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Citation for the original published paper (version of record): Hilletofth, P., Sequeira, M., Adlemo, A. (2019)
Three novel fuzzy logic concepts applied to reshoring decision-making Expert systems with applications, 126: 133-143
https://doi.org/10.1016/j.eswa.2019.02.018
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Three novel fuzzy logic concepts applied to
reshoring decision-making
Per Hilletoftha, 1, 2, Movin Sequeira3, and Anders Adlemo4
1. Department of Supply Chain and Operations Management, School of Engineering, Jönköping University, P.O. Box 1026, SE-551 11, Jönköping, Sweden, E-mail: prof.p.hilletofth@gmail.com
2. Department of Industrial Engineering and Management, University of Gävle, S801 76, Gävle, Sweden, E-mail: prof.p.hilletofth@gmail.com
3. Department of Supply Chain and Operations Management, School of Engineering, Jönköping University, P.O. Box 1026, SE-551 11, Jönköping, Sweden, E-mail: movin.sequeira@ju.se
4. Department of Computer Science and Informatics, School of Engineering, Jönköping University, P.O. Box 1026, SE-551 11, Jönköping, Sweden, E-mail: anders.adlemo@ju.se
Author biographies
Per Hilletofth is a Professor of Operations and Supply Chain Management at Jönköping University in Sweden and Visiting Professor at University of Gävle in Sweden. His research focuses on demand-supply integration, operations strategy, manufacturing relocation, product development, and decision support. He has published articles in international journals including Production Planning and Control, Expert Systems with Applications, Industrial Management and Data Systems, Journal of Business and Industrial Marketing, Innovation: Organization and Management, Journal of Manufacturing Technology Management, and European Business Review. He has editorial assignments in several international journals.
Movin Sequeira (MSc) is a PhD Student at Jönköping University in Sweden. His research interest includes manufacturing relocation and sustainable production. He has an M.Sc. degree in Production Development and Management from Jönköping University.
Anders Adlemo (PhD) is an Associate Professor of Computer System Engineering at Jönköping University in Sweden. His research has a focus on fuzzy logic solutions applied to a number of application domains related to decision-making, one being the production relocation domain. He has published more than 60 papers at international peer-reviewed conferences and in international journals including Control Engineering Practice, Journal of Systems Integration, Advances in Design and Manufacturing, Modern Manufacturing, and International Journal of Computer Integrated Manufacturing.
Three novel fuzzy logic concepts applied to
reshoring decision-making
Abstract
This paper investigates the possibility of increasing the interpretability of fuzzy rules and reducing the complexity when designing fuzzy rules. To achieve this, three novel fuzzy logic concepts (i.e., relative linguistic labels, high-level rules and linguistic variable weights) were conceived and implemented in a fuzzy logic system for reshoring decision-making. The introduced concepts increase the interpretability of fuzzy rules and reduce the complexity when designing fuzzy rules while still providing accurate results.
Key Words: Fuzzy logic, High-level rule, Linguistic variable weight, Relative linguistic label,
Reshoring, Decision-making.
1 Introduction
A significant movement of manufacturing from high to low cost environments has occurred in the past three decades (Ketokivi et al., 2017). The main driver for this offshoring has been to reduce the manufacturing cost, or more specifically the labor cost (Ellram et al., 2013; Canham and Hamilton, 2013; Gylling et al., 2015). In most cases, a cost reduction was achieved as planned, but in many situations it over time became evident that the decision had been based on insufficient, or even erroneous, information (see e.g., Eriksson et al., 2018). Commonly, too simplistic calculations were used, where all the cost related factors were not considered (Platts and Song, 2010; Bailey and De Propris, 2014; Stentoft et al., 2015). These offshoring failures have led to an intensified discussion concerning the opposite movement in recent years, that is when companies decide to move manufacturing back to their home country, reshoring (Gray et al., 2013; Arlbjørn and Mikkelsen, 2014; Wiesmann et al., 2017), or to an adjacent country, nearshoring (Slepniov et al., 2013; Müller-Dauppert, 2016; Fel and Griette, 2017; Panova and Hilletofth, 2017).
Reshoring is a relatively young and unexplored research area within the manufacturing location and relocation field. One issue that has received much attention in this growing research area is drivers or motives of reshoring. Among the more prominent drivers include quality related issues (Arlbjørn and Mikkelsen, 2014; Martínez-Mora and Merino, 2014; Johansson and Olhager, 2018), cost related issues (Engström et al., 2018b; Di Mauro et al., 2018), market related issues (Kinkel and Maloca, 2009; Kinkel, 2012; Tate et al., 2014) and strategy related issues (Ellram et al., 2013; Baraldi et al., 2018). Some frameworks have been developed that have classified reshoring drivers. One such framework group the drivers according to the main focus (cost efficiency or perceived value) and the environment (internal or external) (Fratocchi et al., 2016). Another framework groups the drivers into global competitive dynamics, host country, home country, supply chain and firm-specific issues (Wiesmann et al., 2017). In essence, this research stream shows important factors or criteria to consider in a reshoring decision.
