Interval-valued intuitionistic fuzzy ideals of K-algebras

The notion of interval-valued intuitionistic fuzzy sets was first introduced by Atanassov and Gargov in 1989 as a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this paper we first apply the concept of interval-valued intuitionistic fuzzy sets to K-algebras. Then we introduce the notion of interval-valued intuitionistic fuzzy ideals (IIFIs, in short) of K-algebras and investigate some interesting properties. We characterize Artinian and Noetherian K-algebras by considering IIFIs of a K-algebra K: Characterization theorems of fully invariant and characteristic IIFIs are also discussed.

[1]  M. Akram.  Bifuzzy ideals of K-algebras , 2008 .

[2]  Glad Deschrijver,et al.  Arithmetic operators in interval-valued fuzzy set theory , 2007, Inf. Sci..

[3]  H. Kim,et al.  On K-algebras and BCI-algebras , 2007 .

[4]  K. H. Dar,et al.  On K-Homomorphisms of K-Algebras , 2007 .

[5]  K. H. Dar,et al.  Fuzzy ideals of K-algebras , 2007 .

[6]  Wieslaw A. Dudek,et al.  Intuitionistic fuzzy h-ideals of hemirings , 2006 .

[7]  K. H. Dar,et al.  On Subclasses of K(G)-algebras , 2006 .

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

[9]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU) - an outline , 2005, GrC.

[10]  Jie Meng,et al.  On fuzzy ideals in BCK/BCI-algebras , 2005, Fuzzy Sets Syst..

[11]  J. Bae.  ON (α, β)-FUZZY IDEALS OF BCK/BCI-ALGEBRAS , 2004 .

[12]  John N. Mordeson,et al.  Fuzzy Semigroups , 2003, Studies in Fuzziness and Soft Computing.

[13]  Etienne E. Kerre,et al.  On the relationship between some extensions of fuzzy set theory , 2003, Fuzzy Sets Syst..

[14]  D. Minchev,et al.  An intuitionistic fuzzy sets application in multiagent systems of metamorphic robotic systems , 2002, Proceedings First International IEEE Symposium Intelligent Systems.

[15]  Ranjit Biswas,et al.  An application of intuitionistic fuzzy sets in medical diagnosis , 2001, Fuzzy Sets Syst..

[16]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[17]  J. Manko,et al.  Bifuzzy probabilistic sets , 1995 .

[18]  R. Biswas.  Rosenfeld's fuzzy subgroups with interval-valued membership functions , 1994 .

[19]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[20]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[21]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[22]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[23]  K. Iseki.  An Algebra Related with a Propositional Calculus , 1966 .

[24]  Shotaro Tanaka.  On axiom systems of propositional calculi, XX , 1965 .

[25]  K. Iseki.  On B*-Algebras , 1953 .