Grey relational fractional programming and cross-evaluating method for multi-attribute decision making problem in spherical fuzzy setting

Abstract

To apply the spherical fuzzy sets(SFSs) for multiple attribute decision making (MCDM) problems have the more realistic significance, because of  the assessment data specified by experts are mostly fuzzy and uncertain, the uncertainty and vagueness, ambiguity and subjectivity of the information in an intricate decision making environment, In this paper, a method to acquire attribute weights of interval number form by using the maximization method  of the grey relational relative closeness degree in SFSs circumstance is proposed. To obtain the upper bound and lower bound of relative closeness degree, two fractional programming models are suggested. Possibility matrix is obtained by using the possibility degree of interval numbers, the optimal membership degrees from possibility matrix is obtained.  The decision making method by the optimal membership degrees is proposed. To demonstrate the effectiveness and feasibility of proposed method an illustrate example is presented.