Interval-valued fuzzy quasi-ideals and bi-ideals of semirings

Abstract. The interval-valued prime fuzzy ideals (in brevity, the iv. prime fuzzy ideals) of a semigroup have been recently studied by Kar, Sarkar and Shum [18]. As a continued study of i-v fuzzy ideals, we are going to investigate the properties of i-v fuzzy quasi-ideal and i-v fuzzy bi-ideal of a semiring and then we characterize the regularity and intra-regularity of a semiring in terms of the above i-v fuzzy ideals.

[1]  Anjan Mukherjee,et al.  Interval-valued intuitionistic fuzzy soft rough sets , 2015 .

[2]  G. Röst,et al.  Acta Sci. Math. (Szeged) , 2014 .

[3]  T. K. Dutta,et al.  Interval-valued fuzzy k-ideals and k-regularity of semirings , 2013 .

[4]  K. Shum,et al.  Interval-valued prime fuzzy ideals of semigroups , 2013 .

[5]  T. K. Dutta,et al.  On Interval-Valued Fuzzy Prime Ideals of a Semiring , 2012 .

[6]  J. Ahsan,et al.  Fuzzy Semirings with Applications to Automata Theory , 2012 .

[7]  Sukhendu Kar,et al.  Fuzzy quasi-ideals and fuzzy bi-ideals of ternary semigroups , 2012 .

[8]  P. Sarkar,et al.  Interval-valued fuzzy completely regular subsemigroups of semigroups , 2012 .

[9]  I. Chon.  ON FUZZY BI-IDEALS IN SEMIGROUPS , 2011 .

[10]  Yunqiang Yin,et al.  Interval Valued Fuzzy h-Ideals of Hemirings , 2010 .

[11]  M. Mathematical,et al.  GENERALIZED FUZZY K-IDEALS OF SEMIRINGS WITH INTERVAL VALUED MEMBERSHIP FUNCTIONS , 2009 .

[12]  K. H. Dar,et al.  Interval-valued intuitionistic fuzzy ideals of K-algebras , 2008 .

[13]  C. Park,et al.  Interval Valued ( ∈ , ∈ ∨ q )-Fuzzy Ideal in Rings , 2008 .

[14]  B. Davaz.  FUZZY IDEALS OF NEAR-RINGS WITH INTERVAL VALUED MEMBERSHIP FUNCTIONS , 2001 .

[15]  J. Golan.  Semirings and their applications , 1999 .

[16]  K. Saifullah,et al.  Fuzzy semirings , 1993 .

[17]  Ivor Grattan-Guinness,et al.  Fuzzy Membership Mapped onto Intervals and Many-Valued Quantities , 1976, Math. Log. Q..

[18]  L. A. ZADEH,et al.  The concept of a linguistic variable and its application to approximate reasoning - I , 1975, Inf. Sci..