摘要：
Key issues for resolution-based automated reasoning in lattice-valued first-order logic LF(X) are investigated with truth-values in a lattice-valued logical algebraic structure lattice implication algebra (LIA). The determination of resolution at a certain truth-value level (called alpha-resolution) in LF(X) is proved to be equivalently transformed into the determination of alpha-resolution in lattice-valued propositional logic LP(X) based on LIA. The determination of alpha-resolution of any quasi-regular generalized literals and constants under various cases in LP(X) is further analyzed, specified, and subsequently verified. Hence the determination of alpha-resolution in LF(X) can be accordingly solved to a very broad extent. which not only lays a foundation for the practical implementation of automated reasoning algorithms in LF(X). but also provides a key support for alpha-resolution-based automated reasoning approaches and algorithms in LIA based linguistic truth-valued logics. Crown Copyright (C) 2010 Published by Elsevier Inc. All rights reserved.
期刊：
International Journal of Computational Intelligence Systems,2008年1(3):274-284 ISSN：1875-6883
通讯作者：
Li, XB
作者机构：
[Liu, Jun] Univ Ulster, Sch Comp & Math, Fac Engn, Jordanstown BT37 0QB, Newtownabbey, North Ireland.;[Li, Xiaobing; Xu, Yang] SW Jiaotong Univ, Intelligent Control Dev Ctr, Chengdu 610031, Peoples R China.;[Ruan, Da] Belgian Nucl Res Ctr, SCK CEN, B-9000 Ghent, Belgium.;[Ruan, Da] Univ Ghent, B-9000 Ghent, Belgium.
通讯机构：
[Li, XB] SW Jiaotong Univ, Intelligent Control Dev Ctr, Chengdu 610031, Peoples R China.
关键词：
Transformation functions;multiple attribute group decision making;linguistic-valued weighted aggregation (LVWA) operator;linguistic-valued lattice implication algebra;lattice theory
摘要：
In selecting an optional alternative in an environment of multiple attribute group decision making, different attributes of the alternative are often considered as with quantitative and qualitative information. Consequently, decision making problems may include preference information in different formats. In this paper, a lattice-based linguistic-valued weighted aggregation (LVWA) operator is proposed for multiple attribute group decision making with non-totally ordered linguistic-valued information. Then some transformation functions for unifying different formats of preference information are reviewed and summarized. Finally, an example is illustrated how to use the LVWA operator and transformation functions for multiple attribute group decision making.
期刊：
INFORMATION SCIENCES,2009年179(14):2325-2332 ISSN：0020-0255
通讯作者：
Pei, Z.(pqyz@263.net)
作者机构：
[Pei, Zheng ] Xihua Univ, Sch Math & Comp Engn, Chengdu 610039, Sichuan, Peoples R China.;[ Ruan, Da ] CEN SCK, Belgian Nucl Res Ctr, B-2400 Mol, Belgium.;[ Ruan, Da ] Univ Ghent, B-9000 Ghent, Belgium.;[ Qin, Keyun ; Xu, Yang ] SW Jiaotong Univ, Dept Math, Chengdu 610031, Sichuan, Peoples R China.
通讯机构：
[Pei, Z] Xihua Univ, Sch Math & Comp Engn, Chengdu 610039, Sichuan, Peoples R China.
关键词：
Data sets - Fuzzy statement - Linguistic data summary - Linguistic terms - Numerical examples - Personnel departments - The 2-tuple linguistic representation model - The LOWA operator - Truth degrees
摘要：
A linguistic data summary of a given data set is desirable and human consistent for any personnel department. To extract complex linguistic data summaries, the LOWA operator is used from fuzzy logic and some numerical examples are also provided in this paper. To obtain a complex linguistic data summary with a higher truth degree, genetic algorithms are applied to optimize the number and membership functions of linguistic terms and to select a part of truth degrees for aggregations, in which linguistic terms are represented by the 2-tuple linguistic representation model. Crown Copyright (C) 2009 Published by Elsevier Inc. All rights reserved.
