三种基于不同模糊否定的模糊拒取式推理及其算法<sup>*</sup>

doi:10.16451/j.cnki.issn1003-6059.201502001

Abstract
Figure/Table
References (0)
Related Citation (1)

Download: PDF (362 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract

Fuzzy modus tollens (FMT) is one of the most basic inference forms in fuzzy reasoning. As a premise of FMT, fuzzy negation plays a major role in inference. In this paper, based on the fuzzy propositional logic with contradictory negation, opposite negation and medium negation (FLCOM), contradictory negation, opposite negation and medium negation are proved to be different fuzzy negations, and thus three kinds of fuzzy modus tollens, FMT₁, FMT₂ and FMT₃, are proposed,which are different from FMT respectively based on contradictory negation, opposite negation and medium negation. Furthermore, based on the R-implication operator I_R, a fuzzy NR-implication operator I_NR is defined which is associated with I_R. The algorithms of FMT₁, FMT₂ and FMT₃ are proposed according to the algorithm of FMT, and it is proved that algorithms of FMT₁, FMT₂ and FMT₃ are reducible algorithms when I ≤I_NR.

Key words： Fuzzy Modus Tollens(FMT) Contradictory Negation Opposite Negation Medium Negation Algorithm of Fuzzy Modus Tollens

Received: 27 September 2013

ZTFLH:

TP181

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	PAN Zheng-Hua
	ZHAO Jie-Xin
	WANG Shan-Shan

Cite this article:

PAN Zheng-Hua,ZHAO Jie-Xin,WANG Shan-Shan. Three Kinds of Fuzzy Modus Tollens and Algorithms Based on Different Fuzzy Negations[J]. , 2015, 28(2): 97-104.

URL:

http://manu46.magtech.com.cn/Jweb_prai/EN/10.16451/j.cnki.issn1003-6059.201502001 OR http://manu46.magtech.com.cn/Jweb_prai/EN/Y2015/V28/I2/97

［1］ Mas M, Monserrat M, Torrens J, et al. A Survey on Fuzzy Implication Functions. IEEE Trans on Fuzzy Systems, 2007, 15(6): 1107-1121
［2］ Mas M, Monserrat M, Torrens J. Modus Ponens and Modus Tollens in Discrete Implications. International Journal of Approximate Reasoning, 2008, 49 (2): 422-435
［3］ Trillas E, Alsina C, Renedo E, et al. On ContraSymmetry and MPT Conditionality in Fuzzy Logic. International Journal of Intelligent Systems, 2005, 20(3): 313-326
［4］ Baczynski M, Jayaram B. Fuzzy Implications. Berlin, Germany: Springer, 2008
［5］ Wang G J. On the Logic Foundation of Fuzzy Reasoning. Information Sciences, 1999, 117 (1/2): 47-88
［6］ Zadeh L A. Fuzzy Sets. Information and Control, 1965, 8(3): 338-353
［7］ Atanassov K T. Intuitionistic Fuzzy Sets. Fuzzy Sets and Systems, 1986, 20(1): 87-96
［8］ Pawlak Z. Rough Sets. International Journal of Computer and Information Sciences, 1982, 11(5): 341-356
［9］ Hájek P. Metamathematics of Fuzzy Logic. Dordrecht, the Netherlands: Kluwer Academic Publishers, 1998
［10］ Pan Z H. A New Cognition and Processing on Contradictory Knowledge // Proc of the IEEE International Conference on Machine Learning and Cybernetics. Dalian, China, 2006, III: 1532-1537
［11］ Wagner G. Web Rules Need Two Kinds of Negation // Proc of the International Workshop on Principles and Practice of Semantic Web Reasoning. Mumbai, India, 2003: 33-50
［12］ Ferré S. Negation, Opposition, and Possibility in Logical Concept Analysis // Proc of the 4th International Conference on Formal Concept Analysis. Dresden, Germany, 2006: 130-145
［13］ Kaneiwa K. Description Logics with Contraries, Contradictories, and Subcontraries. New Generation Computing, 2007, 25(4): 443-468
［14］ Pan Z H. A Logic Description on Different Negation Relation in Knowledge // Proc of the 4th International Conference on Intelligent Computing. Shanghai, China, 2008: 815-823
［15］ Pan Z H, Wang C, Zhang L J. Three Kinds of Negations in Fuzzy Knowledge and Their Applications to Decision Making in Financial Investment // Proc of the 2nd International Conference on Computational Collective Intelligence： Technologies and Applications. Gaoxiong, China, 2010， II: 391-401
［16］ Pan Z H, Yang L, Xu J. Fuzzy Set with Three Kinds of Negations and Its Applications in Fuzzy Decision Making // Proc of the 3rd International Conference on Artificial Intelligence and Computational Intelligence. Taiyuan, China, 2011, I: 533-542
［17］ Pan Z H. Three Kinds of Negation of Fuzzy Knowledge and Their Base of Set. Chinese Journal of Computers, 2012, 35(7): 1421-1428 (in Chinese) (潘正华.模糊知识的三种否定及其集合基础.计算机学报, 2012, 35(7): 1421-1428)
［18］ Pan Z H. Three Kinds of Negation of Fuzzy Knowledge and Their Base of Logic // Proc of the 9th International Conference on Intelligent Computing Theories and Technology. Nanning, China, 2013: 83-93