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

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

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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",

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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

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