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

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.

[1]  Zheng Pei,et al.  Extracting complex linguistic data summaries from personnel database via simple linguistic aggregations , 2009, Inf. Sci..

[2]  Francisco Herrera,et al.  The 2-Tuple Linguistic Computational Model. Advantages of Its Linguistic Description, Accuracy and Consistency , 2001, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[3]  Chris Cornelis,et al.  On the representation of intuitionistic fuzzy t-norms and t-conorms , 2004, IEEE Transactions on Fuzzy Systems.

[4]  Nguyen Cat Ho,et al.  A topological completion of refined hedge algebras and a model of fuzziness of linguistic terms and hedges , 2007, Fuzzy Sets Syst..

[5]  Zheng Pei,et al.  The Algebraic Properties of Linguistic Value "Truth" and Its Reasoning , 2007, IFSA.

[6]  Zheng Pei,et al.  Linguistic Values Based Intelligent Information Processing: Theory, Methods and Applications , 2010 .

[7]  Francisco Herrera,et al.  Computing with words in decision making: foundations, trends and prospects , 2009, Fuzzy Optim. Decis. Mak..

[8]  Da Ruan,et al.  A linguistic truth-valued reasoning approach in decision making with incomparable information , 2008, J. Intell. Fuzzy Syst..

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

[10]  Nguyen Cat Ho,et al.  Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm , 2022 .

[11]  Zeshui Xu,et al.  Intuitionistic Fuzzy Aggregation Operators , 2007, IEEE Transactions on Fuzzy Systems.

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

[13]  Didier Dubois,et al.  Terminological difficulties in fuzzy set theory - The case of "Intuitionistic Fuzzy Sets" , 2005, Fuzzy Sets Syst..

[14]  Krassimir T. Atanassov,et al.  Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade's paper "Terminological difficulties in fuzzy set theory - the case of "Intuitionistic Fuzzy Sets" , 2005, Fuzzy Sets Syst..

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

[16]  Francisco Herrera,et al.  A linguistic decision model for personnel management solved with a linguistic biobjective genetic algorithm , 2001, Fuzzy Sets Syst..

[17]  Francisco Herrera,et al.  Computing with Words in Decision support Systems: An overview on Models and Applications , 2010, Int. J. Comput. Intell. Syst..

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

[19]  Lluis Godo,et al.  Monoidal t-norm based logic: towards a logic for left-continuous t-norms , 2001, Fuzzy Sets Syst..

[20]  I. Turksen.  Meta-linguistic axioms as a foundation for computing with words , 2007 .

[21]  Etienne E. Kerre,et al.  On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision , 2007, Inf. Sci..

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

[23]  Zeshui Xu,et al.  Clustering algorithm for intuitionistic fuzzy sets , 2008, Inf. Sci..

[24]  Xin Liu,et al.  A uniform approach of linguistic truth values in sensor evaluation , 2008, Fuzzy Optim. Decis. Mak..

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

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

[27]  Zheng Pei,et al.  A Linguistic-Valued Lattice Implication Algebra Approach for Risk Analysis , 2011, J. Multiple Valued Log. Soft Comput..