Fuzzy Relational Modeling of Cost and Affordability for Advanced Technology Manufacturing Environment

Relational representation of knowledge makes it possible to perform all the computations and decision making in a uniform relational way [46], by means of special relational compositions called triangle and square products. These were first introduced by Bandler and Kohout in 1977 [11],[5],[2] and are referred to as the BK-products in the literature [22],[17],[18]. Their theory and applications have made substantial progress since then. BK-relational product can be used to compare relational structures. Relations so constructed might exhibit some important relational properties that reveal important characteristics and interrelationships of the source of information from which they were generated. Hence, methods for detecting various relational properties of given relations are important. Collecting engineering data concerning various manufacturing processes, parts, subsystems and manufactured goods is usually done by physical measurements of such physical entities that serve as cost drivers. Because one of major concerns is to deal with affordability issues also in the situations when such “hard” data are not available, relational analysis on data and knowledge can be elicited by questioning engineers. A case study of this kind is described in Sec. 3. Here, instead of physical measurement devices we use psychometric tools invented by behavioral scientists called repertory grids (RPG). Our relational analysis can be used to analyze data (e.g. process parameters) collected by physical measurements as well as data obtained by knowledge elicitation from human experts. Relational properties characterizing the structure of knowledge, such as reflexivity, symmetry, and transitivity, and classes such as tolerances, equivalences and partial orders can be extracted from the linguistic information elicited by repertory grids. Testing the fuzzy relational structure for various relational properties allows us to discover dependencies, hierarchies, similarities, and equivalences of the attributes characterizing technological processes and manufactured artifacts in their relationship to costs and performance. How to use our methods for ranking of various technologies with respect to affordability is shown in Sec. 4. In section 5, a more detailed study of cost drivers by means of fuzzy relational products is described. A brief overview of mathematical aspects of BK-relational products is given in Appendix 1 together with further references in the literature. All correspondence to [email protected] Current Affiliation:Prof. Eunjin Kim, Dept. of Computer Science, John D. Odergard School of Aerospace Sciences, University of North Dakota, Grand Forks, ND 582002–9015, USA.