直觉模糊软半环的直觉模糊软理想
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摘要
【目的】通过对半环的研究,使之更好地应用于信息科学等领域。【方法】引入了直觉模糊软半环和直觉模糊软半环的直觉模糊软理想的概念,进行了一系列讨论。【结果】在充分利用各自理论优势的基础上,得到了直觉模糊软半环的直觉模糊软理想的诸多性质。【结论】对进一步研究半环这一重要代数结构有着积极的意义。
[Purposes]In order to study semiring better,and make it better used in information science and other fields.[Methods]The concept of intuitionistic fuzzy soft set is applied to semirings and introduce some new notions:intuitionistic fuzzy soft semiring,intuitionistic fuzzy soft ideal over a semiring,etc.[Findings]Based on the advantage of these theory,it investigates properties of these concepts.[Conclusions]All this work is important to further study algebraic structure of semirings.
[Purposes]In order to study semiring better,and make it better used in information science and other fields.[Methods]The concept of intuitionistic fuzzy soft set is applied to semirings and introduce some new notions:intuitionistic fuzzy soft semiring,intuitionistic fuzzy soft ideal over a semiring,etc.[Findings]Based on the advantage of these theory,it investigates properties of these concepts.[Conclusions]All this work is important to further study algebraic structure of semirings.
引文
[1]MOLODTSOV D.Soft set theory-first results[J].Computers and Mathematics with Applications,1999,37(4/5):19-31.
[2]ATANASSOV K T.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986(20):87-96.
[3]MAJI P K,BISWAS R,ROY A R.Intuitionistic fuzzy soft sets[J].Journal of Fuzzy Mathematics,2001,9(3):677-692.
[4]ATANASSOV K T.Remarks on the intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1995,75(3):401-402.
[5]AKRAM M,DUDEK W A.Intuitionistic fuzzy left k-ideals of semirings[J].Soft Computing,2008,12(9):881-890.
[6]ARAS C G,BAYRAMOV S.Intuitionistic fuzzy soft modules[J].Computers and Mathematics with Applications,2011,62(6):2480-2486.
[7]ZHOU J H,LI Y W,YIN Y Q.Intuitionistic fuzzy soft semigroups[J].Mathematica Aeterna,2011,3:173-183.
[8]SELVACHANDRAN G,MAJI P K,FAISAL R Q.Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets[J].Applied Intelligence,2017,46(152):1-16.
[9]LIU Y Y,LUO J F,WANG B.A theoretical development on the entropy of interval-valued intuitionistic fuzzy soft sets based on the distance measure[J].International Journal of Computational Intelligence Systems,2017,10:569-592.
[10]SHAHZADI S,AKRAM M.Intuitionistic fuzzy soft graphs with applications[J].Journal of Applied Mathematics and Computing,2016,52(1):1-24.
[11]AKRAM M,SHAHZADI S.Novel intuitionistic fuzzy soft multiple-attribute decision-making methods[J].Neural Computing and Applications,2016,27(1):1-13.
[12]GOLAN J S.Semiring and Their applications[M].Dordrecht:Kluwer,1999.
[2]ATANASSOV K T.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986(20):87-96.
[3]MAJI P K,BISWAS R,ROY A R.Intuitionistic fuzzy soft sets[J].Journal of Fuzzy Mathematics,2001,9(3):677-692.
[4]ATANASSOV K T.Remarks on the intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1995,75(3):401-402.
[5]AKRAM M,DUDEK W A.Intuitionistic fuzzy left k-ideals of semirings[J].Soft Computing,2008,12(9):881-890.
[6]ARAS C G,BAYRAMOV S.Intuitionistic fuzzy soft modules[J].Computers and Mathematics with Applications,2011,62(6):2480-2486.
[7]ZHOU J H,LI Y W,YIN Y Q.Intuitionistic fuzzy soft semigroups[J].Mathematica Aeterna,2011,3:173-183.
[8]SELVACHANDRAN G,MAJI P K,FAISAL R Q.Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets[J].Applied Intelligence,2017,46(152):1-16.
[9]LIU Y Y,LUO J F,WANG B.A theoretical development on the entropy of interval-valued intuitionistic fuzzy soft sets based on the distance measure[J].International Journal of Computational Intelligence Systems,2017,10:569-592.
[10]SHAHZADI S,AKRAM M.Intuitionistic fuzzy soft graphs with applications[J].Journal of Applied Mathematics and Computing,2016,52(1):1-24.
[11]AKRAM M,SHAHZADI S.Novel intuitionistic fuzzy soft multiple-attribute decision-making methods[J].Neural Computing and Applications,2016,27(1):1-13.
[12]GOLAN J S.Semiring and Their applications[M].Dordrecht:Kluwer,1999.