On the Definition of Intuitionistic Fuzzy h-ideals of Hemirings
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Using the Lukasiewicz 3-valued implication operator, the notion of an (α,β)-intuitionistic fuzzy left ( right ) h-ideal of a hemiring is introduced, where α,β∈{∈,q,∈∧q,∈∨q}. We define intuitionistic fuzzy left ( right ) h-ideal with thresholds (s,t) of a hemiring R and investigate their various properties. We characterize intuitionistic fuzzy left ( right ) h-ideal with thresholds (s,t) and (α,β)-intuitionistic fuzzy left ( right ) h-ideal of a hemiring R by its level sets. We establish that an intuitionistic fuzzy set A of a hemiring R is a (∈,∈) (or (∈,∈∨q ) or (∈∧q,∈) )-intuitionistic fuzzy left ( right ) h-ideal of R if and only if A is an intuitionistic fuzzy left ( right ) h-ideal with thresholds (0,1) (or (0,0.5) or (0.5,1)) of R respectively. It is also shown that A is a (∈,∈) (or (∈,∈∨q ) or (∈∧q,∈) )-intuitionistic fuzzy left ( right ) h-ideal if and only if for any p∈(0,1] (or p∈(0,0.5] or p∈(0.5,1] ), Ap is a fuzzy left ( right ) h-ideal. Finally, we prove that an intuitionistic fuzzy set A of a hemiring R is an intuitionistic fuzzy left ( right ) h-ideal with thresholds (s,t) of R if and only if for any p∈(s,t], the cut set Ap is a fuzzy left ( right ) h-ideal of R.
Abstract
Using the Lukasiewicz 3-valued implication operator, the notion of an (α,β)-intuitionistic fuzzy left ( right ) h-ideal of a hemiring is introduced, where α,β∈{∈,q,∈∧q,∈∨q}. We define intuitionistic fuzzy left ( right ) h-ideal with thresholds (s,t) of a hemiring R and investigate their various properties. We characterize intuitionistic fuzzy left ( right ) h-ideal with thresholds (s,t) and (α,β)-intuitionistic fuzzy left ( right ) h-ideal of a hemiring R by its level sets. We establish that an intuitionistic fuzzy set A of a hemiring R is a (∈,∈) (or (∈,∈∨q ) or (∈∧q,∈) )-intuitionistic fuzzy left ( right ) h-ideal of R if and only if A is an intuitionistic fuzzy left ( right ) h-ideal with thresholds (0,1) (or (0,0.5) or (0.5,1)) of R respectively. It is also shown that A is a (∈,∈) (or (∈,∈∨q ) or (∈∧q,∈) )-intuitionistic fuzzy left ( right ) h-ideal if and only if for any p∈(0,1] (or p∈(0,0.5] or p∈(0.5,1] ), Ap is a fuzzy left ( right ) h-ideal. Finally, we prove that an intuitionistic fuzzy set A of a hemiring R is an intuitionistic fuzzy left ( right ) h-ideal with thresholds (s,t) of R if and only if for any p∈(s,t], the cut set Ap is a fuzzy left ( right ) h-ideal of R.
참고문헌 (24)
- K. T. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20, pp.87~96 (1986)
- K. T. Atanassov, "New operations defined over the intuitionistic fuzzy sets", Fuzzy Sets and Systems, 61, pp.137~142 (1994)
- K. T. Atanassov, "Intuitionistic fuzzy sets. Theory and applications" (1999), Physica-Verlag
- S. K. Bhakat, "On the definition of a fuzzy subgroup", Fuzzy Sets and Systems, 51, pp.235~241 (1992)
- S. K. Bhakat, "(2, 2 _q)-fuzzy subgroup", Sets and Systems, 80, pp.359~368 (1996)
- S. K. Bhakat, "Fuzzy subrings and ideals redefined", Fuzzy Sets and Systems, 81, pp.383~393 (1996)
- Y. Bin, "The normal intuitionistic fuzzy subgroups", Pro- ceedings of 2010 IEEE International Conference on Intelligent Computing and Intelligent Systems, pp.210~214 (2010)
- Y. Bin, "Intuitionistic fuzzy subrings and ideas", 2011 8th international Conference on Fuzzy Systems and Knowledge Discovery, 1, pp.300~305 (2011)
- B. Davvaz, "Generalized fuzzy Hv-submodules endowed with interval-valued membership functions", Information Sciences, 17, pp.3147~3157 (2008)
- B. Davvaz, "Redefined fuzzy Hv-submodules and many valued implications", Information Sciences, 177, pp.865~875 (2007)
- W. A. Dudek, "( , )- fuzzy ideal of hemirings, Computers and Mathematics with Applications", Computers and Mathematics with Applications, 58, pp.310~321 (2009)
- W. A. Dudek, "Special types of intuitionistic fuzzy left h-ideals of hemirings", Soft comput., 12, pp.359~365 (2008)
- W. A. Dudek, "Intuitionistic fuzzy h-ideals of hemirings", WSEAS Trans. Math., 12, pp.1315~1321 (2006)
- U. Hebisch, "Semirings, Algebraic Theory and Applications in the Computer Science" (1998), World Scientific
- H. Hossein, "Generalized fuzzy k-ideals of semirings with interval-valued membership functions", Bull. Malays. Math. Sci. Soc., 32(3) (2009)
- S. Jonathan, "Semirings and their applications" (1999), Kluwer Academic Publishers
- Y. B. Jun, "On fuzzy h-ideals in hemirings", Information Sciences, 162, pp.211~226 (2004)
- M. Kondo, "On the transfer principle in fuzzy theory", Mathware and Soft Computing, 12, pp.41~55 (2005)
- J. N. Mordeson, "Fuzzy commutative algebra" (1998), World scientific
- S. Rahman, "On the definition of Atanassov’s intuitionistic fuzzy subrings and ideals", Bull. Malays. Math. Sci. Soc.
- A. Rosenfeld, "Fuzzy groups", J. Math. Anal. Appl., 35, pp.512~517 (1971)
- X. H. Yuan, "On the definition of the intuitionistic fuzzy subgroups", Computers and Mathematics with Applications, 59, pp.3117~3129 (2010)
- X. H. Yuan, "The cut sets, decomposition theorems and representation theorems on intuitionistic fuzzy sets and interval-valued fuzzy sets", Science in China Series F: Information Sciences, 39, pp.933~945 (2009)
- L. A. Zadeh, "Fuzzy sets", Inform. Control, 8, pp.338~353 (1965)