Abstract
This paper elaborates the different methods to generate normalized weight vector in multi-criteria decision-making where the given information of both criteria and inputs are uncertain and can be expressed by basic uncertain information. Some general weight allocation paradigms are proposed in view of their convenience in expression. In multi-criteria decision-making, the given importance for each considered criterion may have different extents of uncertainty. Accordingly, we propose some special induced weight-allocation methods. The inputs can be also associated with varying uncertainty extents, and then we develop several induced weight-generation methods for consideration. In addition, we present some suggested and prescriptive weight allocation rules and analyze their reasonability.
Highlights
The consideration of relative importance between the concerned criteria is of great significance in most of the various decision environments and decision theories, including bounded rationality [1], fuzzy group decision-making [2], order-based decision models [3], multi-criteria decision-making (MCDM) [4], non-additive-measure-based decisionmaking [5,6], preference involved decision-making [7], random and stochastic decisionmaking [8], and interactive decision-making [9], and the normalized weight function/vector serves as the very suitable embodiment of the relative importance
There are numerous methods to generate normalized weight function, such as the method considering the roles of eigen things in the analytic hierarchy process (AHP) [10] with a myriad of applications [11,12], and the method used in ordered weighted averaging (OWA) operator [13]
To determine a normalized weight function with certain inducing information, we will use the method originally proposed by Yager in the induced ordered weighted average (IOWA) operator [15,16]
Summary
The consideration of relative importance between the concerned criteria is of great significance in most of the various decision environments and decision theories, including bounded rationality [1], fuzzy group decision-making [2], order-based decision models [3], multi-criteria decision-making (MCDM) [4], non-additive-measure-based decisionmaking [5,6], preference involved decision-making [7], random and stochastic decisionmaking [8], and interactive decision-making [9], and the normalized weight function/vector serves as the very suitable embodiment of the relative importance. Note that in MCDM problems with BUI environment, there are many restrictions on the selections of the methods to merge different inducing information and make the problem more complex. Some theoretical advantages and contributions of this study lie in that it will make it clearer how to reasonably consider several different types of inducing information in MCDM problems and selectively merge some of them in order to generate desirable weight functions with bipolar preferences.
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