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The purpose of this study is extended the TOPSIS method based on interval-valued fuzzy set in decision analysis. After the introduction of TOPSIS method by Hwang and Yoon in 1981, this method has been extensively used in decision-making, rankings also in optimal choice. Due to this fact that uncertainty in decision-making and linguistic variables has been caused to develop some new approaches based on fuzzy-logic theory. Indeed, it is difficult to achieve the numerical measures of the relative importance of attributes and the effects of alternatives on the attributes in some cases. In this paper to reduce the estimation error due to any uncertainty, a method has been developed based on interval-valued fuzzy set. In the suggested TOPSIS method, we use Shannon entropy for weighting the criteria and apply the Euclid distance to calculate the separation measures of each alternative from the positive and negative ideal solutions to determine the relative closeness coefficients. According to the values of the closeness coefficients, the alternatives can be ranked and the most desirable one(s) can be selected in the decision-making process.

The importance of diagnosing breast cancer is one of the most significant issues in medical science. Diagnosing whether the cancer is benign or malignant is extremely essential in ascertaining the type of cure, moreover, to bringing down bills. This study aims to use the tolerance-based intuitionistic fuzzy-rough set approach to pick attributes and data processing with help of machine learning for the classification of breast cancer. The main purpose of selecting a feature is to make a subset of input variables by removing irrelevant variables or variables that lack predictive information. This study shows how to eliminate redundant data in big data and achieve more efficient results. Rough set theory has already been used successfully to set down attributes, but this theory is insufficient to reduce the properties of a real-value dataset because it will possibly drop knowledge through the decomposition procedure. and this prevents us from getting the right results. In this study, we used the tolerance based intuitive fuzzy rough method for attribute selection. In this technique, lower and upper approaches are used to intuitive fuzzy sets from rough sets to remove uncertainty due to having simultaneous membership, nonmembership, and hesitation degrees and obtain better results. The used method is demonstrated to be better performing in the shape of chosen attributes. [ABSTRACT FROM AUTHOR]