Upper and lower values for the level of fuzziness in FCM

A fuzzy analysis of country-size argument for the Feldstein–Horioka puzzle

“…In the literature, several cluster validity indices have been introduced to identify the number of clusters [6,7,12]; and fairly limited studies have been made for the level of fuzziness [22,23] which determines the degree of overlap of fuzzy clusters for m greater than one. The most widely used value for the level of fuzziness is two.…”

“…This value is usually accepted as the rule of thumb. However, it was shown that the proper values for upper and lower bounds of level of fuzziness are 1.4 and 2.6, respectively [22,23]. In our analysis, number of clusters is set to four, in order to partition the countries as ''small", ''medium", ''large" and ''very large" countries and both the upper and the lower bounds for the level of fuzziness are used to obtain two different clustering.…”

Soft computing applied to stem water potential estimation: A fuzzy rule based approach

“…Usually ¼ 0:01. The fuzziness (degree of overlapping) of the resulting clusters depends on the election of a weighting exponent m > 0 (Ozkan and Turksen, 2007). Although m is a context-dependent value, it was set to 2, which is one of the most used fuzziness value (Pal et al, 1993).…”

Development of fuzzy X¯∼-R∼ and X¯∼-S∼ control charts using α-cuts

“…Trillas [20] gave a view that fuzzy sets are mathematical entities giving extension to the predicates. Fuzzy c-means (FCM) clustering methodology was investigated by Ozkan and Turksen [14] to determine the effective upper and lower boundaries of the level of fuzziness in order to capture the uncertainty generated by this parameter. Tuncer and Benli [21] defined k-statistical limit and k-statistical cluster points of a sequence of fuzzy numbers.…”