Reshoring decisions are often based on numerous, vague and uncertain information, which makes these decisions complex to handle. In addition, there is a general lack of decision support that facilitate optimal and resilient decisions (Kinkel, 2012; Hartman et al., 2017; Stentoft et
based on uncertain information. This uncertainty can be manifested in many ways. It can be fuzzy (i.e., not sharp, unclear, imprecise, approximate), vague (i.e., not specific, amorphous) and ambiguous (i.e., too many choices, contradictory). The uncertainty could also be linked to ignorance (i.e., not knowing something, dissonant) or natural variability (i.e., random, chaotic, unpredictable). This type of uncertain information is common in many fields and difficult to handle. The inability of traditional methods to cope with uncertain information has been emphasized in the existing literature (e.g., Williamson, 1994; Kenney and Smith, 1996). Decision problems based on numerous and uncertain information are often complex, both in structure and handling, as the number of decision variables could grow rapidly and make it difficult, or even impossible, to manually identify an optimal solution. In order to handle complex reshoring decision-making in a formal and structured manner, some manually handled frameworks have been proposed (see e.g., Gylling et al., 2015; Bals et al., 2016; Joubioux and Vanpoucke, 2016; Hartman et al., 2017). These frameworks are mainly theoretical exercises and lack automatic support to make decisions. One way to approach these kind of decision problems is to apply a branch in mathematics known as fuzzy logic (Zadeh, 1965). Fuzzy logic has been applied to decision-making issues in a wide range of applications in the operations management field (Azadegan et al., 2011; Chai et al., 2013; Keshavarz Ghorabaee et al., 2017; Liao, 2005). Due to the strong similarities between different applications in this field, fuzzy logic could be considered a feasible method for reshoring decision-making as well.
A fuzzy logic system must be interpretable (i.e., readable by humans) and accurate (i.e., provide exact results). Designing such a system is not a trivial task. One reason for this is that there usually is a tradeoff between high interpretability and high accuracy (Shukla and Tripathi, 2012). Two main modeling approaches have been proposed in the literature (Cpałka, 2017). The first approach (precise fuzzy modelling) focuses on obtaining fuzzy systems distinguished by high accuracy and relies on a large rule base, while the second approach (linguistic fuzzy modelling) focuses on obtaining fuzzy systems distinguished by high interpretability and relies on a small rule base. In the second approach, a Mamdani-type system with fuzzy rules is often used (Mamdani, 1976). Many solutions for improved interpretability have been proposed in the existing literature, including reduction of the number of fuzzy sets (Tsekouras et al., 2018), reduction of the number of fuzzy rules (Alcalá et al., 2006), reduction of the number of antecedents in the fuzzy rules (Ishibuchi and Nojima, 2007), improvement of the distinguishability and interdependence of fuzzy sets (Mencar et al., 2011), and utilization of appropriate membership functions (Bodenhofer and Bauer, 2003).
Another key issue that must be managed when designing a fuzzy logic system is inconsistency (Alcalá et al., 2006; Casillas et al., 2009; Gegov et al., 2017). When a flexible fuzzy rule structure, such as those with antecedent in conjunctive normal form is used, the interpretability of the obtained fuzzy system is notably improved (Casillas et al., 2013; Zhou and Gan, 2008; Cordón, 2011; Gacto et al., 2011; Cpałka, 2017). On the other hand, it is relatively easy to encounter problems, such as inconsistencies, lack of completeness, and redundancies (Gacto et al., 2011; Lughofer, 2013). Two fuzzy rules are inconsistent when their antecedents overlap or are equal, or if they coincide in some labels for each input variable, or if one rule is subsumed by another and the consequent is different (Gegov et al., 2015; Gegov et al., 2017). Such cases of inconsistency cause a linguistic contradiction that should be avoided. Another, less severe problem, when designing a fuzzy logic system is redundancy (Duţu et al., 2018; Lughofer et al., 2011; Štěpničková et al., 2013). This is caused when the antecedent is overlapped and has the same consequent. Therefore, it can be argued that obtaining a fuzzy logic system that is interpretable, accurate and consistent is a challenge.
