Multicriteria group decision-making under uncertainty using interval data and cloud models

Abstract

In this study, we propose a multicriteria group decision-making (MCGDM) algorithm under uncertainty where data is collected as intervals. The proposed MCGDM algorithm aggregates the data, determines the optimal weights for criteria and ranks alternatives with no further input. The intervals give flexibility to experts in assessing alternatives against criteria and provide an opportunity to gain maximum information. We also propose a novel method to aggregate experts' judgements using cloud models. We introduce an experimental approach to check the validity of the aggregation method. After that, we use the aggregation method for an MCGDM problem. Here, we find the optimal weights for each criterion by proposing a bi-level optimisation model. Then, we extend the technique for order of preference by similarity to ideal solution (TOPSIS) for data based on cloud models to prioritise alternatives. As a result, the algorithm can gain information from decisionmakers with different levels of uncertainty and examine alternatives with no more information from decisionmakers. The proposed MCGDM algorithm is implemented on a case study of a cybersecurity problem to illustrate its feasibility and effectiveness. The results verify the robustness and validity of the proposed MCGDM using sensitivity analysis and comparison with other existing algorithms.

Methods of ranking for aggregated fuzzy numbers from interval-valued data

“…Intriguingly, all of the algorithms compared do vary in their results, and as such, there is undoubtedly room for further investigating the effectiveness of IAA combined with TOPSIS. Moreover, the primary focus of [15], the recent MCDGM algorithm shares strikingly similar results with the proposed combined similarity measure (11), which shows promise for its potential effectiveness.…”

“…The IAA Fuzzy Numbers produced from the overall criterion have been used as input for the universal ranking method. For further details regarding the TOPSIS outline refer to [15,17].…”

“…The 9 criteria used were as follows: attack, complexity, interaction, frequency, availability of tool, inherent difficulty, maturity going unnoticed, and overall. Khorshidi and Aickelin [15] proposes a multicriteria group decision-making (MCGDM) algorithm, which applies the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) algorithm [17] (note TOPSIS does not utilize the overall opinion criteria), and compares the results to two other algorithms found within [1] and [18].…”

“…TOPSIS is a method of ranking multi-criteria data, and within its outlined steps it requires both a similarity and ranking method for input data types, opening an opportunity for the application of methods proposed within this study. Following [15] the overall opinion has been removed, and each criteria interval set regarding each attack provided by each expert were converted to IAA Fuzzy Numbers and passed into TOPSIS utilizing the attribute similarity measure (7) and the proposed combined similarity measure (11) as a means of contrast; both of which had the proposed universal ranking method applied when required by TOPSIS. Having the overall criterion removed gives the opportunity to compare the proposed universal ranking method with the results of the TOPSIS combination.…”

“…Whilst it is common that similarity measures may sometimes be also applied as methods of ranking, the similarity measures of previous IAA literature have shortcomings in this regard and require modification. Building upon the findings in [7,9], we propose a new similarity measure and two ranking methods for IAA fuzzy numbers and provide both an update to the previous illustrative example in [9], as well as explore the results from the application in a real-world case study [14,15] as a means to demonstrate their potential use. This paper is organized as follows.…”