Some new types of Fuzzy real numbers

What is it about?

It is difficult to represent the data sets on daily prices for commodities on daily sales, medical signals, stock market values over time by the existing fuzzy real numbers. To overcome this, we propose three kinds of fuzzy real numbers on the real line which are called Lift Fuzzy Real Numbers. A numerical example is used to illustrate the proposed new ideas. This work attempts to present a graphical interpretation to the existence of the Lift Fuzzy Real numbers. The representation of a real number via the Lift Fuzzy Real Numbers is explained. It is observed that every Lift fuzzy real number determines a Left Lift Fuzzy Real number and a Right Lift Fuzzy Real number and a Lift Fuzzy Real Number is induced by a linear Left Lift Fuzzy Real number and a linear Right Lift Fuzzy Real number.

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Why is it important?

Several definitions for fuzzy real numbers had been available in the literature of fuzzy number theory since 1978.The left leg and right leg of these fuzzy real numbers start from the real axis and ends at the height of the fuzzy real number. In this paper, the legs of the fuzzy real number are lifted vertically from the real axis which leads to define Left Lift Fuzzy Real Number, Right Lift Fuzzy Real Number, Lift Fuzzy Real Number. Most of the data sets, in business models, medical field, share market models etc. can be represented by using these proposed types of fuzzy real numbers

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