The aim of this study is to investigate the possibility of increasing the interpretability of fuzzy rules and reducing the complexity when designing fuzzy rules. To achieve this, three novel fuzzy logic concepts (i.e., relative linguistic labels, high-level rules and linguistic variable weights) were conceived and implemented in a fuzzy logic system for reshoring decision-making. The system was configured in two different ways in order to incorporate the novel concepts. The input for each of the two configurations were ten,input (or decision) scenarios that consisted of six decision criteria. The decision scenarios provided the necessary test data to evaluate if the novel concepts provided accurate results.
The remainder of the paper is structured as follows. To begin with, a brief introduction to fuzzy logic with a special focus on decision-making is provided in Section 2. Thereafter, a summary of fuzzy logic related research in the shoring and sourcing domain is given in Section 3. After that, the three novel fuzzy logic concepts are introduced in Section 4. Next, the fuzzy logic system is described in Section 5. Thereafter, the results from the fuzzy logic system are presented and discussed in Section 6 and 7 respectively. Finally, the research is concluded in Section 8.
2 Fuzzy logic review
The theory behind fuzzy logic is based on fuzzy set theory, which is a natural extension of classical set theory (Zadeh 1965, 1975, 2008). Fuzzy logic provides a powerful way of understanding, quantifying and handling numerous and uncertain data (Dutt and Kurian, 2013). Fuzzy logic expresses that nothing can be firmly stated as being either entirely right or entirely wrong. The key goal of the fuzzy logic (or inference) system is decision-making and its basic structure include five functional blocks (Figure 1).
Figure 1. Fuzzy logic system (adapted from Jang, 1993)
The first block (fuzzification interface) transforms the crisp inputs into corresponding linguistic variables. A linguistic variable is a variable whose values are not expressed in numbers but words (i.e., linguistic terms). The concept of a linguistic variable is very pertinent when dealing with situations that are too complex or undefined to be described by conventional quantitative expressions. A linguistic variable can have a set of linguistic values or labels (Zimmermann, 1991). The most common way to define linguistic labels is to use absolute labels such as low-medium-high (Pei and Zheng, 2017). An alternative, that is very rarely used, would be to use relative labels such as positive-neutral-negative (see e.g., Sugeno and Yasukawa, 1993; Phong et al., 2011).
The second block (database) contains membership functions. A membership function defines a fuzzy set that represents a linguistic label (Zadeh, 1965; Gegov et al., 2015). Each element of the set of the linguistic label is mapped to a value between 0 and 1. This value determines the degree of truth in the evaluation (Barnabas, 2013). The selection of a membership function for a linguistic label is generally based on the decision-makers previous knowledge of the linguistic variable and trial and error learning processes. The membership function should be normalized (i.e., has a maximum value of 1), convex (i.e., has only one maxima) and distinct (i.e., has a restricted overlapping between other functions) (Zimmermann, 1991).
The third block (rule base) contains the fuzzy inference (or if-then) rules. The design of the fuzzy rules is the cornerstone in the development of a fuzzy logic system (Mendel, 2017). It is common to involve domain experts in the design since they have a more in-depth knowledge of the domain (Liao, 2005). The design of the rules can be realized in different ways (Duţu et al., 2018). The most common approach is to create all possible combinations based on the available linguistic variables and labels (i.e. a complete set of fuzzy rules). An alternative is to develop a reduced set of fuzzy rules (Xiong and Litz, 2002; Kaynak et al., 2002). This means that only the rules that are relevant to the problem at hand and that are more intuitive to a domain expert are created. A third option is to extract fuzzy rules from training data (Coelho et al., 2016; Odeh et al., 2015; Lughofer, 2016; Wu et al., 2001).
The fourth block (decision-making unit) performs the inference operations on the rules from the fuzzy rule base to determine a fuzzy output (Jang, 1993). The most common fuzzy logic operations, also known as standard operations, are union (i.e., ‘or’), intersection (i.e., ‘and’) and complement (i.e., ‘not’) (Berenji, 1992). The inference operations on fuzzy sets are operations by which several fuzzy sets (the antecedents) are combined in a desirable way to produce a single fuzzy set (the consequent). This is done through a t-norm operator, that performs either multiplication or minimum operation on the input fuzzy sets (the antecedents). The resulting fuzzy set (the consequent) is either crisp or fuzzy depending on the weights of the fuzzy rules (Jang, 1993).
