Modeling words by normal interval type-2 fuzzy sets

A comparison of three approaches for estimating (synthesizing) an interval type-2 fuzzy set model of a linguistic term for computing with words

“…Its median interval approach (MIA) is based on calculating the median boundaries of the range of membership functions associated with the words; however, because it does not directly map the data interval uncertainties into MF uncertainties, as do the IA, EIA and HMA, nor does it fully subscribe to Item 6, nor does it lead to normal IT2 FSs (as does the HMA), it is not described herein.8 Hao and Mendel (2015) state: ''We apologize for being so presumptuous in using our last-name initials for the name of this approach, but, after repeatedly referring to it as ''the new approach'' in the early drafts of this paper, we felt others would later refer to it as the HM Approach and so we just did it ourselves. InHao and Mendel (2014) we refer to the HMA as the HM Method. We decided to change 'Method' to 'Approach' so that its name would be consistent with 'Approach' that is used in the IA and EIA.9 We do not use ''linguistic term'' because most people are unsure about what this means.10 In addition, we instruct the subject that: if you are absolutely certain about the two end-points then you do not have to provide endpoint intervals, you only have to provide the left and right end-points.…”