Inevitability Theory Of Fuzzy Numbers, Sorting And Its Applications

This　paper　has　four　chapters　.The　emphasis　in　the　first　chapter　is　mainly　on　possibility　theory　,fuzzy　numbers,fuzzy　bases　and　fuzzy　interpolation.　The　main　results　in　this　chapter　are　well-known.　For　this　reason,　this　chapter　can　be　omitted　by　the　readers　who　are　familiar　with　the　basic　concepts　and　theories　of　them.　The　main　b ody　has　three　parts,　namely　the　second,　the　third　and　the　fourth　chapter.　In　chapter　two,　first,　we　have　put　forward　the　concept　of　necessity　measure　on　the　basis　of　possibility　theory.　Second,　we　have　put　forward　the　concept　of　fuzzy　infintegral,　proved　the　function　is　fuzzy　infintegral　if　and　only　if　it　is　fuzzy　supintegral,　then　put　forward　the　concept　and　the　characters　of　the　fuzzy　integral.　Third,　we　have　proved　the　necessity　measure　leaded　by　fuzzy　variable　ξ　is　equal　to　which　leaded　by　Π_ξ.　So　we　call　the　two　kind　of　necessity　measure　normal　necessity　measure.　Therefore　the　possibility　theory　is　made　better.　In　the　third　chapter,　sequencing　problem　can　be　solved　to　a　certain　extent,　by　introducing　several　methods　to　rank　fuzzy　numbers.　A　special　class　of　fuzzy　bases　,　called　subfuzzy　bases　,have　introduced　in　chapter　four　,and　we　have　considered　the　characters　of　subfuzzy　bases　and　fuzzy　interpolation　.We　have　shown　that　the　nonlinear　programming　problems　can　be　simplied　by　means　of　fuzzy　interpolation.