The fifth block (defuzzification interface) transforms the fuzzy result into a crisp output. This involves the process of rounding off the fuzzy result to a crisp, single scalar equivalent (i.e., converting the fuzzy result, represented as a membership function, into a real number or even an integer). There exist a vast number of defuzzification method such as center of gravity method, weighted average method, mean of maxima method, basic defuzzification distribution method, semi-linear defuzzification method, center of sums method, center of the largest area method, and maxima method (Van Leekwijck and Kerre, 1999). The selection of a suitable defuzzification method is based on the given application (Barnabas, 2013). The center of gravity and maxima methods seem to provide the best results for a large number of applications (Van Leekwijck and Kerre, 1999).
3 Related works
Fuzzy logic has a wide range of application areas in the field of operations management (Azadegan et al., 2011). Two specific application areas are the evaluation of sourcing and shoring decisions. Out of these two, fuzzy logic for sourcing decisions have been much more explored in the existing literature compared to shoring decisions (Kaur et al., 2018). Fuzzy logic has been proposed to evaluate make-or-buy decisions (Hwang et al., 2007; Cheshmberah et al., 2010; Çebi et al., 2014; Aksoy and Öztürk, 2016) and supplier selection decisions (Chen et al., 2006; Bayrak et al., 2007; Carrera and Mayorga, 2008; Chan et al., 2008; Simić et al., 2017;
Bodaghi et al., 2018; Wang and Tsai, 2018) in the sourcing domain. There are more studies on supplier selection decisions compared to make or buy decisions (Chai et al., 2013; Wu and Barnes, 2011). However, both these areas are rather well explored in the literature. Fuzzy logic has been proposed to evaluate manufacturing relocation decisions (Cedolin et al., 2017; Rikalovic and Cosic, 2015) in the shoring domain. There exist more studies on offshoring decisions (Kaur et al., 2018; Meneses et al., 2016) compared to reshoring decisions (White and Borchers, 2016; Adlemo et al., 2018a, 2018b, 2018c). However, both these areas are rather unexplored in the literature (Kaur et al., 2018).
Several studies have applied fuzzy logic for make-or-buy decisions. Hwang et al. (2007) used a three-step approach. In the first step, a brainstorming model was used to generate the decision criteria and the relationships among them. In the second step, fuzzy analytical hierarchy process and fuzzy set reasoning were used to evaluate the different alternatives. In the third step, the majority rule was applied to rank the alternatives. Five criteria (i.e., manufacturing technology, outsourcing risk, management problems, financial issues and operational issues) were considered in the evaluation. The final decision was either to make in-house, partial make-or-buy, or buy outsourcing. Çebi et al. (2014) used a two-step approach. In the first step, market entry decisions were evaluated while make-or-buy decisions were evaluated in the second step. Four main criteria (i.e., strategic, operational, technological and financial factors) and 18 sub-criteria were considered in the evaluation. The final decision was either to make in-house, buy import or buy subcontract.
Several studies have applied fuzzy logic for supplier selection decisions. Chan and Kumar (2005) used fuzzy extended analytical hierarchy process to facilitate global supplier selection. They implemented four hierarchy levels: overall objective at level 1, main criteria at level 2, sub-criteria at level 3 and decision alternatives at level 4. The overall objective was defined as global supplier selection. Five main criteria (i.e., product cost, product quality, service performance, supplier profile and risk) and 19 sub-criteria were considered in the evaluation. The final output was the best supplier out of the given supplier alternatives. Boran et al. (2009) used intuitionistic fuzzy sets for supplier selection in a group decision-making setting. They described an eight-step approach to implement intuitionistic fuzzy sets. In a numerical example, four criteria were considered (i.e., product quality, relationship closeness, delivery and price) to rate the suppliers among three individual decision makers. The final output was the ranking of alternative suppliers.
Several studies have applied fuzzy logic for manufacturing relocation decisions. Chen and Lin (2018) used a fuzzy set qualitative comparative analysis to measure the success of offshoring projects. Nine criteria (i.e., physical distance, temporal distance, cultural distance and linguistic distance for both intra and inter-organization levels, and co-location with clients) were considered in the evaluation. The output was a measure of the collaborative success of the offshoring projects. White and Borchers (2016) applied a fuzzy analytical hierarchy process to rank the most important factors in reshoring decisions. Eight main criteria (i.e., input/product, cost, labor, logistics, supply chain interruption risk, strategic access, country risk, and government trade policies) and 29 sub-criteria were considered in the evaluation. The output was a ranking of the included criteria. The main criteria cost and the sub-criteria labor cost were ranked as the most important criteria influencing the reshoring decision.
