On an algebra of linguistic truth-valued intuitionistic lattice-valued logic

Authors:
Li Zou;Peng Shi;Zheng Pei;Yang Xu
Affiliations:
School of Computer and Information Technology, Liaoning Normal University, Dalian, P.R. China;School of Electrical and Electronic Engineering, The University of Adelaide, SA, Australia and School of Engineering and Science, Victoria University, Melbourne, VIC, Australia;School of Mathematics and Computer Engineering, Xihua University, Chengdu, China;Center of Intelligent Control and Development, Southwest Jiaotong University, Chengdu, P.R. China
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology - Recent Advances in Soft Computing: Theories and Applications
Year:
2013

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Abstract

In this paper, we propose a kind of linguistic truth-valued intuitionistic fuzzy lattice based on the point view of intuitionistic fuzzy set and linguistic truth-valued lattice implication algebra. As an algebra fundament of linguistic truth-valued intuitionistic fuzzy logic, some properties of linguistic truth-valued intuitionistic fuzzy algebra are discussed. The results show that linguistic truth-valued intuitionistic fuzzy lattice is a residual lattice, but it is not MTL-algebra, R0-algebra, BL-algebra, MV-algebra and quasi lattice implication algebra.