Over the fast development of new technologies, data with low resolution gathered from manufacturing processes, such as the synthesis and characterization of nano-composite processes or surface roughness consisting of the finer irregularities of the surface texture, thus recorded as interval values are commonly seen. There are several situations and examples for interval observations are inevitable existing in today’s engineering processes. During earlier design phases of manufacturing processes, engineers may only know roughly in advance what the quality characteristics are looking for; also, in the manufacturing period, timely and accurate numerical measurements of quality characteristics are sometime too costly to be obtained. Especially data gathered by human’s subjective senses are rarely measured on an exact numerical scale. A typical example for vague observations is the colors of the visible light spectrum usually recorded as an interval number due to insufficient resolution. Moreover, measurements collected from color intensity of pictures, the sharpness or fineness of images, and indicators of an analog equipment are laborious and sometimes controversial to be exact. Even readings on digital measurement equipments are not precise numbers but certain spans since there are only finite numbers of decimals available.
In monitoring and controlling manufacturing processes, many researches have carried out that data collected from the key quality characteristic are in the form of qualitative variables, which by convention are called linguistic variables or categorical variables. Spanos and Chen presented an example in which quality characteristics are measured the roughness of etched sidewalls, then trained operators classify wafers into particular categories such as ”very rough”, ”rough”, ”smooth” and ”very smooth”. Fasulo et al. investigated the surface quality of the thermoplastic olefin (TPO) nano-composites in an extrusion process, where surfaces quality is graded on a 5-point scale with 1 being the best and 5 being the worst based on visual inspections. Wang and Tsung studied a Deep Reactive Ion Etching (DRIE) process, in which categorical observations were collected for the determination of process adjustment. Trochim and Donnelly pointed out that all qualitative data can be coded quantitatively. Then these quantitative values can be manipulated to help decision-makers achieve greater insight into the meaning of the data and further examine specific hypotheses. Obviously, while assigning the qualitative variables to be meaningful numerical values, a certain degree of uncertainty called vagueness other than randomness is involved and thus yields coded data virtually interval-valued.
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