Study On Approach Of Incomplete&Inconsistent Data Analysis Anddecision Making Based On Soft Set Theory

Although massive data have been quickly generating in the big data era，a lot ofvaluable information within big data has rarely been tapped to be utilized. Company’swelfare does not necessarilyincrease by the increasing amount of data. Big data wouldbe valuable only by valid and appropriate analysis, and mining and use of internal rulesand knowledge. However, big data has many new characteristics such as high volume,variety, velocity and low density of value.Variety and Low density of value are inclinedto bring more data quality problems. Among these problems incomplete dataandinconsistent data has been exaggerated sharply in a great extent and brought dataanalysis techniques many unprecedented challenges. Because of some constraints onanalytical tools and capacity, it is impossible to apply traditional techniques to make aquick and timely analysis of data, which is excessive, complex and low-quality.Therefore, one kind of new tools should be researched to make effective, high-speedanalysis of incomplete data andinconsistent data to discover knowledge from big data.Soft sets is a new mathematical tool of dealing with uncertainty and can overcomethe disadvantages of the shortages of parameters tools of the traditional method, so ithas a great advantage on the analysis of the two important forms of uncertaininformation, incomplete and inconsistent data. In addition, soft sets have somecharacteristics different from classical mathematics. Firstly, there are not manyconstraints about the data type and the description form of objects. These objects cannot only be described by structured data, but also can be described by semi-structuredand unstructured data. And they can be described by certain and uncertain data.Secondly, traditional mathematical models are too complicated to find out exactsolutions, thus the approximate solution has to be introduced. Soft sets can establish anapproximate model and seek an approximate solution. Thus, compare with traditionalmethods, the robustness of soft sets is better, the time cost is less and the spacecomplexity is lower. Therefore, based on soft sets and its extended theory this paperputs forward new data analysis tools of incomplete and inconsistent dataand mainlyfocus on the category decision-making problems in data analysis. It further expands theapplication scope of soft sets, enriches analysis tools of incomplete and inconsistentdata and has a certain reference significance of specific data analysis techniques in bigdata environment. This paper analyzes the generated background, development, and related conceptsof big data, and explain the significance. Through the literature review of analysistechniques of incomplete and inconsistent data,this paper presented incomplete andinconsistent data analysis methods based on soft sets.It mainly includes several aspectsin the following:①As to the limitations of existing analysis method based on soft sets forincomplete data, such as computational complexity and unreliable results, a novel dataanalysis method, dominant method, has been proposed in this paper. This method makesa direct analysis of the original data set and obtains the results without predictingunknown data. Comparing dominant method and the existing method based on soft sets,the proposed method covers the disadvantages that analysis result are unbelievablewhen there are a large number of unknown values in corresponding to a parameter. Aswe can see from the decision-making result, dominant method is more accordance withthe definition of sot sets.②Numerous uncertainties and descriptive data cannot be expressed by precisenumerical data. We have to introduce the fuzzy data, so it is necessary to research theanalysis method about incomplete fuzzy data. In order to overcome limitations ofexisting incomplete data analysis methods based on fuzzy soft sets, this paperintroduced the concept of Dempster-Shafer fuzzy soft sets and defined the FUSEoperation on both Dempster-Shafer fuzzy soft sets. We also researched the relationshipbetween incomplete fuzzy soft sets and D–S fuzzy soft sets. According to definitionsand related operations of the Dempster-Shafer fuzzy soft sets and evidence theory, wecan analyze the incomplete fuzzy data, and put forward the incomplete decisionalgorithm of fuzzy data set. This algorithmcould fusion the incomplete fuzzy data in thedecision-making level and directly get decision results without filling these unknowndata. Finally, this method was applied into the Internet decision problems to illuminatethe practicability and validity.③Diverse data sources determine the widely appearance of inconsistent data inbig data. As to the limitations of existing inconsistent data analysis method, such ascomputational complexity and low efficiency, this paper introduced the paraconsistentlogic into soft set theory from the perspective of logical reasoning. The concept ofparaconsistent soft sets and correlation operations were proposed. Paraconsistent softsets can extend the expressive ability of parameters in soft sets. In paraconsistent softsets, the family of parameters sets includes not only parameters of classical soft sets, but also three other parameters called approximate opposite, incomplete and contradictory.We also put forwards the decision algorithm based on definitions and related operationsof paraconsistent soft sets. Thus, we can get category decision-making results throughanalysis of inconsistent data, and apply this algorithm into an investment decisionproblem with inconsistent information to illustrate the application of the algorithm.Finally, this paper also applied paraconsistent soft sets to deal with the hybrid inputproblem in recommendation system. A hybrid input algorithm considering multiplesources and input types was proposed based on paraconsistent soft sets to furtherillustrate the usefulness ofparaconsistent soft sets.