Comprehensive Interval-Induced Weights Allocation with Bipolar Preference in Multi-Criteria Evaluation

Xu Jin,Radko Mesiar,Ronald R Yager,Surajit Borkotokey,Lesheng Jin

doi:10.3390/math9162002

Abstract

Preferences-involved evaluation and decision making are the main research subjects in Yager’s decision theory. When the involved bipolar preferences are concerned with interval information, some induced weights allocation and aggregation methods should be reanalyzed and redesigned. This work considers the multi-criteria evaluation situation in which originally only the interval-valued absolute importance of each criterion is available. Firstly, based on interval-valued importance, upper bounds, lower bounds, and the mean points of each, we used the basic unit monotonic function-based bipolar preference weights allocation method four times to generate weight vectors. A comprehensive weighting mechanism is proposed after considering the normalization of the given absolute importance information. The bipolar optimism–pessimism preference-based weights allocation will also be applied according to the magnitudes of entries of any given interval input vector. A similar comprehensive weighting mechanism is still performed. With the obtained weight vector for criteria, we adopt the weighted ordered weighted averaging allocation on a convex poset to organically consider both two types of interval-inducing information and propose a further comprehensive weights allocation mechanism. The detailed comprehensive evaluation procedures with a numerical example for education are presented to show that the proposed models are feasible and useful in interval, multi-criteria, and bipolar preferences-involved decisional environments.

Highlights

As a typical multi-criteria evaluation problem, when several different criteria are involved, some normalized weight vectors can be assigned to those criteria, presenting the relative importance between different criteria
There are some classical methods to determine this type of weight vector, including the subjective weighting method or Analytic Hierarchy Process (AHP) method [17]
When the inducing interval vector [u, v] = [a, b], the induced ordered weighted averaging (IOWA) defined in Equation (6) is called the interval-ordered weight averaging (IvOWA) operator IvOWAw : I n → I with the BUM function Q : [0, 1] → [0, 1]

Summary

Introduction

Information fusion theories and techniques are important in numerous comprehensive evaluation problems [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24] in which multiple criteria or data sources should be considered rather than a single one. With some given inducing of the vector which is real-valued, we may use the IOWA weighting method to derive some suitable weight vectors for a collection of criteria (or a group of experts, etc.). This method can only embody a single type of weighting style. The bipolar optimism–pessimism preference should be embodied in the interval itself; that is, with more optimism, a higher value in that interval is more preferred and vice versa To solve these problems, this work will apply some newly proposed techniques and propose some integrated preference-involved models to appropriately embody all such concerns.

Bipolar Preferences-Involved Aggregations and Related Weight Allocations

Adjusted Weights with the Optimism–Pessimism Preference under Known Weights

Conclusions