Fuzzy systems in management and information science

Logic is a formal science that studies the princi12 ples of valid argumentation [1], and objects essential 13 to making an argument are declarative sentences. In 14 the classical system of logic any meaningful declara15 tive sentence must either be true or false. Aristotle [2] 16 postulated that the declarative sentence “There will be 17 a sea battle tomorrow” could not be considered true or 18 false. His reasoning can be summarized as follows: 19 if the sentence is true at the moment of being pro20 nounced, nothing can prevent a sea battle from taking 21 place tomorrow. If it is false, the same will be the case, 22 that is, there will be no way to start a sea battle tomor23 row. Therefore, to accept that the sentence is either 24 true or false at the moment it is issued would mean that 25 our future is already determined and will be forever, 26 and, according to Aristotle, this does not make sense 27 since, in general, future events have the possibility of 28 taking place or not. These types of simple declarative 29 sentences about events that may or may not occur 30 in the future are known as “future contingent propo31 sitions”. Łukasiewicz [3], reflecting on Aristotelian 32 future contingents, came to the conclusion that this 33 type of proposition should be considered “not yet 34 determined”, creating a third possibility that differs 35 from the “true” and “false” options. Łukasiewicz for36