Fuzzy subsemigroups and fuzzy ideals with operators in semigroups
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Given a set $\Omega$, the notion of an $\Omega$-fuzzy subsemigroup in semigroups is given. Using Fuzzy subsemigroups, an $\Omega$-fuzzy subsemigroup is described. Conversely, a fuzzy subsemigroup is constructed by using an $\Omega$-fuzzy semigroup. How the homorphic images and inverse images of $\Omega$-fuzzy subsemigroups become $\Omega$-fuzzy subsemigroups is stated. The notion of an $\Omega$-fuzzy left (right) ideal ( an $\Omega$-fuzzy bi-ideal, an $\Omega$-fuzzy interior ideal) generated by an $\Omega$-fuzzy set in semigroups is introduced. The depictions of them are examined.
Abstract
Given a set $\Omega$, the notion of an $\Omega$-fuzzy subsemigroup in semigroups is given. Using Fuzzy subsemigroups, an $\Omega$-fuzzy subsemigroup is described. Conversely, a fuzzy subsemigroup is constructed by using an $\Omega$-fuzzy semigroup. How the homorphic images and inverse images of $\Omega$-fuzzy subsemigroups become $\Omega$-fuzzy subsemigroups is stated. The notion of an $\Omega$-fuzzy left (right) ideal ( an $\Omega$-fuzzy bi-ideal, an $\Omega$-fuzzy interior ideal) generated by an $\Omega$-fuzzy set in semigroups is introduced. The depictions of them are examined.
참고문헌 (10)
- S. M. Hong, "Fuzzy interior ideals in semigroups", Indian J. Pure Appl. Math, 26, pp.859~863 (1995)
- N. Kuroki, "Fuzzy semiprime ideals in semigroups", Fuzzy Sets and Systems, 8, pp.71~79 (1982)
- N. Kuroki, "On fuzzy semigroups", Inform. Sci, 53, pp.203~236 (1991)
- N. Kuroki, "Fuzzy generalized bi-ideals in semigroups", Inform. Sci, 66, pp.235~243 (1992)
- S. Lajos, "A note on semilattice of groups", Acta. Sci. Math, 33, pp.315~317 (1972)
- S. Lajos, "Algebraic Theory of Semigroups", pp.335~340 (1979), North-Holland
- Z. W. Mo, "On pointwise depiction of fuzzy regularity of semigroups", Inform. Sci, 74, pp.265~274 (1993)
- M. Petrich, "Introduction to Semigroups" (1973), Columbus
- M. A. Samhan, "Fuzzy congruences on semigroups", Inform. Sci, 74, pp.165~175 (1993)
- X. P. Wang, "Fuzzy regular subsemigroups in semigroups", Inform. Sci, 68, pp.225~231 (1993)