4 Three novel fuzzy logic concepts
4.1 Relative linguistic labels
Absolute linguistic labels are bound to a common and agreed upon definition consensus among the system users. In practice, it is not easy to implement absolute linguistic labels as they give rise to some common issues. One issue is that an absolute label, such as medium, may have a different meaning for different people (Chen et al., 2014; Pei and Zheng, 2017; Rodríguez et al., 2013; Wang et al., 2018). One way to capture these different interpretations is to establish weight for criteria or importance from every system user (Wu and Mendel, 2007). Another issue is that an absolute label, such as high, could have both a positive and negative meaning depending of the particular variable considered (Rodríguez et al., 2016). For example, high quality is something considered to be positive while high cost is something considered to be negative. This double significance can cause confusion among the system users. The novel concept proposed in this paper (relative linguistic labels) circumvents these issues. Examples of relative labels include positive, neutral and negative. Relative labels eliminate the need to create unique and specific linguistic labels for each variable. The inherent meaning of a relative label is also the same to any system user. This means that their semantics are consistent among human decision makers and this eliminates the confusion associated with absolute labels. For instance, the label positive means that the variable (cost or quality) has a positive impact on the decision (decrease in cost or increase in quality). However, relative linguistic labels are only applicable in conditions where absolute labels are not required. For instance, when several alternatives should be ranked absolute labels are usually preferable.
4.2 High-level rules
A complete set of fuzzy rules eliminates the risk of inconsistencies between the fuzzy rules but decreases the interpretability of the fuzzy rules (Zhou and Gan, 2008; Cordón, 2011; Cpałka, 2017). However, this approach soon become unmanageable with an increasing number of required rules (Guillaume, 2001; Gacto et al., 2011). The required number of rules increase exponentially with the number of linguistic variables and labels. It is challenge to domain experts, to be aware of the difference between numerous fuzzy rules and how these differences should be demonstrated in the output (Chen et al., 2018). A reduced set of fuzzy rules, on the other hand, increases the interpretability of the rules but comes with a risk of inconsistencies between them (Alcalá et al., 2006; Casillas et al., 2009; Gegov et al., 2015; Gegov et al., 2017). Inconsistencies between the fuzzy rules must be dealt with in order to generate accurate results (Herrera and Martínez, 2000). One major drawback of the approach of extracting fuzzy rules from training data is the need of a reasonable amount of training data to work on (Raja and Ramaiah, 2017). The novel concept proposed in this paper (high-level rules) belongs to the reduced set approach and implies that only the rules that are relevant to the problem at hand and that are more intuitive to a domain expert are created, so-called high-level rules. An example of a high-level rule is “if one A criterion is positive, AND one A criterion is negative, AND two B criteria are positive, AND one B criterion is negative, AND one C criterion is negative, then don’t evaluate”. High-level rules drastically reduce the complexity imposed on the domain experts as only a reduced set of rules need to be designed and evaluated. The high-level rules are automatically transformed into fuzzy rules without the involvement of domain experts.
4.3 Linguistic variable weights
The approach of using domain experts to assign the consequent to the fuzzy rules is much easier when a reduced set of fuzzy rules have been designed compared to a complete set of fuzzy rules (Cpałka et al., 2016). However, with an increasing number of fuzzy rules most domain experts
find it complex and time consuming to assign an output to each rule (Gacto et al., 2011; Cpałka, 2017). As argued above it is a major challenge to be aware of the difference between numerous fuzzy rules and how these differences should be demonstrated in the output (Alcalá et al., 2006; Gegov et al., 2017). The novel approach proposed in this paper (linguistic variable weights) address this problem by automatically assigning the consequent to the fuzzy rules. The weight, or value, assigned to a linguistic variable indicate its relative importance in relation to other linguistic variables. The linguistic variable weights (LVW) can range between any two values, for example -2 and +2, that is, LVW ∈ [-2,+2]. A positive value, like +2, is chosen when the membership function of a relative linguistic label is positive while a negative value, like -2, is chosen when the membership function of a relative linguistic label is negative. After assigning the weights, a complete set of fuzzy rules is created, and the consequent is computed by adding and subtracting the linguistic variable weights for each of the rules. A positive consequent of the fuzzy rule indicates that the decision suggestion should be further evaluated while a negative consequent of the fuzzy rule indicates that the decision suggestion should not be further evaluated. The higher the value, the stronger the decision suggestion is.
5 The fuzzy logic system
The three novel fuzzy logic concepts were implemented in a fuzzy logic system for reshoring decision-making. The system was configured in two different ways in order to incorporate the novel concepts. The system was created using the fuzzy logic toolbox found in MATLAB® and was based on knowledge acquired from experts in the reshoring domain. The implementation process consisted of four steps which are further explained below.
