An axiomatizable lattice-ordered linguistic truth-valued logic

Jun Liu; Yang Xu; Da Ruan; Jan Wagemans

doi:10.1142/9789814324700_0009

An axiomatizable lattice-ordered linguistic truth-valued logic

Jun Liu, Yang Xu, Da Ruan, Jan Wagemans

Nuclear Systems Measurements

Research output › peer-review

Abstract

Investigations on an algebraic structure of linguistic truth values in decision making and social science applications still lack a formalism for development of strict linguistic truth-valued logic system and its approximate reasoning scheme in practice. To attain this goal we characterize and construct the structure of linguistic value sets in natural language by a lattice-valued algebra structure - lattice implication algebra (LIA), where Łukasiewicz implication algebra, as a special case of LIA, plays a substantial role. By using Łukasiewicz logic’s axiomatizability in terms of Pavelka type fuzzy logic, we propose a new axiomatizable linguistic truth-valued logic system based on LIA to place an important foundation for further establishing formal linguistic valued logic based approximate reasoning systems. This proposed logic system has a distinct advantage of handling incomparable linguistic terms in perception-based decision making processes.

Original language	English
Title of host publication	Computational Intelligence -- Foundations and Applications
Place of Publication	Singapore, Singapore
Pages	72-78
Number of pages	7
Volume	1
DOIs	https://doi.org/10.1142/9789814324700_0009
State	Published - Aug 2010
Event	2010 - 9th International FLINS Conference on Foundations and Applications of Computational Intelligence - Chengdu Duration: 2 Aug 2010 → 4 Aug 2010 Conference number: FLINS 2010

Publication series

Name	Computer Engineering and Information Science
Number	4

Conference

Conference	2010 - 9th International FLINS Conference on Foundations and Applications of Computational Intelligence
Country/Territory	China
City	Chengdu
Period	2010-08-02 → 2010-08-04

Funding

This work is supported by the National Natural Science Foundation of China (No. 60875034), the Specialized Research Foundation for the Doctoral Program of Higher Education of China (Grant No. 20060613007), and the research project TIN2009-08286 and P08-TIC-3548. † The correspondent author, email: [email protected].

Funders	Funder number
NSFC - National Natural Science Foundation of China	60875034
Specialized Research Fund for the Doctoral Program of Higher Education of China	20060613007, P08-TIC-3548, TIN2009-08286

Access to Document

10.1142/9789814324700_0009License: Unspecified

Cite this

@inproceedings{cfc29c4b4d7141008e6f8645dddcb51f,

title = "An axiomatizable lattice-ordered linguistic truth-valued logic",

abstract = "Investigations on an algebraic structure of linguistic truth values in decision making and social science applications still lack a formalism for development of strict linguistic truth-valued logic system and its approximate reasoning scheme in practice. To attain this goal we characterize and construct the structure of linguistic value sets in natural language by a lattice-valued algebra structure - lattice implication algebra (LIA), where {\L}ukasiewicz implication algebra, as a special case of LIA, plays a substantial role. By using {\L}ukasiewicz logic{\textquoteright}s axiomatizability in terms of Pavelka type fuzzy logic, we propose a new axiomatizable linguistic truth-valued logic system based on LIA to place an important foundation for further establishing formal linguistic valued logic based approximate reasoning systems. This proposed logic system has a distinct advantage of handling incomparable linguistic terms in perception-based decision making processes.",

keywords = "Linguistic truth values, Decision making, Lattice implication algebra",

author = "Jun Liu and Yang Xu and Da Ruan and Jan Wagemans",

note = "Score = 3; 2010 - 9th International FLINS Conference on Foundations and Applications of Computational Intelligence ; Conference date: 02-08-2010 Through 04-08-2010",

year = "2010",

month = aug,

doi = "10.1142/9789814324700_0009",

language = "English",

isbn = "978-981-4324-69-4",

volume = "1",

series = "Computer Engineering and Information Science",

number = "4",

pages = "72--78",

booktitle = "Computational Intelligence -- Foundations and Applications",

}

Liu, J, Xu, Y, Ruan, D & Wagemans, J 2010, An axiomatizable lattice-ordered linguistic truth-valued logic. in Computational Intelligence -- Foundations and Applications. vol. 1, Computer Engineering and Information Science, no. 4, Singapore, Singapore, pp. 72-78, 2010 - 9th International FLINS Conference on Foundations and Applications of Computational Intelligence, Chengdu, China, 2010-08-02. https://doi.org/10.1142/9789814324700_0009

TY - GEN

T1 - An axiomatizable lattice-ordered linguistic truth-valued logic

AU - Liu, Jun

AU - Xu, Yang

AU - Ruan, Da

A2 - Wagemans, Jan

N1 - Conference code: FLINS 2010

PY - 2010/8

Y1 - 2010/8

N2 - Investigations on an algebraic structure of linguistic truth values in decision making and social science applications still lack a formalism for development of strict linguistic truth-valued logic system and its approximate reasoning scheme in practice. To attain this goal we characterize and construct the structure of linguistic value sets in natural language by a lattice-valued algebra structure - lattice implication algebra (LIA), where Łukasiewicz implication algebra, as a special case of LIA, plays a substantial role. By using Łukasiewicz logic’s axiomatizability in terms of Pavelka type fuzzy logic, we propose a new axiomatizable linguistic truth-valued logic system based on LIA to place an important foundation for further establishing formal linguistic valued logic based approximate reasoning systems. This proposed logic system has a distinct advantage of handling incomparable linguistic terms in perception-based decision making processes.

AB - Investigations on an algebraic structure of linguistic truth values in decision making and social science applications still lack a formalism for development of strict linguistic truth-valued logic system and its approximate reasoning scheme in practice. To attain this goal we characterize and construct the structure of linguistic value sets in natural language by a lattice-valued algebra structure - lattice implication algebra (LIA), where Łukasiewicz implication algebra, as a special case of LIA, plays a substantial role. By using Łukasiewicz logic’s axiomatizability in terms of Pavelka type fuzzy logic, we propose a new axiomatizable linguistic truth-valued logic system based on LIA to place an important foundation for further establishing formal linguistic valued logic based approximate reasoning systems. This proposed logic system has a distinct advantage of handling incomparable linguistic terms in perception-based decision making processes.

KW - Linguistic truth values

KW - Decision making

KW - Lattice implication algebra

UR - http://ecm.sckcen.be/OTCS/llisapi.dll/open/ezp_109450

UR - http://ecm.sckcen.be/OTCS/llisapi.dll/open/ezp_109450_2

UR - http://ecm.sckcen.be/OTCS/llisapi.dll/open/ezp_109450_3

UR - http://knowledgecentre.sckcen.be/so2/bibref/7413

U2 - 10.1142/9789814324700_0009

DO - 10.1142/9789814324700_0009

M3 - In-proceedings paper

SN - 978-981-4324-69-4

VL - 1

T3 - Computer Engineering and Information Science

SP - 72

EP - 78

BT - Computational Intelligence -- Foundations and Applications

CY - Singapore, Singapore

T2 - 2010 - 9th International FLINS Conference on Foundations and Applications of Computational Intelligence

Y2 - 2 August 2010 through 4 August 2010

ER -