Fuzzy sets approach to the design of engineering systems

s 107 ultimate moment); and productivity Ip = (/mat + /man + It)/Iman. Practically, for the fuzzification process (/mat, Ir,a,, It, and Ia are interpreted as fuzzy goals and Isi and Ip as fuzzy constraints), an exponential membership function lk = e -klxl (where k is the importance coefficient) is proposed. Thus by this procedure, the optimal investment is alternative a3, and the hierarchization of the alternatives is a3, a4, a2, a~. A computer program was written to process the data and produce the results. Address correspondence to Eugene L Roventa. Set-Valued Temporal Knowledge Representation for Fuzzy Temporal Retrieval in ICAI Elke A. R u n d e n s t e i n e r , Lois W . H a w k e s and W y l l i s Band le r Computer Science Department, Florida State University, Tallahassee, Florida, 32306 The Student Record (SR) is an essential part of any Intelligent Tutoring System (ITS), since it represents the key to individualized instruction. The SR's task is to capture the system's knowledge about each student including his or her development over time during the whole sequence of sessions. This paper proposes a relational representation as an underlying model for a Student Record and then extends this by allowing a set-valued extension of the representation and finally by adding temporal aspects to this relational representation. The impact of these two enhancements of the relational data model on the representation and on the manipulation is analyzed; then the relational algebra, a query language for the relational data model, is extended to cope with these aspects. The result is a fuzzy temporal relational algebra (FTRA). An essential feature of this approach is its completeness--the operations of this query language default to their crisp nontemporal counterparts if no fuzzy or temporal extensions are specified in them. Altogether, a setvalued temporal relational representation schema with fuzzy temporal retrieval capabilities is presented, which is claimed to be of use as a knowledge representation schema for other artificial intelligence applications. Address correspondence to Elke A. Rundensteiner. Decision Making and Fuzzy Windows J. C. S a n t a m a r i n a Department o f Civil and Environmental Engineering, Polytechnic University, 333 Jay Street, Brooklyn, New York 11201 J. L. C h a m e a u School o f Civil Engineering, Purdue University, Grissom Hall, West Lafayette, Indiana 47907 Physical classification consists of performing tests and comparing results to the ranges in value of alternative classes. Matching test results to the acceptable range (i.e., "standard") for a parameter within a class is like forcing the former through a filter or a