5.1 Step 1: Define linguistic variables
In the first implementation step, the linguistic variables are defined. In this study, a linguistic variable is a reshoring criterion. Reshoring criteria could be regarded as the factors influencing the reshoring decisions and could be found in the drivers, enablers and barriers of reshoring (Benstead et al., 2017; Barbieri et al., 2018; Stentoft et al., 2016; Wiesmann et al., 2017). We have chosen to use six high-level reshoring criteria that correspond to common competitive priorities within the operations strategy field (Miller and Roth, 1994; Frohlich and Dixon, 2001; Sansone et al., 2017). The reason for choosing common competitive priorities as the main evaluation criteria for the reshoring decision, is that they provide a holistic view on how to create competitiveness, which is the main goal of any manufacturing relocation decision.
Figure 2. The six reshoring criteria with their corresponding sub-criteria
The six criteria are: cost, quality, time, flexibility, innovation and sustainability (Figure 2). The criteria comprise several sub-criteria, however, the fuzzy logic system used in this study only considers the criteria level. The choice to make use of only the criteria level could be considered a limitation. Still, there is a tradeoff between complexity and implementability and the chosen approach is considered appropriate for the evaluation of the applicability of fuzzy logic for reshoring decision-making. The six criteria serve as input to the fuzzy logic system. Apart from the six input criteria, there exists one output criterion. The output criterion indicates whether a specific combination of input criteria values, called an input scenario further on, is sufficient to recommend a reshoring evaluation (i.e., output = evaluate) or not (i.e., output = do not evaluate). In this study, the different linguistic variables (or criteria) are grouped based on their level of importance. The level of importance could of course differ between different decision-makers and countries. The importance of each criterion is assigned according to the involved reshoring experts. The color coding in Figure 2 indicates the order of importance of the criteria. Green indicates the most important criteria from a reshoring point-of-view, yellow indicates lesser important criteria and orange indicates the least important criterion. The six criteria are thus grouped into three sets, each signaling a level of importance. Cost and quality are assigned the highest importance (green). This means that if cost or quality should be negative (i.e., if cost increases or if quality decreases), this would have a high impact on the final decision. Time, flexibility, and innovation are assigned medium importance (yellow) and sustainability is assigned the lowest importance (orange).
The rationale behind the grouping is in alignment with recent studies on critical operations capabilities in high cost environments (Sansone et al., 2016) as well as with existing reshoring literature where cost and quality are often considered the main drivers for reshoring to high cost
environments (De Backer et al., 2016; Sansone et al., 2016; Heikkilä et al., 2018; Engström et al., 2018b). For instance, Swedish companies that have reshored during the period 2010-2015 have indicated quality and cost as the main drivers (Engström et al. 2018a; Engström et al., 2018b; Johansson and Olhager, 2018).
5.2 Step 2: Define linguistic labels
In the second implementation step, the linguistic labels are defined. In this study, relative linguistic labels were applied in the fuzzy logic system. The relative labels positive-negative are used in both the configurations. The reason for choosing relative labels are the common issues with absolute labels discussed in Section 4. Apart from avoiding these common issues, the relative labels also could be used for all of the six criteria selected in the previous step, without a need to create unique and specific labels for each criterion. Furthermore, the inherent meaning of the relative labels remains the same to any user of the fuzzy logic system.
5.3 Step 3: Define membership functions
In the third implementation step, the membership functions are defined. The six input linguistic variables (criteria) are represented by two membership functions in both of the configurations (Figure 3) and the output linguistic variable is also represented by two membership functions in both of the configurations (Figure 4).
Figure 3. The membership functions used for all the input linguistic variables
in both of the configurations.
Figure 4. The membership functions used for the output linguistic variable
in both of the configurations.
configurations. The shape of the membership functions is the same for all of the six linguistic variables in each of the two configurations.
5.4 Step 4: Define fuzzy rules
In the fourth implementation step, the fuzzy rules are defined. The system was configured in two different ways in order to incorporate the novel concepts. The first configuration applied the concept of high-level rules while the second configuration applied the concept of linguistic variable weights. The first configuration increases the interpretability of the fuzzy rules by keeping the number of rules to a minimum. This comes with a risk of inconsistencies between the rules, which must be dealt with to generate accurate results. The second configuration reduces the interpretability by considering all possible fuzzy rules but improves the situation through a simple scheme that creates fuzzy rules that are interpretable and consistent. The definition of fuzzy rules for the two configurations are shown below.
