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Decisions related to supplier improvement and selection are inherently multiple criteria decision making (MCDM) problems and are strategically important to companies. Although efforts have been made to discover systematic methods to select the proper supplier, these efforts have assumed that the criteria are independent, which is not actually the case. Some studies that have treated the criteria as interdependent use additive models to obtain aggregate performance. We propose a novel fuzzy integral-based model that addresses the interdependence among the various criteria and employs the non-additive gap-weighted analysis. The structure of the relationships among the criteria and the criteria weights are developed using Decision Making Trial and Evaluation Laboratory (DEMATEL) combined with a fundamental concept of an analytic network process (ANP) called DANP. The fuzzy integral is then used to aggregate the gaps using the weights obtained from the DANP. The proposed model addresses the shortcomings of prior models and provides a more reasonable representation of the real world. The method is demonstrated using supplier evaluation and improvement data from a Taiwanese company.

Supplier evaluation and improvement processes are the most significant variables in the effective management of globalization, as they improve organizations through the channels of high-quality products and customer satisfaction. The traditional approach has been to rank and select suppliers solely on the basis of price. However, moving from ranking/selection to selection/improvement decisions in the contemporary supply-chain network is complicated, as potential options for selection/improvement decisions are evaluated using multiple criteria. Therefore, supplier selection/improvement has become an MCDM problem that includes several tangible and intangible factors [3] and [54]. Recently, these criteria have become increasingly complex, interdependent, and dynamic as environmental, social, political, and customer satisfaction concerns have been added to the traditional factors of quality, delivery, cost, and service. Additionally, traditional MCDM methods have generally only employed an additive model to evaluate, rank, and/or select the alternatives. More important, and from a practical standpoint, solving the problem of criteria gaps (gaps between actual performance and aspiration levels) while incorporating a non-additive (or super-additive) framework to address interdependence and feedback problems is a current trend within the MCDM field. Kahneman and Tversky [23] developed the basic concept of non-additive (or super-additive) value-function aggregation in multi-criteria problems. This concept has led researchers to an important question on how these two concepts (non-additive value functions and aspiration levels) can be applied to real world inter-relationship (dependence and feedback) problems. This article contributes a novel, hybrid, fuzzy integral-based DANP (DEMATEL-based ANP) model for reducing the gaps between each dimension and criterion to reach a given aspiration level in real world inter-relationship problems. Effective supplier selection/improvement demands robust analytical methods and tools that are applicable to the supplier decision and able to analyze multiple subjective and objective criteria [2]. A series of literature reviews has summarized the criteria and decision methods that have appeared in papers since the mid-1960s. For example, in an exhaustive review of 76 articles, Weber et al. [53] found that 47 articles address the involvement of more than one criterion. Two journal articles [10] and [59] reviewed the literature regarding supplier evaluation and improvement/selection models. Ho et al. [16] extended these reviews by surveying multi-criteria supplier evaluation and improvement/selection approaches through a literature review and a classification of international journal articles from 2000 to 2008. They concluded that only extensive, multi-criteria decision-making approaches have been proposed for supplier selection. The approaches include the analytic hierarchy process (AHP), analytic network process (ANP), data envelopment analysis (DEA), fuzzy set theory, genetic algorithms (GA), mathematical programming, the multi-attribute rating technique (i.e., gray relation, VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), technique for order preference by similarity to an ideal solution (TOPSIS), and their hybrids. Prior studies have made significant contributions to supplier selection; however, they have assumed the criteria to be independent when modeling the supplier selection problem. In the real world, the criteria are seldom independent. In fact, the relationships between the criteria are all, to some extent, interactive and occasionally include dependence and feedback effects [20], [36] and [46]. Others [19], [27], [30], [18], [29] and [12] have accounted for this interdependence (i.e., by using the ANP) but nonetheless employed additive models (i.e., VIKOR, gray relation or TOPSIS) to aggregate performances and weights. However, these methods are inconsistent with the assumption that the criteria are interdependent. A means of avoiding this inconsistency is to apply non-additive fuzzy integrals to integrate the interdependent performance values. In this study, we improve on prior research in three ways. First, the