期刊：
Mathematics and Computers in Simulation,2008年77(5-6):512-521 ISSN：0378-4754
通讯作者：
Liu, X.(lxhdoctor@sina.com)
作者机构：
[ Zeng, Xianyi ; Koehl, Ludovic ] The ENSAIT Textile Institute, 9 rue de l'Ermitage, F-59100 Roubaix, France;[Liu, Xiaohong ] College of management, Southwest University for Nationalities, Sichuan Chengdu, 610041, China;[ Xu, Yang ] College of Science, Southwest Jiaotong University, Sichuan Chengdu, 610031, China
关键词：
Customer satisfaction index - Fuzzy techniques - Linguistic value
摘要：
Customer satisfaction index (CSI) is an important concept for evaluating the quality of service in e-commerce. It permits to evaluate the validity of an e-commerce operation from the point of view of consumers. In this paper, we present a model of CSI in e-commerce using fuzzy techniques and provide a method for calculating CSI, expressed in a five levels quantity table. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.
作者：
Chen, Shuwei;Liu, Jun;Wang, Hui;Xu, Yang;Augusto, Juan Carlos
期刊：
INFORMATION SCIENCES,2014年258:266-276 ISSN：0020-0255
通讯作者：
Chen, SW
作者机构：
[Chen, Shuwei; Wang, Hui; Liu, Jun] School of Computing and Mathematics, University of Ulster at Jordanstown, Newtownabbey BT37 0QB, United Kingdom;[Liu, Jun; Xu, Yang] School of Mathematics, Southwest Jiaotong University, Chengdu 610031, Sichuan, China;[Augusto, Juan Carlos] Department of Computer Science, School of Science and Technology, Middlesex University, London, United Kingdom
作者机构：
[ Liu, Jun ] School of Computing and Mathematics, Faculty of Engineering, University of Ulster at Jordanstown, Newtownabbey BT37 0QB, United Kingdom;[Pei, Zheng ] School of Mathematics and Computer Engineering, Xihua University, Chengdu, Sichuan 610039, China;[ Ruan, Da ] Dept. of Applied Math. and Computer Science, Ghent University, B-9000 Gent, Belgium;[ Ruan, Da ] Belgian Nuclear Research Centre (SCK-CEN), Boeretang 200, B-2400 Mol, Belgium;[ Xu, Yang ] Department of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
通讯机构：
[Pei, Z] Xihua Univ, Sch Math & Comp Engn, Chengdu 610039, Sichuan, Peoples R China.
关键词：
Aggregation operator - Aggregation process - Belief degrees - Complete information - Conflict information - Fuzzy linguistics - Hierarchical analysis - Hierarchical structures - Nuclear activities - Nuclear Safeguards - Physical model - Uncertain evaluation - Weight information
期刊：
Journal of Intelligent and Fuzzy Systems,2008年19(4-5):335-343 ISSN：1064-1246
通讯作者：
Li, Z.
作者机构：
[Li, Zou ] School of Computer and Information Technology, Liaoning Normal University, Dalian, 116029, China;[Li, Zou ; Yang, Xu ] Department of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, 610031, China;[ Ruan, Da ] Belgian Nuclear Research Centre (SCKCEN), Boeretang 200, Mol 2400, Belgium;[ Zheng, Pei ] School of Mathematics and Computer Engineering, Xihua University, Chengdu, Sichuan, 610039, China
通讯机构：
[Li, Z] Liaoning Normal Univ, Sch Comp & Informat Technol, Dalian 116029, Peoples R China.
摘要：
In the framework of the linguistic truth-valued logic, a linguistic truth-valued reasoning approach for decision making with both comparable and incomparable truth values is proposed in this paper. By using the lattice implication algebra, an 18-element linguistic truth lattice-valued logic system with linguistic hedges is established for the linguistic truth-valued logic to better express both comparable and incomparable truth values. Mathematical properties of disjunction, conjunction, negation and implication for the linguistic truth-valued propositional logic are further investigated respectively. As reasoning and operation are directly acted by linguistic truth values in the decision process, the issue on how to obtain the weight for rational decision making results is discussed. An illustration example shows the proposed approach seems more effective for decision making under a fuzzy environment with both comparable and incomparable linguistic truth values.
期刊：
POLYMER ENGINEERING AND SCIENCE,2014年54(5):1162-1169 ISSN：0032-3888
通讯作者：
Chen, X.(chenxl612@sina.com)
作者机构：
[Sun, Zhidan ; Chen, Xiaolang ; Chen, Man ; Ma, Yonghong ; Hu, Shuchun ; Xu, Yang ] Key Laboratory of Advanced Materials Technology Ministry of Education, School of Materials Science and Engineering, Southwest Jiaotong University, Chengdu 610031, China;[Sun, Zhidan ; Zhang, Zhibin ] School of Life Science and Engineering, Southwest Jiaotong University, Chengdu 610031, China;[ Yu, Jie ] National Engineering Research Center for Compounding and Modification of Polymer Materials, Guiyang 550014, China
通讯机构：
[Chen, XL] Southwest Jiaotong Univ, Sch Mat Sci & Engn, Minist Educ, Key Lab Adv Mat Technol, Chengdu 610031, Peoples R China.
