Six-Element Linguistic Truth-Valued Intuitionistic Reasoning in Decision Making

A kind of intuitionistic 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 six-element linguistic truth-valued intuitionistic propositional logic system is established which can express both truth degree and falsity degree. The implication operation of linguistic truth-valued intuitionistic propositional logic can be deduced from four times implication of their truth values. Therefore, we can use more information in the process of reasoning and eventually improve the precision of reasoning. 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 linguistic information environment with both truth degree and falsity degree.

[1]  Jun Ma,et al.  Linguistic Truth-Valued Lattice Implication Algebra and Its Properties , 2006, The Proceedings of the Multiconference on "Computational Engineering in Systems Applications".

[2]  Abraham Kandel,et al.  Universal truth tables and normal forms , 1998, IEEE Trans. Fuzzy Syst..

[3]  Zheng Pei,et al.  LATTICE IMPLICATION ALGEBRA MODEL OF LINGUISTIC VARIABLE TRUTH AND ITS INFERENCE , 2004 .

[4]  Li Zou,et al.  A Kind of Resolution Method of Linguistic Truth-Valued Propositional Logic Based on LIA , 2007, Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD 2007).

[5]  Jerry M. Mendel,et al.  Centroid of a type-2 fuzzy set , 2001, Inf. Sci..

[6]  Etienne E. Kerre,et al.  alpha-Resolution principle based on lattice-valued propositional logic LP(X) , 2000, Inf. Sci..

[7]  Jun Ma,et al.  A framework of linguistic truth-valued propositional logic based on lattice implication algebra , 2006, 2006 IEEE International Conference on Granular Computing.

[8]  Yang Xu,et al.  Resolution Method of Linguistic Truth-valued Propositional Logic , 2005, 2005 International Conference on Neural Networks and Brain.

[9]  George Gargov,et al.  Elements of intuitionistic fuzzy logic. Part I , 1998, Fuzzy Sets Syst..

[10]  N. C. Ho,et al.  Hedge algebras: an algebraic approach to structure of sets of linguistic truth values , 1990 .

[11]  Jun Liu,et al.  On the consistency of rule bases based on lattice‐valued first‐order logic LF(X) , 2006, Int. J. Intell. Syst..

[12]  Jun Liu,et al.  Lattice-Valued Logic - An Alternative Approach to Treat Fuzziness and Incomparability , 2003, Studies in Fuzziness and Soft Computing.

[13]  N. C. Ho,et al.  Extended hedge algebras and their application to fuzzy logic , 1992 .

[14]  K. N. King.  2006 IEEE International Conference on Granular Computing , 2006, IEEE Comput. Intell. Mag..

[15]  Van-Nam Huynh,et al.  An algebraic approach to linguistic hedges in Zadeh's fuzzy logic , 2002, Fuzzy Sets Syst..

[16]  Yang Xu,et al.  On the consistency of rule bases based on lattice-valued first-order logic LF(X): Research Articles , 2006 .

[17]  Etienne E. Kerre,et al.  alpha-Resolution principle based on first-order lattice-valued logic LF(X) , 2001, Inf. Sci..

[18]  Ho C. Nguyen,et al.  Ordered structure-based semantics of linguistic terms of linguistic variables and approximate reasoning , 2001 .

[19]  Francisco Herrera,et al.  A fusion approach for managing multi-granularity linguistic term sets in decision making , 2000, Fuzzy Sets Syst..

[20]  Van-Nam Huynh,et al.  A parametric representation of linguistic hedges in Zadeh's fuzzy logic , 2002, Int. J. Approx. Reason..