interdependent relationships between, and weights of, the criteria are constructed and calculated using DEMATEL and a fundamental concept of the ANP called DANP. This method can derive weights directly from the DEMATEL results and accommodate the different degrees of influence across dimensions. It also avoids the time-consuming process of performing pair-wise comparisons between criteria required in the original ANP analysis. Second, based on the concepts of VIKOR, the traditional relative good solution from the existing alternatives is replaced by the aspiration levels to avoid the “Choose the best among inferior choices/options/alternatives”, i.e., avoid “Pick the best apple among a barrel of rotten apples” option. Third, a non-additive fuzzy integral is used to obtain influence weighted gaps that enable managers to better measure and understand the gaps between aspiration levels and actual levels and establish improvement priorities. Using this hybrid model, we can remedy the inconsistency in our prior studies [18] and [29] that assume interdependent criteria but apply additive models. This study may present the first model that integrates the concepts of a non-additive value function and interdependence with feedback effects in the supplier selection problems. Moreover, the emphasis in the MCDM field has shifted from ranking and selection when determining the most preferable approaches to performance improvement. Our model provides a systematic approach to identify the source of problems rather than addressing the systems of the problems. We used data from a Taiwanese company to demonstrate this model. This generic model can be easily extended to other industries to aid other types of firms in selecting their optimal suppliers. 2. A brief review of the existing literature Over the last two decades, various decision-making methods have been proposed to address supplier evaluation and selection problems. Critical reviews have summarized the criteria and decision methods employed in the supplier selection process, for example, Ho et al. [16], De Boer et al. [9], Degraeve et al. [10] Wu et al. [55] and Weber et al. [54]. Based on prior studies, we categorize the methodologies used to analyze the supplier selection problem as follows: (1) multi-attribute decision-making, (2) mathematical programming models, (3) intelligent approaches, and (4) integrated approaches.

This paper analyzes supplier evaluation using a fuzzy integral-based model. We improve on previous models in several ways. First, the traditional models assume that the criteria are independently and hierarchically structured; however, in reality, decision problems are frequently characterized by interdependent criteria and dimensions and may even exhibit feedback-like effects. We applied the DEMATEL method to construct the network relationship. The DEMATEL-based ANP method is then used to derive the influence weights that, in a way, eliminate the time-consuming pair-wise comparisons in the original ANP. Second, relatively good solutions from the existing alternatives are replaced by aspiration levels to meet the demands of contemporary competitive markets. In this paper, VIKOR concepts are used to transform the performance levels into weighed gaps (the smaller the better) in each aspiration level. This enables a decision maker to reduce the gaps in alternatives to reach the aspiration levels and not simply a given performance level. Third, the emphasis on the MCDM applications has shifted from ranking and selection when determining the most preferable approaches to improving the performance of existing methods. The INRM identifies how and in which directions the criteria influence each other, which helps managers understand the root causes of performance issues and devise strategies for improvement. Fourth, information fusion techniques, including the fuzzy integral method, have been developed to aggregate the performance values. We utilized a fuzzy integral methodology to integrate the weights and gaps, which should be more applicable than conventional additive models. The empirical example indicates that the effect of the interdependencies among criteria is significant. We believe that the results of this application of our method are promising. Therefore, we conclude that the application of a fuzzy integral-based model to support decisions related to supplier selection can be fruitful. Although the present study makes a significant contribution to the literature, it does have limitations. To obtain the non-additive effect, we applied the λ fuzzy measure and assumed the λ value of each criterion to be the same within each dimension. A different method or various λ values could be possible for each criterion, which would better represent the real world by creating various operating environments. Although we developed an empirical evaluation tool, we occasionally were forced to spend a substantial amount of time explaining the questionnaire to respondents. Therefore, another avenue for improvement is the development of a more effective fuzzy measure. As an additional limitation, the conclusions drawn from our study are based on service industry data; thus, we explored only a portion of our model. Other cases in manufacturing could be used to test our model across different industries to draw comparisons, thereby providing greater insight into the interdependence and non-additive effects in supplier selection/improvement problems.