Sequential representation of fuzzy similarity relations

A flexible classification method for evaluating the utility of automated workpiece classification system

“…If ~ is a similarity relation on X, and c~-cut of the membership matrix (/)=), c~ E [0,1], is a similarity relation on X. These similarity relations can be used to classify elements in X [15,16]. Such a classification is called fuzzy clustering analysis.…”

“…If the fuzzy relation /~ on X is reflexive, symmetric, and transitive, then /) is said to be a similari O, relation on X, denoted by /} [15]. If ~ is a similarity relation on X, and c~-cut of the membership matrix (/)=), c~ E [0,1], is a similarity relation on X.…”

An efficient method for creating benchmark classifications for automatic workpiece classification systems

“…If the fuzzy relation /~ on X is reflexive, symmetric, and transitive, th.en /~ is said to be a similarity relation on X, denoted by/~ [15]. Because /~ is a similarity relation on X that exiats and is unique, then for any a-cut of membership matrix…”

“…This similarity level in a fuzzy set can be thought of as a fuzzy relation, R. The fuzzy relation /~ is both reflexive and symmetric. If it is also transitive~ then ~ is said to be a similarity relation [15], denoted by R._By properly selecting an a-cut of the membership matrix (/~) for this similarity relation, one obtains an ordinary similarity relation. The equivalency of similarity relations among clustered objects can be used to carry out clustering.…”

A similarity inference method for reducing the cost of pair comparison

“…These methods include: (1) the Hamming distance method [13,14]; (2) the max-min method [12,15]; (3) the interval average method [12]; and (4) the weighing interval average method [13]. However, these four methods are not accurate enough in inferring the unknown data.…”