Normal Parameter Reduction Research Articles

A New Approach for Normal Parameter Reduction Using σ-Algebraic Soft Sets and Its Application in Multi-Attribute Decision Making

The soft set is one of the key mathematical tools for uncertainty description and has many applications in real-world decision-making problems. However, most of the time, these decision-making problems involve less important and redundant parameters, which make the decision making process more complex and challenging. Parameter reduction is a useful approach to eliminate such irrelevant and redundant parameters during soft set-based decision-making problems without changing their decision abilities. Among the various reduction methods of soft sets, normal parameter reduction (NPR) can reduce decision-making problems without changing the decision order of alternatives. This paper mainly develops a new algorithm for NPR using the concept of σ-algebraic soft sets. Before this, the same concept was used to introduce the idea of intersectional reduced soft sets (IRSSs). However, this study clarifies that the method of IRSSs does not maintain the decision order of alternatives. Thus, we need to develop a new approach that not only keeps the decision order invariant but also makes the reduction process more simple and convenient. For this reason, we propose a new algorithm for NPR using σ-algebraic soft sets that not only overcome the existing problems of IRSSs method but also reduce the computational complexity of the NPR process. We also compare our proposed algorithm with one of the existing algorithms of the NPR in terms of computational complexity. It is evident from the experimental results that the proposed algorithm has greatly reduced the computational complexity and workload in comparison with the existing algorithm. At the end of the paper, an application of the proposed algorithm is explored by a real-world decision-making problem.

Parameter reduction analysis under interval-valued m-polar fuzzy soft information

This paper formalizes a novel model that is able to use both interval representations, parameterizations, partial memberships and multi-polarity. These are differing modalities of uncertain knowledge that are supported by many models in the literature. The new structure that embraces all these features simultaneously is called interval-valued multi-polar fuzzy soft set (IVmFSS, for short). An enhanced combination of interval-valued m-polar fuzzy (IVmF) sets and soft sets produces this model. As such, the theory of IVmFSSs constitutes both an interval-valued multipolar-fuzzy generalization of soft set theory; a multipolar generalization of interval-valued fuzzy soft set theory; and an interval-valued generalization of multi-polar fuzzy set theory. Some fundamental operations for IVmFSSs, including intersection, union, complement, “OR”, “AND”, are explored and investigated through examples. An algorithm is developed to solve decision-making problems having data in interval-valued m-polar fuzzy soft form. It is applied to two numerical examples. In addition, three parameter reduction approaches and their algorithmic formulation are proposed for IVmFSSs. They are respectively called parameter reduction based on optimal choice, rank based parameter reduction, and normal parameter reduction. Moreover, these outcomes are compared with existing interval-valued fuzzy methods; relatedly, a comparative analysis among reduction approaches is investigated. Two real case studies for the selection of best site for an airport construction and best rotavator are studied.

A new parameter reduction algorithm for soft sets based on chi-square test

Redundancy is an extremely significant challenge in data integration and decision making based on the model of soft set which is able to process data under uncertainty. There are four available methods which are designed to reduce the redundant parameters of the soft set. But there is a very low success rate on a large number of data sets obtained from practices by these methods. In order to overcome the inherent weakness, we propose a parameter reduction method based on chi square distribution for the model of soft set. Experimental results on two real-life application cases and thirty randomly generated data sets demonstrate that our algorithm largely improves the success rate of parameter reduction, redundant degree of parameter, and has higher practicability in comparison with the four existing normal parameter reduction algorithms.

A new expert system in prediction of lung cancer disease based on fuzzy soft sets

Every year, millions of people worldwide (including a major portion in China) are suffering from lung cancer disease (Chinese report of Smoking and Health 2017). The aim of this paper is to develop a new fuzzy soft expert system which can be used to predict lung cancer disease. A prediction process using this fuzzy soft expert system is composed of four main steps: (1) Transform real-valued inputs into fuzzy numbers. (2) Transform fuzzy numbers of data into fuzzy soft sets. (3) Reduce, using normal parameter reduction method, the obtained family of fuzzy soft sets into a new family of fuzzy soft sets. (4) Use the proposed algorithm to get the output data. An experiment is conducted on forty five patients (thirty males, fifteen females, all are cigarette smokers) who endure treatment in the Respiratory Department of Nanjing Chest Hospital, China. The number of training data taken was 55 records, and the remaining 45 records were used for the testing process in our system by using weight loss, shortness of breath, chest pain, persistence a cough, blood in sputum, and age of patients. The quantized accuracies of the proposed system were found to be $$100\%$$ . In this work, we developed a fuzzy soft expert system based on fuzzy soft sets; we used a fuzzy membership functions and an algorithm to predict those patients who may suffer lung cancer. In this way, it is possible to conclude that the use of fuzzy soft expert system can produce valuable results for lung cancer detection. It is found that the fuzzy soft expert system developed is useful to the expert doctor to decide if a patient has lung cancer or not. Finally, we introduce comparison diagnosed between our proposed system and the fuzzy inference system.