期刊：
JOURNAL OF THERMAL ANALYSIS AND CALORIMETRY,2014年115(1):689-695 ISSN：1388-6150
通讯作者：
Chen, X.(chenxl612@sina.com)
作者机构：
[ Sun, Zhidan ; Zhang, Zhibin ] School of Life Science and Engineering, Southwest Jiaotong University, Chengdu 610031, China;[ Bo, Xiaojin ; Xu, Yang ; Chen, Xiaolang ; Chen, Zining ; Ning, Xin ; Yang, Le ; Chen, Man ; Ma, Yonghong ] Key Laboratory of Advanced Materials Technology, Ministry of Education, Southwest Jiaotong University, Chengdu 610031, China;[ Yu, Jie ] National Engineering Research Center for Compounding and Modification of Polymer Materials, Guiyang 550014, China
通讯机构：
[Chen, XL] Southwest Jiaotong Univ, Key Lab Adv Mat Technol, Minist Educ, Sch Mat Sci & Engn, Chengdu 610031, Peoples R China.
期刊：
Computers and Mathematics with Applications,2008年56(6):1604-1616 ISSN：0898-1221
通讯作者：
Zhan, J.(zhanjianming@hotmail.com)
作者机构：
[Zhan, Jianming ] Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province 445000, China;[ Xu, Yang ] Department of Applied Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
期刊：
INFORMATION SCIENCES,2008年178(2):403-413 ISSN：0020-0255
通讯作者：
Pan, XD
作者机构：
[Pan, Xiaodong; Xu, Yang] Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, 610031 Sichuan, China;[Pan, Xiaodong] Department of Mathematics, Southwest Jiaotong University, Chengdu, 610031 Sichuan, China
期刊：
INFORMATION SCIENCES,2010年180(10):1990-2002 ISSN：0020-0255
通讯作者：
Lai, J.(eagles_laijiajun7309@126.com)
作者机构：
[Lai, Jiajun ] School of Information Science and Technology, Southwest Jiaotong University, Chengdu, 610031, China;[Lai, Jiajun ; Xu, Yang ] Intelligent Control Development Center, Southwest Jiaotong University, Chengdu, 610031, China
通讯机构：
[Lai, JJ] SW Jiaotong Univ, Intelligent Control Dev Ctr, Chengdu 610031, Peoples R China.
期刊：
International Journal of Innovative Computing, Information and Control,2009年5(12):4745-4752 ISSN：1349-4198
通讯作者：
Li, Z.(zoulicn@163.com)
作者机构：
[Li, Zou ] School of Computer and Information, Liaoning Normal University, Dalian 116029, China;[Li, Zou ; Yang, Xu ] Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, China;[ Zheng, Pei ] School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, China;[ Xin, Liu ] Mathematics College, Liaoning Normal University, Dalian 116029, China
通讯机构：
[Zou, L] Liaoning Normal Univ, Sch Comp & Informat, Dalian 116029, Peoples R China.
关键词：
Academic ideas - Intuitionistic fuzzy - Intuitionistic fuzzy sets - Lattice implication algebra - Linguistic truth value - Natural languages - Satisfiability
摘要：
This paper focuses on resolution-based automated reasoning theory in a lattice-valued logic system with truth values that are defined in a lattice-valued logical algebraic structure-lattice implication algebras (LIAs)-which essentially aims to extend the classical logic to handle automated deduction under an uncertain environment. Concretely, we investigate a generalization of the known conjunctive normal form (CNF) in the classical logic representation that we call the generalized conjunctive normal form (GCNF), which aims to characterize the constants and implication connectives that are essentially different from the ones in classical logic. We then extend the established resolution principle at a certain truth-value level alpha (called alpha-resolution) in this lattice-valued logic to a more general form, i.e., from binary alpha-resolution to multiary alpha-resolution. The extension to multiary alpha-resolution starts from lattice-valued propositional logic LP(X), while its theorems of both soundness and completeness are proved. Multiary alpha-resolution principle is then further established in the corresponding lattice-valued first-order logic LF(X), along with its soundness theorem, lifting lemma, and completeness theorem. Meanwhile, an important result that multiary alpha-resolution principle in LF(X) can be equivalently transformed into that in LP(X) to some extent is obtained. All these works will theoretically support the establishment of an automated reasoning algorithm and its implementation with further applications into automated deduction and decision-making problems under uncertainty.
