The Approximation To Two Fuzzy Concept Extesion

Intreval-valued fuzzy sets(IVFS for short)and Both-branch fuzzy sets (BBFS for short)are two extensions of traditional fuzzy sets. For IVFS, because an IVFS provides more choices for the attribute description of an object and has stronger ability to express uncertainty than an ordinary fuzzy set, it has gained extensive attentsion from the academic circles and the circles of engineering and technology. For presentation of BBFS, it solves some problem which can't be solved in engineering decisin and engneering control.The original definition of "factor space" was proposed by Peizhuang Wang in 1981, factor space theory presents a general frame for the representation of concepts, this paper studies the approximation to two fuzzy concept (intervalvalued fuzzy concept, Both-branch fuzzy concept)extension in factor space, this paper contains mainly four parts:The first part discusses mainly three basical theorem of the ordinary fuzzy sets, present three new decomposition theorem and proof accordingly. There are three new representation theorem and three new equivalence definitions of extension principle, give a new extension principle of ordinary fuzzy sets.The second part studies extension priniples of interval-valued fuzzy sets and some properties of extension theorem. Firstly, present four different types of entension principle of interval-valued fuzzy sets:max-max extension principle, min-min extension principle, min-max extension principle, max-min extension principle.Then, discuss equivalence definitions of max-max extension principle and prove some properties of entension principles.The third part studies mainly the approximate to interval-valued fuzzy concept extension. Present four kinds of representation extension of interval-valued fuzzy concept, based on them, four types of feedback extensions are proposed, some important properties of four types of feedback extension and representation extension are obtained. Also, four envelopes are introduced, lastly, analyze the application area of every envelope by use of approach degree formula.The four part discusses mainly extension principles of Both-branch fuzzy sets and the approximate to Both-branch fuzzy concept extension, give four different types of extension principle of Both-branch fuzzy sets, Present four kinds of representation extension of Both-branch fuzzy concept, based on them, four type of feedback extensions are proposed, some important properties of four type of feedback extension are obtained. Also, four envelopes are introduced,lastly, the application area of every envelope is shown.