| ¡¡ | Chinese Journal of Computers Full Text |
| Title | Measure of Medium Truth Scale and Its Application (¢ò) |
| Authors | HONG Long1),2) XIAO Xi-An3) ZHU Wu-Jia2) |
| Address | 1)(College of Computer, Nanjing University of Posts and Telecommunications, Nanjing 210003) 2)(College of Information Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 210016) 3)(College of Science, PLA University of Science and Technology, Nanjing 210016) |
| Year | 2007 |
| Issue | No.9(1551¡ª1558) |
| Abstract & Background | Abstract It is introduced concisely that researching measure of medium truth scale (MMTS) for application is essential after analyzing the characteristics of semantics of fuzzy negation and truth-value degree. The MMTS of sets is discussed from both discrete and continuous based on MMTS of individual. After establishing medium standard pointer, fuzzy scale and medium entropy are proposed, and the greatest value of medium entropy is discussed. In accordance with de-emphasizing "maximum difference" between concepts with opposite properties, the idea of weakening polarization and strengthening transition are presented. After a general discussion on transition and polarization, normal numerical quantification mapping and generalized numerical quantification mapping are constructed, and the sufficient condition for converting transition to opposing polarization is established. This shows all cases existed transition may be process as object opposites while processing vague phenomenon in engineering and scientific research, so that MMTS can find wide application in more fields. keywords truth scale; set; measure; fuzzy scale; medium entropy; transition background Vague phenomenon exists widely in natural would and real society, and it is a frequent problem confronting us and having to solve by us in engineering and scientific research. Zadeh L A in 60¡¯s of 20th century and Pawlak Z in 80¡¯s of 20th century established mathematical methods for processing fuzzy phenomenon respectively. To lay the mathematics foundation of processing fuzzy phenomenon, Zhu Wu-Jia and Xiao Xi-An, two authors of this paper, proposed medium rule in 80¡¯s of 20th century, and they established medium axiomatic set theory using the medium logic created by themselves as inferential tools, which realized the extension of the mathematics study objects from precise quantity objects to fuzzy quantity objects. Since Zhu and Xiao¡¯s research is original and interesting, scholars in different disciplines around the world have dedicated tremendous amount of effort to the study of medium mathematics systems. So far, several hundred-influence papers based on medium logic have been published in international conferences and famous journals. To make medium mathematics theory be use directly on wide and practical applied fields, the authors researched into the quantification of fuzzy negative and truth grad in medium logic recently. The reference £Û5£Ý and this paper are main reports about the research achievements, in which a quantification method which was based on logics and different from fuzzy set and rough set for processing fuzzy phenomenon was established and the foundation for the study and application in future was set. The group¡¯s current research interests are focused on applying MMTS (measure of medium truth scale)to information science, and have got first results in computer architecture, digital image processing, intelligent algorithm, data mining, measuring performance and so on. This work is supported by the National Natural Science Foundation of China under grant No.60273037 and the National Basic Research Program of China (973 Program) under grant No.1999032701. |