#### Abstract

This paper has explored theoretical methods of evaluation in the identification of the boundedness of the generalized fuzzy gamma ideals. A functional approach was used to undertake a characterization of this structure leading to a determination of some interesting gamma hemirings theoretic properties of the generated structures. Gamma hemirings are the generalization of the classical agebraic structure of hemirings. Our aim is to extend this idea and, to introduce the concept of generalized fuzzy gamma ideals, generalized fuzzy prime (semiprime) gamma ideals, generalized fuzzy h -gamma ideals and generalized fuzzy k - gamma ideals of gamma hemirings and related properties are investigated. We have shown that intersection of any family of generalized fuzzy (left, right) h - gamma ideals (k-gamma ideals) of a hemiring is a generalized fuzzy (left, right) h -gamma ideal (k-gamma ideal) of H. Similarly we proved that the intersection of any family of generalized fuzzy prime (resp. semiprime) gamma ideals of H is a generalized fuzzy prime (resp. semiprime) gamma ideal of H. We have proved that a fuzzy subset μ of H is fuzzy h -gamma ideal (k-gamma ideal) if and only if μ is a generalized fuzzy h -gamma ideal (k-gamma ideal) of H. Further level cuts provide a useful linkage betwean the classical set theorey and the fuzzy set theorey. Here we use this linkage to investigate some useful aspects of gamma hemirings and characterize the gamma hemmirings through level cuts in terms of generalized fuzzy (left, right, prime, semiprime) gamma ideals of gamma hemirings. We have also used the concept of support of a fuzzy set in order to obtain some interesting results of gamma hemirings using the generalized fuzzy (left, right, prime, semiprime) gamma ideals of hemirings.

#### Recommended Citation

Gulistan, Muhammad; Shahzad, Muhammad; Ahmed, Sarfraz; and Ilyas, Mehwish
(2015).
Characterization of Gamma Hemirings by Generalized Fuzzy Gamma Ideals,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 10,
Iss.
1, Article 29.

Available at:
https://digitalcommons.pvamu.edu/aam/vol10/iss1/29