Indistinguishability operators in measurement theory, Part I: Conversions of indistinguishability operators with respect to scales
For two given ordinal scales in a measurement process, the present paper investigates how an indistinguishability operator evaluated according to one of these ordinal scales can be converted to another indistinguishability operator w.r.t. the other ordinal scale, and establishes the mathematical base of these conversions under the framework of measurement theory [Krantz, D.H., Luce, R.D., Suppes, P., Tversky, A. (1971) Foundations of Measurement , Vol. 1 (Academic Press, San Diego)]. Additionally, this work exposes the rudimentary facts behind the studies in ["Fuzzy Numbers and Equality Relations", Proc. FUZZ'IEEE 93 (1993) 1298-1301; "Fuzzy Sets and Vague Environments", Fuzzy Sets and Systems 66 (1994) 207-221; "Fuzzy Control on the Basis of Equality Relations-with an Example from Idle Speed Control", IEEE Transactions on Fuzzy Systems 3 (1995) 336-350; and " T -partitions of the Real Line Generated by Idempotent Shapes", Fuzzy Sets and Systems 91 (1997) 177-184], and points out the measurement theoretic derivations of the results in these studies.
indistinguishability operator measurement theory scale fuzzy equivalence relation fuzzy equality scale transformation