Theories And Methods Of Decision Making With Preference Relations Based On Multiplicative Consistency

Decision-making problems are commonlycharacterized by multiple decision objectives,dynamic time and uncertainty of decision state,which results in the fact that more and more uncertain information isinvolved in these problems.Intervals and triangular fuzzy numbers,which are two kinds of special fuzzy sets,are more suitable todescribe human thinking and uncertain information in real-life decision-making problems.This paper mainly discusses theories and applications of three types of preference relations based on multiplicative consistency: interval mulplicative preference relations(IMPRs),interval-valued fuzzy preference relations(IVFPRs)and triangular mulplicative preference relations(TMPRs).In what follows,five main contributions are given.(1)The IMPR is a kind of preference relations by combining intervals with mulplicative preference relations.Fristly,this paper analyses the characterics of geometrical consistency of IMPRs and proposes the geometrically logarithmic compatibility degree of two IMPRs.Then,a geometrically logarithmic consistency index of IMPRs is presented.To minimize the geometrically logarithmic compatibility degree of each individual IMPR and the collective IMPR,a convex programming model is built to determine the experts' weights.Lastly,an individual decision-making method with an IMPR and a group decision-making method with IMPRs are proposed.(2)After analyzing the shortcomings of some existing possibility degree of intervals,a new possibility degree of intervals is proposed.Based on the new possibility degree of intervals,a new admissible order of intervals is defined and used to compare a series of intervals.Based on the multiplicative consistency definition of IMPRs,a new consistency index of IMPRs is proposed.By means of simulation experiments,thresholds of the new consistency index are provided.For group decision making with IMPRs,a group consensus index is defined.An interactively convergent iterative algorithm is designed to improve the group consensus.(3)By analyzing the shortcomings of some existing consistency definitions of IMPRs,we define a new consistency definition of IMPRs which satisfies two properities: invariance and robustness.Moreover,comparative analyses are conducted to reveal the relationships among five existing consistency definitions and this new consistency definition of IMPRs.Based on the new consistency definition of IMPRs,a new consistency index is introduced to measure the consistency degree of i IMPRs.An iterative algorithm is proposed to improve the consistency level of an inconsistent IMPR.Subsequently,a goal programming model is built to derive an interval priority vector from an acceptably consistent IMPR.Eventually,a new individual decision making method with an IMPR is put forward.Numerical examples and simulation analyses are conducted to illustrate the superiority and validity of the proposed individual decision-making method.(4)This paper mainly focuses on the multiplicative consistency analysis of IVFPRs.A new multiplicative consistency of IVFPRs is defined.This definition is proven to be robust and invariable to thecompared objects' labels.The concept of an acceptabe incomplete IVFPR s proposed.An algorithm is brought up to evaluate the missing elements of an acceptabe incomplete IVFPR.Based on the p-norm of vector,the total deviation of two complete IVFPRs is defined.By minimizing the total deviation of two complete IVFPRs,a programming model is built to determine an interval weight vector from a complete IVFPR.Then,a new decision-making method with an IVFPR is proposed.A line construction plan of a multinational drug company is used to validate the proposed decision-making method.To further show the effectiveness and advantages of the proposed decision-making method,a numerical example and simulation-based comparative analyses are provided.(5)The TMPR is an efficient technology,which can make experts to comfortably express their paired comparisons.Existing consistency definitions of TMPRs overlook experts' trust levels on their judgments.Considering experts' trust levels,this paper proposes a left and right(L-R)geometric consistency definition of TMPRs and develops a new group decision-making method.The L-R geometric mean of triangular fuzzy number is defined.Then,L-R geometric consistency of TMPRs is given combining experts' trust levels about their judgments.To improve the consistency,a programming model is constructed to derive an acceptably consistent TMPR from an unacceptably consistent one.Using the difference degree between two TMPRs,a new approach is presented to extract experts' weights.Two methods of individual decision-makingwith a TMPR and group decision-making with TMPRs are established.A simulation algorithm is devised to verify the superiority of the proposed individual decision-making with a TMPR.Simulation results reveal that the proposed individual decision-making method outperforms existing methods in logarithmic Hamming distance and difference degree.L-R geometric consistency makes contribution to TMPRs since it considers experts' trust levels and has reciprocity,invariance and robustness.Several real-life examples are furnished to explain the validity of two proposed decision-making methods.