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Meat and meat products are important sources of protein in human diets, in which pork is consumed at most (about 15.8 kg/capita/year) (Font-i-Furnols & Guerrero, 2014). However, pork prices are influenced by local conditions related to farm production resources, feed costs, demand, supply, porcine diseases and so on (Li & Wang, 2017; Stępien & Polcyn, 2016; Chen & Zapata, 2015). Consequently, we argue that the most effective scheme to stabilize the pork price of pork markets is to develop different strategies according to different pork price in different regions. After region division, the attributes of pork price in each region are similar, and the policy maker can establish more suitable policies based on results of region division to stabilize the pork market consequently. Therefore, this paper aims to propose a more effective and robust method to make region division of pork markets according to different pork price.
Figure 1. Visual representation of time series clustering results by fuzzy interval number k-means. a. Visual representation of ‘High’ Cluster. b. Visual Representation of ‘Low’ cluster.
Since region division is often formulated as clustering problem (Wang, 2014; Song, Liu, & Li, 2017; Wang, Wu, Zhao, & Jin, 2010), region division of pork markets is also formulated as clustering problem. In addition, this paper considers region division of pork markets according to the pork price with a period of a few months, in which data take the form of time series (see Figure 1). So, region division of pork market is regarded as time series clustering. In time series clustering studies, many general-purpose clustering algorithms, including k-means (Li, Deng, Wu, &Liu, 2013; Deng, Li, He, &Wu, 2013), Fuzzy C-Means (FCM) (Golay et al., 1998) and so on, are commonly used (Kakizawa, Shumway, &Taniguchi, 1998; Niennattrakul & Ratanamahatana, 2007). K-means is one of the most popular methods due to its efficiency and simplicity.
Nevertheless, the applicability of k-means is more or less restricted because of noise of time series data caused by the measuring instrument and the external environment (Wang & Su, 2011; Jolion & Rosenfeld, 1989; Dave, 1991; Ester et al., 1996; Möller-Levet et al., 2005; Dubes & Jain, 1988). K-means clustering algorithm is very sensitive to the initial centroids so that the clustering results will be very different result from different initial cluster centroids. Since noisy points are far from data-intensive areas, the calculation of the mean point would be affected, and the new cluster centroids may deviate from the true data-intensive area, which eventually leads to a clustering output result with large deviation (Wang & Su, 2011). Many modified attempts for k-means have been made to overcome the problem that is sensitive to noise, such as introducing noise filtering technology before operating the algorithm (Tang & Khoshgoftaar, 2004). However, these improved methods only adapt to numerical data and cannot address the disparate types of data, such as symbols, fuzzy sets, in clustering. Therefore, many scholars have tried to convert the data in the Euclidean space into the data in other spaces, in which a complete measure system is established to address more general case of clustering. For instances, Kaburlasos and Petridis convert disparate types of data including vectors of numbers, fuzzy sets, symbols, graphs, etc., into fuzzy lattices, and then present FL-framework associated with established theories for learning and/or decision-making including probability theory, fuzzy set theory, Bayesian decision-making, theory of evidence, and adaptive resonance theory to cluster and classify by a class activation function with respect to an inclusion measure σ (Kaburlasos, Petridis, Brett, & Baker, 1999; Kaburlasos & Petridis, 1997, 2000, 2002; Petridis, & Kaburlasos, 1998, 1999, 2001). Hong-Ying Zhang et al. (2016) convert numerical data into intuitionistic fuzzy values and interval-valued intuitionistic fuzzy values, and then propose hybrid monotonic inclusion measures to group decision making.