Negative information plays an important role in fuzzy knowledge representation and reasoning. This paper distinguishes between contradictory negative relation and opposite negative relation in fuzzy concept, and discovers a characteristic of fuzzy concept that if a pair of opposite concepts are fuzzy concepts, then there must exists a "medium" fuzzy concept between them; conversely, if there is a medium fuzzy concept between the two opposite concepts, then opposite concepts must be fuzzy concepts. Thus, negation of fuzzy concept is considered to include contradictory negation, opposite negation and medium negation. In order to provide a base of logic for the three kinds of negations, this paper proposes a fuzzy propositional logic, FLCOM, with contradictory negation, opposite negation and medium negation, discusses operations and interesting properties as well as characteristics of FLCOM, presents a semantic interpretation of FLCOM, and proves reliability theorem. In order to show that FLCOM is applicable for dealing with fuzzy proposition and its different negations in practical problem, the paper studies applications of FLCOM to fuzzy decision making in an example. Based on FLCOM, the study discusses formal representation of fuzzy proposition and different negations in decision rules, presents an approach to measure truth value of fuzzy proposition and threshold of truth value, and describes reasoning and realization of fuzzy decision making in the example based on fuzzy production rules.