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A Consistency and Consensus-Based Goal Programming Method for Group Decision-Making With Interval-Valued

Zhiming Zhang, Witold Pedrycz

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|July 12, 2018

Summary

This summary is machine-generated.

This study introduces a novel consistency-based algorithm for group decision-making (GDM) using interval-valued intuitionistic multiplicative preference relations (IVIMPRs). The method enhances decision consistency and determines optimal weights for improved GDM outcomes.

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Area of Science:

Decision Sciences
Operations Research
Fuzzy Mathematics

Background:

Interval-valued intuitionistic multiplicative preference relations (IVIMPRs) offer a robust framework for handling uncertain preferences in decision-making.
Group decision-making (GDM) necessitates methods to reconcile diverse and potentially inconsistent judgments from multiple decision-makers (DMs).
Existing methods may lack sufficient mechanisms for ensuring and improving consistency within complex preference structures.

Purpose of the Study:

To develop a novel consistency-based algorithm for GDM problems utilizing IVIMPRs.
To introduce methods for evaluating and optimizing the consistency of intuitionistic multiplicative preference relations (IMPRs) and IVIMPRs.
To establish a framework for determining DM weights and aggregating preferences to achieve maximum consensus.

Main Methods:

Introduction of a consistency index and optimization approach for IMPRs.
Development of consistency definitions and a goal programming approach for IVIMPRs.
Formulation of a maximum consensus-based goal program for DM weighting and an aggregation approach for collective preferences.
Utilization of linear programming to derive priority weights of alternatives.

Main Results:

A novel consistency-based GDM algorithm is proposed, integrating consistency optimization and consensus maximization.
The algorithm effectively determines DM weights and aggregates individual IVIMPRs into a collective one.
Priority weights for alternatives are derived from the collective IVIMPR using linear programming.
A practical example demonstrates the algorithm's applicability and comparative advantages.

Conclusions:

The proposed consistency-based GDM algorithm effectively handles uncertain preferences within IVIMPRs.
The method improves decision consistency and achieves maximum consensus among decision-makers.
The algorithm provides a valuable tool for complex GDM scenarios, offering advantages over existing approaches.