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A unified approximate reasoning theory suitable for both propositional calculus system L and predicate calculus system K

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Science in China(Series F) 2005年第1期48卷 1-14页

作者： WANGGuojun CHINK.S DANGC.Y. DepartmentofManufacturingEngineeringandEngineeringManagement CityUniversityofHongKongHongKongChina InstituteofMathematics ShaanxiNormalUniversityXi'an710062China//ResearchCenterforScienceXi'anJiaotongUniversityXi'an710049China

The concepts of metric R0-algebra and Hilbert cube of type RO are introduced. A unified approximate reasoning theory in propositional caculus system ? and predicate calculus system (?) is established semantically as w... 详细信息

关键词： metric R0-algebra Hilbert cube of type R0 metric Lindenbaum algebra of type R0 approximate reasoning complete theorem.

Theory of approximate reasoning in Two-Valued Predicate Logic Based on the Quasi-truth Degrees

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Journal of Donghua University(English Edition) 2012年第1期29卷 23-27页

作者：秦晓燕刘军徐扬陈树伟刘熠 Intelligent Control Development Center Southwest Jiaotong University College of Mathematics and Computer Science Shanxi Normal University School of Computing and Mathematics University of Ulster

Based on the theory of the quasi-truth degrees in two-valued predicate logic, some researches on approximate reasoning are studied in this paper. The relation of the pseudo-metric between first-order formulae and the quasi-truth degrees of first-order formulae is discussed, and it is proved that there is no isolated point in the logic metric space (F, ρ ). Thus the pseudo-metric between first-order formulae is well defined to develop the study about approximate reasoning in the logic metric space (F, ρ ). Then, three different types of approximate reasoning patterns are proposed, and their equivalence under some condition is proved. This work aims at filling in the blanks of approximate reasoning in quantitative predicate logic.

关键词： approximate reasoning pseudo-metric quasi-truth degree predicate logic

Quantitative Method Based on Cotangent Similarity Degree in Three-Valued ?ukasiewicz Logic

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Chinese Journal of Electronics 2021年第1期30卷 134-144页

作者： YU Peng School of Arts and Sciences Shaanxi University of Science and Technology

The main purpose of this paper is to establish a type of quantitative model by using the contangent similarity function in the three-valued?ukasiewicz propositional logic system ?;. We introduce the concepts of the cotangent similarity degree, cotangent pseudo-distance and cotangent truth degree of the propositions, together with their basic properties in ?;.We investigate the relationship between the cotangent truth degree and contangent pseudo-distance, and prove the continuity of the logical connectives ?, ∨ and → in the ?;logical metric space. We propose a graded reduction method and three types of graded reasoning frameworks on the propositions set F（S）, and provide several examples and basic properties of it.

关键词： Cotangent similarity degree approximate reasoning Quantitative logic Three-valued logic

A variable precision rough set approach to knowledge discovery in land cover classification

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International Journal of Digital Earth 2016年第12期9卷 1206-1223页

作者： Iftikhar U.Sikder Department of Information System Cleveland State UniversityOHUSA Department of Electrical Engineering and Computer Science Cleveland State UniversityOHUSA

This paper presents a granular computing approach to spatial classification and prediction of land cover classes using rough set variable precision *** particular,it presents an approach to characterizing large spatially clustered data sets to discover knowledge in multi-source supervised *** evidential structure of spatial classification is founded on the notions of equivalence relations of rough set *** allows expressing spatial concepts in terms of approximation space wherein a decision class can be approximated through the partition of boundary *** paper also identifies how approximate reasoning can be introduced by using variable precision rough sets in the context of land cover *** rough set theory is applied to demonstrate an empirical application and the predictive performance is compared with popular baseline machine learning algorithms.A comparison shows that the predictive performance of the rough set rule induction is slightly higher than the decision tree and significantly outperforms the baseline models such as neural network,naïve Bayesian and support vector machine methods.

关键词： Rough set theory soft computing granular computing remote sensing approximate reasoning

Intelligent reasoning and management decision making with grey rough influence diagrams

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International Journal of Intelligent Computing and Cybernetics 2016年第4期9卷 336-353页

作者： Haiqing Hu Bingqiang Liu Tao Shen School of Electrical Engineering University of JinanJinanChina School of Mathematics Shandong UniversityJinanChina

Purpose-Influence diagrams(IDs)have been widely applied as a form of knowledge expression and a decision analysis tool in the management and engineering *** measurements and expectation values are computed depending on probability distributions in traditional IDs,however,most information systems in the real world are nondeterministic,and data in information tables can be interval valued,multiple valued and even ***,conventional numeric models of IDs are not suitable for information processing with respect to imprecise data whose boundaries are *** paper aims to discuss these ***/methodology/approach-The grey system theory and rough sets have proved to be effective tools in the data processing of uncertain information systems,approximate knowledge acquisition and representation are also the objectives in intelligent reasoning and decision ***,this study proposes a new mathematical model by combining grey rough sets with IDs,and approximate measurements are used instead of probability distribution,an implicational relationship is utilized instead of an indiscernible relationship,and all of the features of the proposed approach contribute to deal with uncertain ***-The focus of this paper is to provide a more comprehensive framework for approximate knowledge representation and intelligent decision analysis in uncertain information systems and an example of decision support in product management systems with the new approach is ***/value-Collaboration of IDs and grey rough sets is first proposed,which provides a new mathematical and graphical tool for approximate reasoning and intelligent decision analysis within interval-valued information systems.

关键词： Uncertainty approximate reasoning Influence diagrams Intelligent decision Interval value

Randomization of classical inference patterns and its application

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Science in China(Series F) 2007年第6期50卷 867-877页

作者： WANG GuoJun1,2 & HUI XiaoJing1,31 Institute of Mathematics, Shaanxi Normal University, Xi’an 710062, China 2 Research Center for Science, Xi’an Jiaotong University, Xi’an 710049, China 3 College of Mathematics and Computer Science, Yan’an University, 716000, China Institute of Mathematics Shaanxi Normal University Xi’an China Research Center for Science Xi’an Jiaotong University Xi’an China College of Mathematics and Computer Science Yan’an University China

By means of randomization, the concept of D-randomized truth degree of formulas in two-valued propositional logic is introduced, and it is proved that the set of values of D-randomized truth degree of formulas has no isolated point in [0,1]. The concepts of D-logic pseudo-metric and D-logic metric space are also introduced and it is proved that there is no isolated point in the space. The new built D-randomized concepts are extensions of the corresponding concepts in quantified logic. Moreover, it is proved that the basic logic connectives are continuous operators in D-logic metric space. Lastly, three different types of approximate reasoning patterns are proposed.

关键词： D-randomized mapping D-randomized truth degree D-similarity D-logic metric space approximate reasoning