In the first configuration a reduced set of fuzzy rules was created. This was accomplished by using high-level rules. The idea behind high-level rules is to ease the task of the reshoring experts so that they do not have to be directly involved in the design of fuzzy rules. Thus, instead of defining all possible combinations of fuzzy rules they only focus on high-level rules that are relevant to the problem at hand and that are more intuitive to them. The application of high-level rules is shown in Table 1. A three-step procedure was used. First a weight was assigned to each linguistic variable (step 1). After that, high-level rules were created based on the variable weights (step 2). In total, eight high-level rules were created. Finally, the high-level rules were translated into fuzzy rules (step 3). For instance, it was sufficient with one fuzzy rule to translate the first high-level rule while three fuzzy rules had to be created to fully translate the third high-level rule. In total, the eight high-level rules were translated into 18 fuzzy rules. The reshoring experts were only involved in creating the high-level rules (step 1 to 2).
Table 1 The design of fuzzy rules in the first configuration
Step Description Application
1 Assign a weight to each
linguistic variable Cost=4; Quality=5; Time=2; Flexibility=2; Innovation=2; Sustainability=1 2 Define the high-level rules (1) If Cost is positive AND Quality is positive, then evaluate
(2) If Cost is negative AND Quality is negative, then don’t evaluate (3) If Cost is negative AND Quality is positive AND two yellow
criteria are positive, then evaluate
(4) If Cost is negative AND Quality is positive AND two yellow criteria are negative, then don’t evaluate
(5) If Cost is positive AND Quality is negative AND three yellow criteria are positive, then evaluate
(6) If Cost is positive AND Quality is negative AND two yellow criteria are positive AND one yellow criterion is negative, AND one orange criterion is positive then evaluate
(7) If Cost is positive AND Quality is negative AND two yellow criteria are positiveAND one yellow criterion is negative, AND one orange criterion is negative then don’t evaluate
(8) If Cost is positive AND Quality is negative AND two yellow criteria are negative, then don’t evaluate
3 Transform the high-level
rules to fuzzy rules High-level rules Fuzzy rules (1) → 1
(2) → 1
(3) → 3
(4) → 3
(5) → 1
(7) → 3 (8) → 3 ∑ = 18
In the second configuration a complete set of fuzzy rules was created. These fuzzy rules were created through a semi-automatic approach and the consequent was automatically assigned using linguistic variable weights. The application of linguistic variable weights is shown in Table 2. A three-step procedure was used. First a weight was assigned to each linguistic variable (step 1). After that, the complete set of fuzzy rules was created based on the variable weights (step 2). With six linguistic variables (criteria) that have an impact on the decision and two linguistic labels for each variable the total number of fuzzy rules is 26 = 64. Finally, the
consequent part of each fuzzy rule was computed by adding or subtracting the linguistic variable weights in the rule (step 3). The reshoring experts were only involved in assigning the linguistic variable weights (step 1).
Table 2 The design of fuzzy rules in the in second configuration
Step Description Application
1 Assign a weight to each
linguistic variable Cost=4; Quality=5; Time=2; Flexibility=2; Innovation=2; Sustainability=1 2 Create a complete set of
fuzzy rules (1) if Cost is negative AND Quality is negative AND Time is negative AND Flexibility is negative AND Innovation is negative AND Sustainability is negative, then x1
…
(32) if Cost is negative AND Quality is positive AND Time is positive AND Flexibility is positive AND Innovation is positive AND Sustainability is positive, then x32
…
(64) if Cost is positive AND Quality is positive AND Time is positive AND Flexibility is positive AND Innovation is positive AND Sustainability is positive, then x64
3 Compute the consequent part of each fuzzy rule by adding or subtracting the linguistic variable weights in the rule.
(1) [(-4) + (-5) + (-2) + (-2) + (-2) + (-1) ≤ 0]; ∴ x1= “don’t evaluate” … (32) [(-4) + (5) + (2) + (2) + (2) + (1) > 0]; ∴ x32= “evaluate” … (64) [(4) + (5) + (2) + (2) + (2) + (1) > 0]; ∴ x64= “evaluate”
6 Results from the fuzzy logic system
The goal when using the fuzzy logic system is to provide an output that consists of a decision recommendation that is as close as possible to that of reshoring experts. If there exists a major discrepancy, the system needs to be tuned. To be able to perform this tuning, some valid input data is required. The input for each of the two configurations were ten input (or decision) scenarios that consisted of six decision criteria. The input scenarios were created by academic experts from the reshoring domain.
The decision scenarios provided the necessary test data to evaluate if the novel concepts provided accurate results. A scenario consists of a 6-tuple made up of input values of the 6 criteria that range from -5 to +5. -5 indicates that the criterion would be affected in an extremely negative way if reshoring would take place while +5 indicates that the criterion would be affected in an extremely positive way. The output value ranges from -5.00 to +5.00 where values between -5.00 to 0.00 indicate ‘don’t evaluate’ while 0.01 to +5.00 indicate ‘evaluate’. A higher (or lower) value gives a stronger indication whether to evaluate (or not evaluate) reshoring.
