Contents

Preface

Chapter 1 Introduction.

 1.1 Hemirings

 1.2 Fuzzy sets

 1.3 Rough sets

 1.4 Soft sets

Chapter 2 Fuzzy h-ideals.

 2.1 Fuzzy h-ideals

 2.2 Fuzzy h-bi-(h-quasi-， h-interior) ideals

 2.3 (∈， ∈∨q)-fuzzy h-ideals

 2.4 (∈， ∈∨q)-fuzzy h-bi-(h-quasi-， h-interior) ideals

 2.5 (∈γ， ∈γ ∨qδ)-fuzzy h-ideals

 2.6 (∈γ， ∈γ ∨qδ)-fuzzy h-bi-(h-quasi-， h-interior) ideals

Chapter 3 Hemirings via (∈γ， ∈γ ∨qδ)-fuzzy h-ideals

 3.1 h-hemiregular hemirings via (∈γ， ∈γ ∨qδ)-fuzzy h-ideals

 3.2 h-intra-hemiregular hemirings via (∈γ， ∈γ∨qδ)-fuzzy h-ideals

 3.3 h-quasi-hemiregular hemirings via (∈γ， ∈γ∨qδ)-fuzzy h-ideals

 3.4 h-semisimple hemirings via (∈γ， ∈γ∨qδ)-fuzzy h-ideals

Chapter 4 Fuzzy soft hemirings

 4.1 Soft hemirings

 4.2 h-(h-bi-， h-quasi-， h-interior) idealistic soft hemirings

 4.3 Four kinds of hemirings by soft h-idealistic ideals

 4.4 (∈γ， ∈γ∨qδ)-fuzzy soft h-(h-bi-， h-quasi-， h-interior) ideals

 4.5 Four kinds of hemirings by (∈r， ∈r ∨ qδ)-fuzzy soft h-ideals

Chapter 5 (M，N)-SI-hemirings

 5.1 (M，N)-SI-hemirings

 5.2 (M，N)-SI-h-ideals

 5.3 (M，N)-SI-h-bi-(h-quasi-) ideals

Chapter 6 (M，N)-SU-hemirings.

 6.1 (M，N)-SU-h-hemirings.

 6.2 (M，N)-SU-h-ideals.

 6.3 (M，N)-SU-h-bi-(h-quasi-) ideals

Chapter 7 Hemirings via (M，N)-SI-h-ideals

 7.1 h-hemiregular hemirings via (M，N)-SI-h-ideals.

 7.2 h-intra-hemiregular hemirings via (M，N)-SI-h-ideals

 7.3 h-quasi-hemiregular hemirings via (M，N)-SI-h-ideals

Chapter 8 Hemirings via (M，N)-SU-h-ideals

 8.1 h-hemiregular hemirings via (M，N)-SU-h-ideals

 8.2 h-intra-hemiregular hemirings via (M，N)-SU-h-ideals

Chapter 9 Rough soft hemirings

 9.1 Fuzzy congruences and fuzzy strong h-ideals

 9.2 Rough fuzzy (fuzzy rough) strong h-ideals

 9.3 Rough soft hemirings

References.

Index

詹建明编著的《半环的不确定性理想理论(英文版)》介绍了，Semirings which are regarded as a generalization of rings have been found usefulin solving problems in different disciplines of applied mathematics and informationsciences because a semiring provides an algebraic framework for modelling. By ahemiring, we mean a special semiring with a zero and with a commutative addition.In applications, hemirings are useful in automata and formal languages. Many as-pects of the theory of matrices and determinants over semirings have been studiedby Beasley et al. in [36], [37], [315], and others. In this book, we attempt to obtain some analogues ring theo-rems for semirings. Indeed, many results in rings apparently do not have analogousresults in semirings if we only consider their ideals.