) for parameter reduction of soft sets through discernibility matrices, and it is implemented in detecting the risk factor of heart disease problems by using six types of machine learning techniques. The parameters are extracted from the heart disease patient data by the SSPRDM algorithm, and then six machine learning techniques (LDA, KNN, SVM, CART, NB, RF) are performed in the prediction of risk factors for heart disease. The experimental results showed that the present hybrid approach provides an accuracy of 88.46% in the Random Forest technique, whereas the same Random Forest classifier provides an accuracy of 69.23% in the prediction of risk factors of cardiovascular disease (CVD) diagnosis in the earlier work which is a drastic improvement. Moreover, out of 18 parameter reductions, the core component is identified as Total Cholesterol, which is to be considered in all types of CVD diagnosis, whereas Sugar-Fasting (C), Total-Cholesterol (G), and HDL-Cholesterol (I) are the core components identified in three parameter reductions ABCEGHI, ACFGIJ, and BCFGIJK.

Some Efficient Algorithms on the Parameter Reduction of Soft Sets for Decision making Problems

In the present paper, we propose the efficient algorithm for the parameter reduction of soft sets and we implement it in diagnosing the risk of heart disease problem. Moreover, the efficiency of the algorithm is investigated. The time complexity of the $${\textit{Map}}_-{\textit{Matix}}$$ is given by total number of comparisons made to construct $${\textit{map}}_-{\textit{matrix}}$$ . For n number of objects and f number of attributes, the total number of comparisons is $$n \times f$$ . Therefore, the time complexity is given O(nf). The algorithm $${\textit{Generate}}_-{\textit{Powerset}}$$ takes the total of features f as input and its time complexity is given by $$O(2^f)$$ . Moreover, the overall efficiency is given by $$O(2^f)$$ .

New Normal Parameter Reduction Method in Fuzzy Soft Set Theory

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.

A survey of parameter reduction of soft sets and corresponding algorithms

As is well known, soft set theory can have a bearing on making decisions in many fields. Particularly important is parameter reduction of soft sets, an essential topic both for information sciences and artificial intelligence. Parameter reduction studies the largest pruning of the amount of parameters that define a given soft set without changing its original choice objects. Therefore it can spare computationally costly tests in the decision making process. In the present article, we review some different algorithms of parameter reduction based on some types of (fuzzy) soft sets. Finally, we compare these algorithms to emphasize their respective advantages and disadvantages, and give some examples to illustrate their differences.

Comments on “Normal parameter reduction in soft set based on particle swarm optimization algorithm”

This paper aims to bring in some notes and improvements for the paper (Kong et al., 2015). Firstly, we give some notes and suggestions on its assumption for numbers of dispensable parameter subsets in soft sets. This helps make the theories in Kong et al. (2015) much more logical clear and consistent. Then we propose a linear programming mathematical representation for normal parameter reduction problems of soft sets. This allows us to solve normal parameter reduction problems of soft sets with Lingo or MATLAB software. By the way, we point out that the answer of Example 6.1 in Kong et al. (2015) is not correct and figure out the right answer with our linear programming method.

An Algorithm on the Parameter Reduction of Soft Sets

Soft set theory is a mathematical tool for dealing with uncertain. In this paper, the parameter reduction of soft sets is investigated by means of the attribute reduction in information systems and its algorithm is obtained. Moreover, an example is given by using this algorithm.

Normal parameter reduction in soft set based on particle swarm optimization algorithm

Parameter reduction in soft set is a combinatorial problem. In the past, the problem of normal parameter reduction in soft set is usually be solved by deleting dispensable parameters, that is, by the trial and error method to search the dispensable parameters. This manual method usually need much time to reduce unnecessary parameters, and the method is more suitable for small data. For the large data, however, it is impossible for people to reduce parameters in soft set. In this paper, the particle swarm optimization is applied to reduce parameters in soft set. Firstly, a definition is introduced to define the dispensable core, and some cases about the dispensable core are discussed. Then the normal parameter reduction model is built and the particle swarm optimization algorithm is employed to reduce the parameters. Experiments have shown that the method is feasible and fast.

Normal Parameter Reduction in Soft Set Based on Harmony Search Algorithm

The normal parameter reduction in soft set is difficult to application in data mining because of great calculation quantity. In this paper, the intelligent optimization algorithm, the harmony search algorithm, is applied to solve the problem. The normal parameter reduction model is constructed and the harmony search algorithm is designed. Experience has shown that the method is feasible and fast..

A new efficient normal parameter reduction algorithm of soft sets

Kong et al. [Kong, Z., Gao, L., Wang, L., and Li, S., The normal parameter reduction of soft sets and its algorithm, Computers and Mathematics with Applications 56 (12) (2008) 3029–3037] introduced the definition of normal parameter reduction in soft sets and presented a heuristic algorithm of normal parameter reduction. However, the algorithm is hard to understand and involves a great amount of computation. In this paper, firstly, we give some new related definitions and proved theorems of normal parameter reduction. Then we propose a new efficient normal parameter reduction algorithm of soft sets based on the oriented-parameter sum, which can be carried out without parameter important degree and decision partition. The comparison result on a dataset shows that the proposed algorithm involves relatively less computation and is easier to implement and understand as compared with the algorithm of normal parameter reduction proposed by Kong et al.

The normal parameter reduction of soft sets and its algorithm

This paper is concerned with the reduction of soft sets and fuzzy soft sets. Firstly, the problems of suboptimal choice and added parameter set of soft sets are analyzed. Then, we introduce the definition of normal parameter reduction in soft sets to overcome these problems. In addition, a heuristic algorithm of normal parameter reduction is presented. Two new definitions, parameter important degree and decision partition, are proposed for analyzing the algorithm of normal parameter reduction. Furthermore, the normal parameter reduction is also investigated in fuzzy soft sets.