Intuitionific Fuzzy Relation And Its Application

Content: In this paper, the definition of intuitionific fuzzy relation equation wasproposed on the basis of theory of fuzzy relation equation. Intuitionific fuzzy relationequation is a L-fuzzy relation equation. In this paper, the method with specialsignificance is obtained as the lattice is embodied, the necessary condition and thesufficient and necessary condition for intuitionific fuzzy relation equation to has asolution are obtained, the maximal solution of intuitionific fuzzy relation equation isresearch, the method for the sets of all solution of intuitionific fuzzy relation equationis given. The relation between intuitionific fuzzy subgroups and intuitionific fuzzysimilarity is research, and some significative results was obtained. The main resultsobtained are as follows:1. On the foundation of reading some papers of fuzzy relation equation, in thesecond chapter, we embody the lattice of L of L-fuzzy relation equation and inquiresystematically the intuitionific fuzzy relation equation. First, we analysis the characterof intuitionific fuzzy relation equation and the necessary condition for the equation tohas a solution is given, we get a lemma. The lemma is ready for proving the sufficientand necessary condition. We find that (?)·R=S is the sufficient and necessarycondition for the intuitionific fuzzy relation equation of X·R=S (R∈IFR(V×W),S∈IFR(U×W)) to has a solution, the (?) is the maximal solution of the equation.Second, we research the intuitionific fuzzy relation equation on the finite setssystematically. For the equation to has a solution, we give the form of representationof the necessary condition and the sufficient and necessary condition.the method forthe maximal solution and the sets of all solution of the equation is given.2. In chapter 3, first, by generalizing the relation between fuzzy subgroups andfuzzy similarity, we obtained some significative result: any intuitionific fuzzysubgroups of transformative group on the set S can determine a intuitionific fuzzysimilarity on the set S. on the other hand, any intuitionific fuzzy similarity on the setS can determine a intuitionific fuzzy subgroups of transformative group on the setS. second, by generalizing the relation between similarity and pseudo metric, we getthe relation between intuitionific fuzzy similarity and pseudo metric. Assume thatd:S×S→[0,1] is a map and that R(x,y)=(1-d(x,y) d(x,y)),(?)x,y∈S, thenthat R is a intuitionific fuzzy similarity is a sufficient and necessary condition for d is a pseudo metric on S. finally, we get the relation between intuitionific fuzzysubgroups and pseudo metric: any intuitionific fuzzy subgroups of transformativegroup on the set S can determine a super-pseudo metric; on the other hand, anysuper-pseudo metric can determine a intuitionific fuzzy subgroups of transformativegroup on the set S.