A fuzzy integral fusion approach in analyzing competitiveness patterns from WCY2010
Introduction
National competitiveness represents a fusion power for a nation to enhance its people’s lives and cope with worldwide challenges [1], [2], [3]. The fusion techniques can provide an aggregated information to expound features [4], [5], pattern [6], [7], and multiple criteria decision making [8], [9], [10], [11]. However, the fusion techniques still have difficulty in analyzing the diverse competitiveness. There are two potential problems in this issue. First, the fused competitiveness cannot be decomposed to provide thorough information, making the implications short of sufficient information. Second, fusion uncertainty always brings complexity [7], [12], which can be observed especially on the three types of fusion results: positive, negative, and independent, resulting to mixed combinations [4], [5]. A fusion result is positive when the fused result is more than the sum of the individuals. In contrast, a negative result means that the fused result is less than the sum of the individuals. An independent result stays in the middle of both, which causes more uncertainty in the combinations and makes the fusion techniques limited on their applications.
With the aforementioned problems, the key challenges for analyzing competitiveness are summarized as the following:
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Short of fusion information. Fusion information is becoming more and more important for the nations to survive the diverse competition in this e-era of globalization. World Competitiveness Yearbook (WCY) is the most well-known annual report of national competitiveness [2]. It linearly aggregates diverse competitiveness. However, neither fused nor decomposed information is provided.
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Challenges of inconsistency. Currently, the most popular fusion technique for utilities is by integrating the fuzzy measure and the fuzzy integral. However, it faces inconsistency challenges. For instance, applying the fuzzy integral and the fuzzy measure on two criteria and two utilities might encounter ‘Why is u2 involved in the interaction effects while u1 is not?’, which is formulated with gray color in Eq. (1) and illustrated in Fig. 1.
In Eq. (1), k represents an object, Q = {q1,q2} is a criteria set, u represents a utility function, g represents a fuzzy measure function, u1 and u2 are utility values of criteria q1 and q2 with respect to k, g1 and g2 are fuzzy densities of criteria q1 and q2, and λ is an interaction degree.
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Challenges of uncertainty reduction. The fusion uncertainty from both the fuzzy measure and the fuzzy integral makes their integration a more serious uncertainty. So far, there has been no any proposed decomposing technique for information fusion, thus making the uncertainty reduction still short of a penetrating function.
To overcome the above challenges, the fuzzy integral, the fuzzy measure, and a fitness fusion are integrated, termed as the fuzzy integral fusion (FIF), to generate fusion features, provide both fused and decomposed information, and feedback selected criteria for further fusion, as shown in Fig. 2 with three stages. In Stage I, DRSA and the fuzzy measure identification are integrated into a generalized fuzzy integral, presented in Proposition 3 of Section 3 [13], [14], [15], [16], [17]. In Stage II, Applying the generalized fuzzy integral generates the fusion features. Stage III, a fitness fusion is designed to select a candidate criterion for the next round or terminates the fusion. Furthermore, decomposed information of the features such as the benchmarking, fused effect, and qualities are collected at the right bottom corner.
This paper has two main parts. The first part discusses the design and implementation of FIF. The second applies FIF to analyze the European crisis nations (Greece, Italy, Portugal, and Spain) and the European welfare nations (Denmark, Finland, Norway, and Sweden) based on WCY 2010. The remainder of this paper is organized as follows: Section 2 reviews the information fusion, Section 3 presents the fuzzy integral fusion, Section 4 addresses application results of FIF, and Section 5 presents discussions and implications for the European crisis nations. Finally, concluding remarks are stated to close the paper.
Section snippets
Literature review
The International Institute for Management Development (IMD) annually publishes World Competitiveness Yearbook (WCY), a well-known report which ranks and analyzes how a nation’s environment can create and develop sustainable enterprises. Information from this report is used as the competitiveness dataset in this research [2]. Discussions related to the competitiveness fusion are presented in the following.
The Fuzzy Integral Fusion (FIF)
The competitiveness reflects the fusion power of a nation, and has multi-criteria as defined by WCY, and discussed in Section 3.1. The fuzzy integral fusion, comprising three stages illustrated in Fig. 2, is designed to illustrate the competitiveness with fusion features. Not only characteristic of dominance-based features, but also information of fusion features is provided to help users to get sufficient understanding of the dominance competitiveness. Its illustration includes four parts, as
Application of results
The resulted CFDs and λ intervals for the top ten and the upper half nations are presented in Table A1. They reveal that none of the criteria can completely classify dominance classes. Only a single type of λ means these densities are reliable without uncertainty disturbance.
Based on the reliable results, four fusion features are induced by applying FIF on the top ten and the upper half nations. The fusion information of these features has two categories. The first includes feature qualities (CR
Discussions and implications
This section has two parts. One is about technique discussion. The other is a case study about the European crisis and the European welfare patterns.
The inconsistency of integrating the fuzzy measure and the fuzzy integral for competitiveness has been solved in Section 3.2. Furthermore, FIF takes advantages of the fitness fusion to reduce uncertainty. For example, Algorithm I filters out criteria such as q4, q7, q8, q9, q10, q11, q16, q18, q19, and q20 which have either negative or independent
Concluding remarks
The proposed FIF integrates the fuzzy integral, the fuzzy measure identification, and the fitness fusion to generate fusion features and successfully decomposes a dominance approximation into the benchmarking (core) and the fusion effect (noncore) nations. It can help users to get an insight of the dominance nations. The benchmarking represents the characteristics of the top competitiveness and the fusion effect illustrates the criteria interdependence becomes more important in the high
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