Characterizations for Matrices of Dominant Support Parameters in Soft Sets

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.

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

This article 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 article 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.

An improved algorithm for normal parameter reduction of soft set

The normal parameter reduction is used as a useful approach to identify the irrelevant parameters in soft set-based decision making systems. It finds a subset with least number of parameters that preserve the original classification of the decision alternatives. A number of algorithms have been dev eloped for the normal parameter reduction of soft set but the case of repeated columns (i.e., ei = ej) was only considered by Danjuma et al. In this study, first we address the limitations of the Danjuma et al.’s approach to normal parameter reduction of soft set. Then, we propose a new algorithm for normal parameter reduction of soft set which is free of all such limitations. Moreover, we compare the proposed algorithm with some of the existing algorithms of normal parameter reduction of soft set to show its efficiency. Finally, the application of the proposed algorithm is elaborated by a medical diagnostic problem.

Normal parameter reduction algorithm in soft set based on hybrid binary particle swarm and biogeography optimizer

Existing classification techniques that are proposed previously for eliminating data inconsistency could not achieve an efficient parameter reduction in soft set theory, which effects on the obtained decisions. Meanwhile, the computational cost made during combination generation process of soft sets could cause machine infinite state, which is known as nondeterministic polynomial time. The contributions of this study are mainly focused on minimizing choices costs through adjusting the original classifications by decision partition order and enhancing the probability of searching domain space using a developed Markov chain model. Furthermore, this study introduces an efficient soft set reduction-based binary particle swarm optimized by biogeography-based optimizer (SSR-BPSO-BBO) algorithm that generates an accurate decision for optimal and sub-optimal choices. The results show that the decision partition order technique is performing better in parameter reduction up to 50%, while other algorithms could not obtain high reduction rates in some scenarios. In terms of accuracy, the proposed SSR-BPSO-BBO algorithm outperforms the other optimization algorithms in achieving high accuracy percentage of a given soft dataset. On the other hand, the proposed Markov chain model could significantly represent the robustness of our parameter reduction technique in obtaining the optimal decision and minimizing the search domain.

Soft Set Based Parameter Value Reduction for Decision Making Application

The soft set theory is a completely new mathematical tool for modeling vagueness and uncertainty, which can be applied to decision making. However, in the process of making decision, there are some unnecessary and superfluous information which should be reduced. Normal parameter reduction is a good way to reduce superfluous information, which keeps the entire decision ability. However, the algorithm has a low redundant degree, which involves a great amount of computation. It is not certain that normal parameter reduction has the solution, that is, it has a low success rate of finding reduction. Parameterization value reduction is another reduction method, which improves redundant degree, amount of computation, and success rate of finding reduction. However, this method only considers the best choice, but it does not concern the suboptimal choice, the sequence of choice, and added parameter, that is, it loses some part of decision ability. In order to settle these problems, in this paper, we introduce the parameter value reduction which keeps the entire decision ability while having a very high redundant degree and success rate of finding reduction and low amount of computation. Maximal parameter value reduction is defined as the special cases of parameter value reduction and the related heuristic algorithms are presented, which reaches an extreme degree to reduce the redundant information. The comparison result among maximal parameter value reduction, parameterization value reduction, and normal parameter reduction on 30 datasets shows that the proposed algorithm outperforms parameterization value reduction and normal parameter reduction.

A Novel Approach to Parameter Reduction of Fuzzy Soft Set

The fuzzy soft set (FSS) that combines soft set theory with fuzzy set theory has been introduced to deal with uncertainty in many practical decision-making problems. However, there exist some less important and superfluous information in the decision-making process which should be removed. In order to settle these problems, different methods have been developed for parameter reduction of FSS which are based on different decision criteria. In this paper, the problem of parameter reduction of FSS is studied based on choice value criteria. Initially, some previous reduction approaches such as; normal parameter reduction (NPR), proximate normal parameter reduction (PNPR) and distance-based parameter reduction (DBPR) of FSS are analyzed and their inherent difficulties are discussed. Then, a new method for parameter reduction of FSS is proposed and its heuristic algorithm is given. The proposed algorithm is compared with NPR, PNPR and DBPR algorithms from the aspects of success rate of finding reduction, reduction ratio and decision ability, respectively. The comparison results show that the proposed algorithm has much higher applicability and efficiency as compared to rest of the three algorithms. Finally, an application of our proposed algorithm is discussed in a real life decision-making problem.

