Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy sets and fuzzy logic: theory and applications
Fuzzy sets and fuzzy logic: theory and applications
Solving fuzzy relational equations through logical filtering
Fuzzy Sets and Systems
Specificity shift in solving fuzzy relational equations
Fuzzy Sets and Systems
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Fuzzy Relation Equations and Their Applications to Knowledge Engineering
Attribute implications in a fuzzy setting
ICFCA'06 Proceedings of the 4th international conference on Formal Concept Analysis
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We show that the well-known results regarding solutions of fuzzy relational equations and their systems can easily be generalized to obtain criteria regarding constrained solutions such as solutions which are crisp relations. When the constraint is empty, constrained solutions are ordinary solutions. The generalization is obtained by employing intensifying and relaxing linguistic hedges, conceived in this paper as certain unary functions on the scale of truth degrees. One aim of the paper is to highlight the problem of constrained solutions and to demonstrate that this problem naturally appears when identifying unknown relations. The other is to emphasize the role of linguistic hedges as constraints.