Recently we proposed the linguistic Copenhagen interpretation of quantum mechanics, which is called quantum language or measurement theory. This theory is valid for both quantum and classical systems. Thus we think th...Recently we proposed the linguistic Copenhagen interpretation of quantum mechanics, which is called quantum language or measurement theory. This theory is valid for both quantum and classical systems. Thus we think that quantum language is one of the most powerful scientific theories, like statistics. In this paper we justify Zadeh’s fuzzy sets theory in quantum language, that is, fuzzy propositions are identified with binary measurements. This implies that the definition of “proposition” is, for the first time, acquired in the field of non-mathematics. Further, we assert that fuzzy logic is more natural than crisp logic in science. And furthermore, we discuss and solve Saussure’s linguistics, Moore’s paradox, Quine’s analytic-synthetic distinction and Lewis Carroll’s logical paradox. Therefore, from the philosophical point of view, our result gives a complete answer to Wittgenstein’s problem: “Why does logic work in our world?” and “What is a scientific proposition?” in his picture theory. That is, we simultaneously justify both Zadeh’s fuzzy sets and Wittgenstein’s picture theory in the quantum mechanical worldview.展开更多
In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semant...In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semantically. The membership functions of fuzzy concepts form chains which satisfy Zadeh algebra axioms. These chains are based on important relationship condition (1) represented in the introduction where the binary relation Rm of a simple concept m is defined more general in Definition 2.10. Then every chain of membership functions forms a Zadeh algebra. It demands a lot of preliminaries before we obtain this desired result.展开更多
文摘Recently we proposed the linguistic Copenhagen interpretation of quantum mechanics, which is called quantum language or measurement theory. This theory is valid for both quantum and classical systems. Thus we think that quantum language is one of the most powerful scientific theories, like statistics. In this paper we justify Zadeh’s fuzzy sets theory in quantum language, that is, fuzzy propositions are identified with binary measurements. This implies that the definition of “proposition” is, for the first time, acquired in the field of non-mathematics. Further, we assert that fuzzy logic is more natural than crisp logic in science. And furthermore, we discuss and solve Saussure’s linguistics, Moore’s paradox, Quine’s analytic-synthetic distinction and Lewis Carroll’s logical paradox. Therefore, from the philosophical point of view, our result gives a complete answer to Wittgenstein’s problem: “Why does logic work in our world?” and “What is a scientific proposition?” in his picture theory. That is, we simultaneously justify both Zadeh’s fuzzy sets and Wittgenstein’s picture theory in the quantum mechanical worldview.
文摘In this work we create a connection between AFS (Axiomatic Fuzzy Sets) fuzzy logic systems and Zadeh algebra. Beginning with simple concepts we construct fuzzy logic concepts. Simple concepts can be interpreted semantically. The membership functions of fuzzy concepts form chains which satisfy Zadeh algebra axioms. These chains are based on important relationship condition (1) represented in the introduction where the binary relation Rm of a simple concept m is defined more general in Definition 2.10. Then every chain of membership functions forms a Zadeh algebra. It demands a lot of preliminaries before we obtain this desired result.
