Hedges
In the 1970s, Zadeh introduced and mastered the theory of detrimental reasoning based on the concept of linguistic variables and FL. Informally, by linguistic variable, we designate a variable whose value is a word in natural or tense language as an intermediate point. For example, Age is a language variable with linguistic values such as young, old, very young, very old, increasingly younger, not very young, not very old, etc. Language from primary terms (e.g. young and old in a sample of linguistic variable age) by values various language hedges (e.g. very, increasingly or less) and connections (e.g. and, or not) as well known creation of variables. In terms of Zadeh's FL, the truth value is verbal. For example, "True," "Very true," "False," "False," "Possibly False," etc. can be used to express the value of the language variable Truth. In this sense, malicious reasoning (also tab-separated fuzzy reasoning) is mostly qualitative rather than quantitative in nature, and upon closer examination, everything falls outside the sphere of applicability of classical logic. The main purpose of detrimental reasoning theory is to mimic human verbal reasoning, especially when describing the behavior of humancentric systems. In the same way as Zadeh's rule for qualification for truth, propositions such as "Lucia is very young" are considered to be semantically equivalent to the proposition "Lucia is young." This semantic equivalence relationship plays an important role in false reasoning. In a fuzzy set-based approach to fuzzy inference, primary linguistic truth values, such as true and false, are stipulated to correspond to the fuzzy set specified in an interval (0,1) designed to interpret the meaning of that primary term. Then, the complex language truth value is computed using a tracking procedure:
- • For example, more or less linguistic hedges are specified as unary operators in fuzzy sets.
- • Logical concatenations such as "and," "or," "not," and "if... then" are specified by operators such as "t-norm," "t-conorm," "negation," and "implication," respectively. As is well known, one of the inherent problems of fuzzy inference models is linguistic approximation, that is, how to name the resulting fuzzy set of the inference process in linguistic terms. This depends on the shape of the resulting fuzzy set with respect to the main fuzzy set and operator. Based on the two characteristics of linguistic variables introduced by Zadeh (i.e. the con- text-independent meaning of linguistic hedge and linkage, the universality of the domain of language) and the meaning of linguistic hedge in natural language, Nguyen and Wechler proposed a flow of trigonometry. Moreover, the assistant gives us the possibility to introduce verbal reasoning methods that can directly deal with linguistic terms and thus avoid the problem of linguistic approximation.
Expansion Principle
An extension principle learned by Zadeh is a function for fuzzy sets. Thus, it generalizes the global point-to-point mapping of the function to the mapping between fuzzy sets.
