# A fuzzy proposition is a declarative sentence that can only vaguely distinguish truth from falsehood

The most common fuzzy logic systems are fuzzy propositional calculus and fuzzy predicate calculus.The logic formulas are fuzzy proposition formula and fuzzy predicate formula respectively.① Vague propositions.A declarative sentence that can only vaguely distinguish truth from falsehood.For example, it is a general statement to state that “Zhang SAN is over 1.8 meters tall”.It can be rigorously judged as true or false.But if you change the above statement to “Zhang SAN is tall,” it cannot be strictly true or false.That’s a fuzzy proposition.Its truth value can only be stated in terms of a fuzzy number or language value, etc.Fuzzy proposition is an atomic logic formula in the calculus of fuzzy proposition.② Fuzzy predicates.Fuzzy proposition with variable, or fuzzy proposition function.When the variable in it is determined to be constant, it becomes a fuzzy proposition and thus has a fuzzy truth value.For example, the statement “X is tall” will become “Zhang SAN is tall” when X is taken as Zhang SAN. Its truth value cannot be simply answered by true or false, because its truth degree is between true and false, so its truth value can only be expressed by some fuzzy value.Fuzzy predicates are atomic logic formulas in the calculus of fuzzy predicates.The general term for predicate logic with more than two truth values in many-valued logic and narrow fuzzy logic.Generally, it refers to the logic with finite kinds of truth values, which is the predecessor of fuzzy logic.Since there are only limited kinds of truth values in all the synthetic logic formulas, all kinds of logical operations (including or, and, not, implication, equivalence, etc.) can be defined by truth table.The most thoroughly studied multi-valued logic is three-valued logic, in which there is a third truth value in addition to the two truth values of “true” (T) and “false” (F).Different ternary logic can be obtained according to different meanings of the third truth value.When the truth value of multi-valued logic can be any real number in the interval [0,1], it is generally called narrow fuzzy logic.The concept of fuzzy logic in a broad sense was developed by THE Iranian American mathematician and founder of fuzzy mathematics L.A.It is called Zadeh fuzzy logic.Fuzzy reasoning Reasoning based on various fuzzy logic.Fuzzy reasoning can be divided into subjectively complete confidence reasoning and subjectively incomplete confidence reasoning according to how the confidence of premise is transformed into the confidence of conclusion.The former is called fuzzy deductive reasoning in which the confidence of the conclusion is equal to the confidence of the premise.The latter is called fuzzy inductive reasoning, in which the confidence of the conclusion is less than that of the premise.The “syllogism” defined in various fuzzy logic is actually a rule to calculate the truth value of a conclusion from the truth value of an implication and its premises.Because of the different calculation rules defined in various fuzzy logic, different fuzzy reasoning methods are produced accordingly.Starting from a set of axioms, the set of all fuzzy conclusions that can be deduced by finite step fuzzy reasoning is called the set of fuzzy theorems derived from the set of axioms.In order to prove a fuzzy theorem, the forward reasoning method, called forward fuzzy reasoning, can be used to deduce the theorem to be proved step by step from axioms.It can also be used to start from the theorem to prove, and gradually boil down to the axiom set of reverse verification method, called reverse fuzzy reasoning.In reverse fuzzy reasoning, the fuzzy theorem can be proved if all the formulas are axioms.Unlike exact reasoning, every proven fuzzy theorem has a fuzzy truth degree, not a perfect truth.In fuzzy reasoning, two thresholds, true threshold and false threshold, are usually agreed (or specified by the user).When the truth degree of a conclusion is greater than the truth threshold, the conclusion is considered to be true.When the truth of the conclusion is less than the false threshold, the conclusion is considered to be false, that is, the conclusion cannot be deduced.A kind of fuzzy reasoning can be regarded as the process of inferring the truth of the conclusion according to the confidence of the fuzzy rules and the truth of the premises.Thus, in a broad sense, the process of solving an algebraic equation in terms of associative, distributive, and equivalent substitutions is also a form of reasoning.Because it involves only quantitative relations, it is called quantitative algebraic reasoning or simply algebraic calculation.”Qualitative algebraic reasoning” deals with some so-called “qualitative objects” and “qualitative relations” (that is, relations that can only be described qualitatively with each other) that cannot be accurately expressed quantitatively.For example, in forecasting the development of the national economy, although it is sometimes impossible to give an exact figure, it can be inferred that the economy will “rise”, “decline”, “slow development” and “leap forward”.These are vague qualitative descriptors.Qualitative algebra is a symbolic algebraic system based on the qualitative concept, which can be deduced into a series of qualitative algebraic calculations due to the definition of various algebraic operations on various qualitative objects.Qualitative algebra can also be included in the category of fuzzy logic because it can be used to express qualitative concepts or knowledge.