New Improved Normal Parameter Reduction Method for Fuzzy Soft Set

There are many redundant parameters in the actual decision-making process based on fuzzy soft sets. Kong et al. [Z. Kong, J. Ai, L. Wang, P. Li, L. Ma, and F. Lu, “New Normal Parameter Reduction Method in Fuzzy Soft Set Theory,” in IEEE Access, vol. 7, pp. 2986-2998, 2019] described the parameter reduction method with regard to four special dispensable sets based on score decision criteria. However, this method is complicated and has high computational complexity. This paper firstly gives some new calculation methods of comparison matrix, and then proposes a new improved normal parameter reduction method. The comparison results on two real-life datasets validate that the proposed algorithm reduces the complexity of the algorithm and greatly simplifies the process of parameter reduction compared with the algorithm of Kong et al.

A Distance-Based Parameter Reduction Algorithm of Fuzzy Soft Sets

Kong et al. introduced the concept of normal parameter reduction in fuzzy soft sets. However, due to entries of fuzzy soft sets belonging to the unit interval [0, 1], it is nearly impossible to obtain the normal parameter reduction of fuzzy soft sets in the real applications. At the same time, this method involves a great amount of computation. In order to solve these problems, in this paper, we propose a distance-based parameter reduction of fuzzy soft set, which has much higher applicability and involves much less computation compared with the method of normal parameter reduction of fuzzy soft sets. Two case studies and twenty synthetic generated datasets show our contributions.

Achieving Efficient Decision Making Through Hybrid Reduction in Soft Set Theory

The main intention of proposing an alternative technique is to ensure consistency is been upheld besides successfully reducing the file. Of all the reduction techniques available currently, only normal parameter reduction has managed to address the issue of consistency at optimal and suboptimal level. In this paper, we initiated another form of reduction known as hybrid reduction by complementing the normal parameter reduction with object reduction. It has already demonstrated that the proposed hybrid reduction has successfully reduced data by 55% with the sample used, thus proving that it as a good alternative for the process of decision making using less amount of data.

An Alternative Approach to Normal Parameter Reduction Algorithm for Soft Set Theory

The soft set theory is a mathematical tool that deals with uncertainty, imprecise, and vagueness in decision systems. It has been widely used to identify irrelevant parameters and make reduction set of parameters for decision making in order to bring out the optimal choices of the decision systems. Many normal parameter reduction algorithms exist to handle parameter reduction and maintain consistency of decision choices. However, they require much time to repeatedly run the algorithm to reduce unnecessary parameters using either parameter important degree or oriented parameter sum. In this paper, we propose an alternative algorithm for parameter reduction and decision making based on soft set theory. We show that the proposed algorithm can reduce the computational complexity and run time compared with baseline algorithms. To evaluate the proposed algorithm, we perform thorough experiments on a binary-valued data set. The experimental result shows that the proposed algorithm is feasible and has relatively reduced the computational complexity and running time. In addition, the algorithm is relatively easy to understand compared with the state of the art of normal parameter reduction algorithm. The proposed algorithm is able to avoid the use of parameter important degree, decision partition, and finding the multiple of the universe within the sets.

Fuzzy Soft Expert System in Prediction of Coronary Artery Disease

Coronary artery disease affects millions of people all over the world including a major portion in Egypt every year. Although much progress has been done in medical science, early detection of this disease is still a challenge for prevention. In this paper we, will extend the concept of fuzzy soft set theory so as to develop a knowledge-based system in medicine and devise a prediction system named fuzzy soft expert system consisting of four main components. These are a fuzzification which translates inputs into fuzzy values, fuzzification of data sets to obtain fuzzy soft sets, a new fuzzy soft set by normal parameter reduction of fuzzy soft set and an algorithm to produce the resultant output. The fuzzy soft expert system developed is then used to predict for coronary artery disease using systolic blood pressure, low-density lipoprotein cholesterol, maximum heart rate, blood sugar, old peak and age of patients. A preliminary study is conducted on nine male patients undergoing treatment in the Cardiac Unit of the Faculty of Medicine, Assiut University, Egypt. It is found that the fuzzy soft expert system developed is able is to help the expert doctor to decide whether a patient needs to be given drug therapy or intervention.

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

This paper aims to find better algorithms for solving parameter reduction problems of soft sets and gives their potential applications. Firstly, we define the matrix of dominant support parameters and use it to explain the essential reasons for the different choice values of arbitrary pair of objects. Then we propose techniques for translating the normal and pseudo parameter reduction problems of soft sets into several equivalent 0–1 linear programming models, thus reduction problems of soft sets can be solved by any computational software for integer programming. Compared with the algorithm proposed by Ma et al., experimental results show that our method for normal parameter reduction is more efficient particularly when the number of parameters is big. At last we build a software system to show the potential applications of our methods in decision support.

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.

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..

Application of a New Efficient Normal Parameter Reduction Algorithm of Soft Sets in Online Shopping

A new efficient normal parameter reduction algorithm of soft set in decision making was proposed. However, up to the present, few documents have focused on real-life applications of this algorithm. Accordingly, we apply a New Efficient Normal Parameter Reduction algorithm into real-life datasets of online shopping, such as Blackberry Mobile Phone Dataset. Experimental results show that this algorithm is not only suitable but feasible for dealing with the online shopping.