期刊：
Fuzzy Optimization and Decision Making,2008年7(4):387-397 ISSN：1568-4539
通讯作者：
Zou, L.(zoulicn@163.com)
作者机构：
[Zhengjiang Wu; Yang Xu] Intelligent Control and Development Center, Southwest Jiaotong University, Chengdu, Sichuan 610031, China;[Xin Liu] Mathematics College, Liaoning Normal University, Dalian 116029, China;[Li Zou] School of Computer and Information Technology, Liaoning Normal University, No. 850 Huanghe Road, Dalian 116029, China
通讯机构：
[Zou, L] Liaoning Normal Univ, Sch Comp & Informat Technol, 850 Huanghe Rd, Dalian 116029, Peoples R China.
关键词：
Linguistic truth value;Standard linguistic truth value;Sensor evaluation
摘要：
During the sensor evaluation procedure, each valuator uses his/her own ordinary linguistic truth values for the same factor because of different preference. That will brings some disadvantages to aggregate the information. For a uniform criterion, the standard linguistic truth value (SLTV) set is proposed. Based on the former hypothesis of transformation models of linguistic truth values, four transformation models are discussed: the model of point to point, the model of fuzzy set to point, the model of point to fuzzy set and the model of fuzzy set to fuzzy set. An example is to analyze it. Using the applicability measure we can choose appropriate SLTV for the different sensory evaluation system.
摘要：
This paper focuses on resolution-based automated reasoning approaches in a lattice-valued first-order logic LF(X) with truth-values defined in a logical algebraic structure-lattice implication algebra (LIA), which aims at providing the logic foundation to represent and handle both imprecision and incomparability. In order to improve the efficiency of alpha-resolution approach proposed for LF(X), firstly the concepts of alpha-lock resolution principle and deduction are introduced for lattice-valued propositional logic LP(X) based on LIA, along with its soundness and weak completeness theorems. Then all the results are extended into LF(X) by using Lifting Lemma. Finally an alpha-lock resolution automated reasoning algorithm in LF(X) is proposed for the implementation purpose. This work provides a theoretical foundation for more efficient resolution-based automated reasoning algorithm in lattice-valued logic LF(X). (C) 2011 Elsevier Ltd. All rights reserved.
期刊：
INFORMATION SCIENCES,2013年247:123-130 ISSN：0020-0255
通讯作者：
Qin, KY
作者机构：
[Pei, Zheng] School of Mathematics and Computer Engineering, Xihua University, Chengdu, Sichuan 610039, China;[Yang, Jilin] College of Fundamental Education, Sichuan Normal University, Chengdu, Sichuan 610068, China;[Xu, Yang; Qin, Keyun] College of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, China
期刊：
Mathematical and Computer Modelling,2008年47(11-12):1089-1098 ISSN：0895-7177
通讯作者：
Lai, S.(laishaoy@swufe.edu.cn)
作者机构：
[Lai, Shaoyong ] Department of Economic Mathematics, Southwestern University of Finance and Economics, 610074 Chengdu, China;[ Xu, Yang ] Department of Applied Mathematics, Southwest JiaoTong University, Chengdu, 610031, China
期刊：
Journal of Multiple-Valued Logic and Soft Computing,2011年17(4):293-303 ISSN：1542-3980
通讯作者：
Zou, L
作者机构：
[Zou, Li; Xu, Yang] Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, China;[Pei, Zheng] School of Mathematics and Computer Engineering, Xihua University, Chengdu 610039, China;[Ruan, Da] SCKCEN and Ghent University, Boeretang 200, 2400 Mol, Belgium;[Zou, Li] School of Computer and Information Technology, Liaoning Normal University, Dalian 116029, China
通讯机构：
[Zou, L] Liaoning Normal Univ, Sch Comp & Informat Technol, Dalian 116029, Peoples R China.
关键词：
Evaluating linguistic values;lattice implication algebra;risk analysis;incomparable linguistic values