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 cyber-physical systems, multidimensional data fusion is an important method to achieve comprehensive evaluation decisions and reduce data redundancy. In this paper, a data fusion algorithm based on fuzzy set theory...In cyber-physical systems, multidimensional data fusion is an important method to achieve comprehensive evaluation decisions and reduce data redundancy. In this paper, a data fusion algorithm based on fuzzy set theory and Dempster-Shafer(D-S) evidence theory is proposed to overcome the shortcomings of the existing decision-layer multidimensional data fusion algorithms. The basic probability distribution of evidence is determined based on fuzzy set theory and attribute weights, and the data fusion of attribute evidence is combined with the credibility of sensor nodes in a cyber-physical systems network. Experimental analysis shows that the proposed method has obvious advantages in the degree of the differentiation of the results.展开更多
A new fuzzy set theory, C-fuzzy set theory, is introduced in this paper. It is a particular case of the classical set theory and satisfies all formulas of the classical set theory. To add a limitation to C-fuzzy set s...A new fuzzy set theory, C-fuzzy set theory, is introduced in this paper. It is a particular case of the classical set theory and satisfies all formulas of the classical set theory. To add a limitation to C-fuzzy set system, in which all fuzzy sets must be ＂non-uniform inclusive＂ to each other, then it forms a family of sub-systems, the Z-fuzzy set family. It can be proved that the Z0-fuzzy set system, one of Z-fuzzy set systems, is equivalent to Zadeh＇s fuzzy set system. Analysis shows that 1） Zadeh＇s fuzzy set system defines the relations A = B and A C B between two fuzzy sets A and B as ＂A↓u ∈U, （μA ∈（u）=μB（u））＂ and ＂A↓u E U, （μA（u） ≤μB（u））＂ respectively is inappropriate, because it makes all fuzzy sets be ＂non-uniformly inclusive＂; 2） it is also inappropriate to define two fuzzy sets＇ union and intersection operations as the max and rain of their grades of membership, because this prevents fuzzy set＇s ability to correctly reflect different kinds of fuzzy phenomenon in the natural world. Then it has to work around the problem by invent unnatural functions that are hard to understand, such as augmenting max and min for union and intersection to min{a ＋ b, 1} and max{a＋ b - 1, 0}, but these functions are incorrect on inclusive case. If both pairs of definitions are used together, not only are they unnatural, but also they are still unable to cover all possible set relationships in the natural world; and 3） it is incorrect to define the set complement as 1 - μA（U）, because it can be proved that set complement cannot exist in Zadeh＇s fuzzy set, and it causes confusion in logic and thinking. And it is seriously mistaken to believe that logics of fuzzy sets necessarily go against classical and normal thinking, logic, and conception. The C-fuzzy set theory proposed in this paper overcomes all of the above errors and shortcomings, and more reasonably reflects fuzzy phenomenon in the natural world. It satisfies all relations, formulas, and operations of the classical set theory. It is consistent with normal, natural, and classical thinking, logic, and concepts.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.
基金supported by the National Natural Science Foundation of China (No. 61462089)the Fundamental Research Funds for Beijing University of Civil Engineering and Architecture (No. X18002)
文摘In cyber-physical systems, multidimensional data fusion is an important method to achieve comprehensive evaluation decisions and reduce data redundancy. In this paper, a data fusion algorithm based on fuzzy set theory and Dempster-Shafer(D-S) evidence theory is proposed to overcome the shortcomings of the existing decision-layer multidimensional data fusion algorithms. The basic probability distribution of evidence is determined based on fuzzy set theory and attribute weights, and the data fusion of attribute evidence is combined with the credibility of sensor nodes in a cyber-physical systems network. Experimental analysis shows that the proposed method has obvious advantages in the degree of the differentiation of the results.
基金supported by the National Natural Science Foundation of China under Grant No.60343010the National Basic Research 973 Program of China under Grant No.2003 CB317000the Foundation of Institute of Computing Technology,ChineseAcademy of Sciences under Grant No.20056510
文摘A new fuzzy set theory, C-fuzzy set theory, is introduced in this paper. It is a particular case of the classical set theory and satisfies all formulas of the classical set theory. To add a limitation to C-fuzzy set system, in which all fuzzy sets must be ＂non-uniform inclusive＂ to each other, then it forms a family of sub-systems, the Z-fuzzy set family. It can be proved that the Z0-fuzzy set system, one of Z-fuzzy set systems, is equivalent to Zadeh＇s fuzzy set system. Analysis shows that 1） Zadeh＇s fuzzy set system defines the relations A = B and A C B between two fuzzy sets A and B as ＂A↓u ∈U, （μA ∈（u）=μB（u））＂ and ＂A↓u E U, （μA（u） ≤μB（u））＂ respectively is inappropriate, because it makes all fuzzy sets be ＂non-uniformly inclusive＂; 2） it is also inappropriate to define two fuzzy sets＇ union and intersection operations as the max and rain of their grades of membership, because this prevents fuzzy set＇s ability to correctly reflect different kinds of fuzzy phenomenon in the natural world. Then it has to work around the problem by invent unnatural functions that are hard to understand, such as augmenting max and min for union and intersection to min{a ＋ b, 1} and max{a＋ b - 1, 0}, but these functions are incorrect on inclusive case. If both pairs of definitions are used together, not only are they unnatural, but also they are still unable to cover all possible set relationships in the natural world; and 3） it is incorrect to define the set complement as 1 - μA（U）, because it can be proved that set complement cannot exist in Zadeh＇s fuzzy set, and it causes confusion in logic and thinking. And it is seriously mistaken to believe that logics of fuzzy sets necessarily go against classical and normal thinking, logic, and conception. The C-fuzzy set theory proposed in this paper overcomes all of the above errors and shortcomings, and more reasonably reflects fuzzy phenomenon in the natural world. It satisfies all relations, formulas, and operations of the classical set theory. It is consistent with normal, natural, and classical thinking, logic, and concepts.
