Elsevier

Knowledge-Based Systems

Volume 37, January 2013, Pages 86-93
Knowledge-Based Systems

An extended fuzzy measure on competitiveness correlation based on WCY 2011

https://doi.org/10.1016/j.knosys.2012.07.010Get rights and content

Abstract

The fuzzy measure can highlight important information in analyzing component features, patterns, and trends. However, fuzzy densities and interaction effects are usually unknown or uncertain for implications thus making the fuzzy measure limited in applications. This research proposes an extended fuzzy measure to derive the conditional fuzzy densities from dominance-based rough set approach (DRSA), multiply preferences and the derived densities into utilities, fulfill fuzzy measure identification, and empower the fuzzy measure to aggregate utilities. For illustration, the extended fuzzy measure is applied on World Competitiveness Yearbook 2011 to imply policy-making information for Greece, Italy, Portugal, and Spain.

Introduction

National competitiveness plays an important role as an aggregation power of a nation to enhance its people’s lives and cope with worldwide challenges [1], [2], [3]. The fuzzy measure can highlight component information in analyzing features [4], [5], patterns [6], [7], and multi-criteria decision making (MCDM) [8], [9], [10], [11]. However, applying the fuzzy measure to analyze competitiveness has difficulties. First, the fuzzy densities based on outcome probabilities are not designed for ‘if…then…’ implications [12], [13]. Substituting the fuzzy densities by conditional probabilities makes the fuzzy measure identification hard because the aggregation boundaries for the conditional probabilities and the outcome probabilities might be different. Second, the fuzzy measure cannot identify the interaction effects of compound components, composed of preferences and densities [14], [15], [16]. There are two reasons for this identification problem. One is that the fuzzy measure is designed for a single type of components. The other is because the interaction effects might have mixed types and cause ambiguity in estimating the competitiveness. The three typical interaction types are additive, sub-additive, and super-additive effects. The additive type is that interaction effect is similar to the expected effects. It is desired by users due to ease of assuming the components to be independent. The sub-additive interaction, however, yields some substitution effects and reduces the expectation of components independence, while the super-additive interaction yields additional effects than the expected effects.

With the aforementioned problems, key challenges for analyzing competitiveness are summarized as the followings:

  • World Competitiveness Yearbook (WCY) is the most well-known annual report of national competitiveness [2]. It presents preferences for national performance with criteria values. However, it neither assumes criteria weights for grouping nations nor provides competitiveness features for decision making.

  • Dominance-based rough set approach (DRSA) can provide preference features however it cannot handle analysis on components aggregation. Contrarily, the fuzzy measure can aggregate densities while it cannot identify densities for ‘if…then’ implications.

To overcome the above challenges, an Extended Fuzzy Measure (EFM), as shown in Fig. 1, is designed. It makes the fuzzy measurements possible in the information system of DRSA. Firstly, EFM associates criteria to a given class by DRSA to derive the Conditional Fuzzy Densities (CFD) for ‘if…then’ implications. CFDs are used to replace the fuzzy densities of the fuzzy measure and substitute the weights of the utility functions. The integration between the fuzzy measure and utility theory thus becomes possible. Secondly, EFM multiplies a preference and a CFD into a utility and aggregate utilities into a multiplicative utility function [17], [18]. In this research the multiplicative utility function is proved to perform aggregation as well as the fuzzy measure. Thirdly, EFM fulfills fuzzy measure identification on the aggregated utilities and chooses a resulted λ to provide competitiveness values. Finally, EFM analyzes correlations of the competitiveness values among four factors. Users can easily read and understand relationship among economic performance, government efficiency, business efficiency, and infrastructure. The terms in Fig. 1 alternatively includes a dominating class and preference orders to generate CFD.

This paper has two main parts. The first is the implementation of EFM. The second is a case study about the application of EFM which focuses on Greece, Italy, Portugal, and Spain. The remainder of this paper is organized as follows: Section 2 reviews DRSA and fuzzy measure, Section 3 presents EFM by the multiplicative utility function, Section 4 addresses results of an EFM application, Section 5 presents discussions on EFM and the case study, and finally concluding remarks are stated to close the paper.

Section snippets

Literature review

To date, the International Institute for Management Development (IMD) annually publishes the most well-known report, World Competitiveness Yearbook (WCY), which ranks and analyzes how a nation’s environment can create and develop sustainable enterprises. Its reports are used as the competitiveness data in this research. To get inside of the competitiveness features DRSA is applied, which is reviewed below.

DRSA is a powerful technique of relational structure and has been successfully applied in

The extended fuzzy measure for competitiveness features

EFM aims to multiply CFDs and preferences into utilities and then empower the fuzzy measurement to aggregate utilities for competitiveness components. Followings are their descriptions. Section 3.1 is about the dataset. As the new proposals, Section 3.2 is the information system for EFM, and Section 3.3 is the derivation of the conditional fuzzy densities. Section 3.4 proves that the multiplicative utility function can perform as well as the fuzzy measure. Section 3.5 is about identifying the

Results

The conditional fuzzy densities of Proposition 4 for the upper half nations of WCY 2011 are calculated by Model I and summarized in the left part of Table 2. The results reveal some disclosures. First, none of the conditional fuzzy densities equals to 1, which means none of criteria can completely classify dominance classes. Second, the resulted λ, −0.028⩽ λ  −0.010, has min_λ = −0.028 and max_λ = −0.010. Obviously, only a single type of interaction exists for the aggregation. This makes EFM reliable

Discussions and implications

This research uses EFM instead of Choquet’s integral to aggregate utilities. There are two reasons for this choice. Firstly, a huge number of additions up to n(2m  1) times have to be considered by Choquet’s integral when involving m criteria and n nations. Secondly, the corresponding preferences to the conditional fuzzy densities are hard to get for Choquet’s integral. In our empirical experiments, EFM processes computation as easy as a utility function.

According to Section 4, the resulted λ

Concluding remarks

This research has achieved some merits: Successfully extending the fuzzy measure on ‘if…,then…’ implications, empowering the fuzzy measure to aggregate utilities, fulfilling the fuzzy measure identification for the aggregated utilities, implying correlations to highlight competitiveness features, and estimating characteristics of government efficiency for Greece, Italy, Portugal, and Spain. Furthermore, the case study on WCY 2011 provides some disclosures of intelligent analysis. A

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