Propositions fuzzy

In a crude way, it is useful to distinguish the following four types of fuzzy propositions, each of which may, in addition, be quantified by an appropriate fuzzy quantifier. 

Reasoning based on fuzzy propositions of the four types, possibly quantified by various fuzzy quantifiers, is usually referred to as approximate reasoning. Although approximate reasoning is currently a subject of intensive research, its basic principles are already well established. For example, the most common inference rules of classical logic, such as modus ponens,... 

From these basic properties of possibility measures, the full calculus of possibility theory, analogous to the calculus of probability theory, has been developed. Its primary role is to deal with incomplete information expressed in terms of fuzzy propositions. Due to limited space, it is not possible to cover here details of this calculus. 

Fuzzy propositions are assigned to fuzzy sets. Suppose proposition P is assigned to the fuzzy set A, then the truth value of a proposition, (P), is given by T P) = P/ x) where 0 < pj < 1. 

The fundamental difference between classical propositions and fuzzy propositions is in the range of their truth values. While each classical proposition is required to be either true or false, the truth or falsity of fuzzy propositions is a matter of degree (Klir and Yuan 1995). Assuming that tmth and falsity are expressed by values 1 and 0, respectively, the degree of tmth of each fuzzy proposition is expressed by a number in the unit interval [0,1]. 

In general, fuzzy quantifiers are fuzzy numbers that take part in fuzzy propositions. They are of two kinds. Fuzzy quantifiers of the first kind are defined onR and characterize linguistic terms such as about 10, much more than 100, and at least about 5. Fuzzy quantifiers of the second kind are defined on [0,1] and characterize linguistic terms such as almost all, about half, and most. 

FL is based on a collection of IF-THEN rule statements used to formulate conditional fuzzy propositions. 

There are four types of fuzzy propositions. Unconditional and unqualified propositions are of the form... 

In 1932 Gddel [3] proved that in any axiomatic mathematical system (theory), there are fuzzy propositions, that is, propositions which cannot be proved or disproved within the axioms of this system. 

What is the difference between possibility and probability Zadeh writes Intuitively, possibility relates to our perception of the degree of feasibility or ease of attainment, whereas probability is associated with the degree of belief, likelihood, frequency, or proportion.According to Zadeh, the relation between the fuzzy proposition (statement) P containing the fuzzy variable X whose base set is U and the fuzzy set A that is a fuzzy subset of U is represented by... 

Suppose we have linguistic variables temperature (f) and yield (y). The discrete membership functions are given in Table 1, rows /Z/i(f), Ms(> )- The conditional fuzzy proposition... 

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