Besides the usual “true” and “false” statements, there is also a place for
“vague” or "fuzzy” statements in the real-world of decision-making problems. The
linguistic statements may also be “possible,” “almost sure,” “hardly fulfilled,”
“approximately equal to,” “considerable larger to,” etc. The essential elements of fuzzy
logic consist of the following main elements. The single-objective fuzzy logic
programming is presented first. Next, we show its natural extension to multi-objective
optimization problems. The symmetric method for SOO fuzzy problems consists of
different steps which include the determination of the membership functions, the fuzzy
feasible set, and the fuzzy set of the optimal value. The problem is solved by using a
maximin operator. The extension to multiple objectives is based on similar principles.
Membership functions are associated with objectives and constraints. A fuzzy decision
set can result from the Bellman-Zadeh principle that forms an appropriate aggregation
approach. Different fuzzy decision sets can be considered, depending on the chosen rule
(i.e., the intersection rule, the convex rule, and the product rule). Using the Belman-Zadeh
criterion, the problem maximises a satisfaction level subject to -inequality
constraints for objectives and the inequality constraints of the problem. An example
illustrates the full process for finding - parametrized solutions.
Keywords: Aspiration level, Bellman-Zadeh criterion, Degree of attainment,
Fuzzification, Fuzzy constraint, Fuzzy decision set, Fuzzy goal programming,
Fuzzy logic programming, Fuzzy objectives, Fuzzy rules, Imprecise data,
Intersection rule, Maximin operator, Membership function, Parametric
programming, Ranking relation, Soft constraints, Symmetric method, Trade
balance problem, Triangular fuzzy number.