On Strong Solutions in Linear Programming Problems with a Fuzzy Goal

In decision-making problems, a situation often arises when a decision maker cannot confidently determine the goal function. This may be due to both the peculiarities of human thinking and incompleteness and inaccuracy of data. In such a case, the fuzzy goal function can be used. A fuzzy goal function is a fuzzy set of acceptable goals by a decision maker. This paper considers a linear programming problem with a fuzzy objective. For such a problem, two stable solutions are formalised. The first proposed solution, the strong solution remains unchanged when any goal allowed by the decision maker is achieved. The second proposed solution remains unchanged only when the goal is highly admissible. Model examples of the proposed solutions are given.