Research On Multiple Attribute Group Decision-making Grey Target Method

Grey multi-attribute group decision-making is an important aspect of greydecision-making system, which is widely exist in management, economics, behavioralscience, and engineering. It is greatly significant to apply grey target decision methodto grey multi-attribute group decision-making in theory and applications. This paperresearch on problems of grey multiple attributes group decision-making with intervalgrey numbers, hybrid numbers, and risk form, and establishes grey target decisionmodel for each problem.This paper covers the following aspects:(1) For grey multi-attribute group decision-making, when attribute values areinterval grey numbers, attribute weight and decision makers’ weights are known, byunifying decision information of each decision makers, weighted group positive andnegative off-target distance for each scheme is calculated, then we can get groupoff-target deviation to evaluate each scheme.(2)For the case that attribute information, attribute weight and decision makersweights are interval grey numbers, based on the idea of “group decision-making resultshould be similar to ideal solution of each member”, combining grey targetdecision-making with group decision-making TOPSIS method, build up groupoff-target deviation matrix. The concept of group positive and negative target andgroup off-target deviation is proposed, and calculation method is given. Superiority ofeach scheme is measured by its group off-target deviation value.(3) Research on problem that attributes are made up of precise numbers, intervalnumbers and fuzzy numbers, while attribute weights are interval grey numbers, Thispaper comes up with a new attribute weighted method, multiply each attributeparameters with each weight parameters, reserved initial information by maximum. (4)This paper proposed distance formula for grey numbers with any amount ofparameters, and proved it. Then came to hybrid attribute vector’s off-target distancecalculating method, established hybrid off-target decision-making model.(5)Research on hybrid multiple attribute group decision-making problem, eachdecision makers’ preference is obtained by calculating comprehensive off-targetdistance of each scheme. Then standardization to eliminate the impact of differentevaluation standard among decision makers, by unifying decision information of eachdecision makers, and combining group off-target decision-making model, groupcomprehensive off-target distance is calculated to evaluate each scheme.(6) Grey multiple attribute group decision-making under risk problem that eachattribute with different natural states, while attribute values are interval grey numbers,is studied. The decision method based on expected off-target distance is proposed.Firstly, the risk positive and negative target is determined for each decision maker, theexpected distance between each attribute and risk positive and negative target iscalculated by the distance of each state. Then, the expected positive and negativeoff-target distance and expected off-target deviation for each scheme can be calculated.Then apply group TOPSIS method to group expected off-target deviation matrix,evaluate each scheme by calculating its group off-target deviation value. This paperutilize the way calculating distance under each state before calculating expecteddistance, comparing to the way replacing attribute value with expected value fordecision-making, more information of each state is revealed, the characteristics ofdecision-making under risk is reflected.This paper applies grey target decision method to solve the problems of groupdecision-making, establishes decision-making algorithm for it, enriched gray decisiontheory system.