The same fuzzy inference settings were used in both of the configurations. Minimum (Min) was used for AND method while maximum (Max) was used for OR method. The OR method does not impact the system since there are no OR operations in the fuzzy rules. Minimum (Min) was used as implication method while maximum (Max) was used as aggregation method. Finally, middle of maximum (Mom) was used as defuzzification method. The fuzzy logic toolbox provides more setting alternatives for each parameter but only the most relevant setting for each parameter was considered based on the existing literature (see e.g., Syn et al., 2011; Liu, 2018). The results from the first configuration (i.e., high-level rules) are shown in Table 3. The Expert opinion shows the reshoring experts evaluation of the input scenarios while the System output (Config 1) shows the result from the fuzzy logic system. The results from System output indicate a correct evaluation from the fuzzy logic system for all the input scenarios when compared to the reshoring experts. For most of the input scenarios, the differences between the
reshoring experts and the system is relatively low. For instance, in input scenario 1, the reshoring experts’ opinion is a strong recommendation to not evaluate reshoring (-5.00) and the fuzzy logic system’s recommendation is very similar, only slightly weaker (-4.20). In addition, for input scenario 9 the fuzzy logic system’s recommendation is the same as for the reshoring expert (+5.00). As indicated in Table 3, the Mean Absolute Error (MAE) for the 10 scenarios is 0.90 which indicates a close resemblance between the opinion of the reshoring experts and the result from fuzzy logic system. It can be concluded that the high-level rules that were translated into fuzzy rules provided an accurate system
Table 3. Expert and system recommendations for both configurations
Scenario
Criteria opinion Expert System output (Config 1) System output (Config 2) Decision Conflict
Co st Q ua lit y Ti m e Fl ex ib ili ty In nov at ion Su st ai na bi lit y 1 -5 -1 -3 -2 -3 3 -5 -4.20 -4.20 Don´t evaluate No 2 2 5 -1 3 4 1 4 5.00 4.20 Evaluate No 3 -3 -4 -3 -1 4 -1 -4 -5.00 -4.20 Don´t evaluate No 4 3 -4 -1 -3 -5 -3 -4 -5.00 -4.20 Don´t evaluate No 5 -4 -2 5 -1 -1 5 -4 -5.00 -4.20 Don´t evaluate No 6 4 2 -4 2 2 -5 4 5.00 5.00 Evaluate No 7 -4 2 1 2 2 5 4 5.00 4.20 Evaluate No 8 2 -1 3 -1 1 5 3 4.20 4.20 Evaluate No 9 3 5 5 2 5 -3 5 5.00 5.00 Evaluate No 10 -3 -5 3 -2 5 -2 -4 -5.00 -5.00 Don´t evaluate No MAE 0.90 0.50
The results from the second configuration (i.e., linguistic variable weights) are shown in Table 3. The Expert opinion shows the reshoring experts evaluation of the decision scenarios while the System output (Config 2) shows the result from the fuzzy logic system. The results from System output indicate a correct evaluation from the fuzzy logic system for all the input scenarios when compared to the reshoring experts. Some of the recommendations from the reshoring experts and the systems are very close (e.g., scenarios 2, 3, 4, 5, 7 and 9) while others differ more (e.g., scenarios 6, 8 and 10). As indicated in Table 3, the MAE for the 10 scenarios is 0.50 which indicates a close resemblance between the opinion of the reshoring experts and the result from fuzzy logic system. The second configuration preforms better than the first one on an overall level (comparing MAE) and this is linked to the use of a complete set of fuzzy rules. However, the difference between the two configurations is not that great and for half of the input scenarios, the configurations provide same outputs (e.g., scenarios 1, 6, 8, 9, and 10).
7 Discussion
The common way to define linguistic labels is to use absolute labels. However, implementing absolute labels in practice is not an easy task due to several issues. One issue is that an absolute label, such as medium, may have a different meaning for different people (Chen et al., 2014; Pei and Zheng, 2017; Rodríguez et al., 2013; Wang et al., 2018). Another issue is that an
particular criteria considered (Phong et al., 2011; Rodríguez et al., 2016). Based on these issues, the concept of relative linguistic labels was applied in this study. One advantage of relative labels is that the same labels can be used for all the linguistic variables in a specific application without a need to create unique and specific labels for each variable. Another advantage is that the inherent meaning of a relative label is the same to any user of the fuzzy logic system. A third advantage of relative labels is that they eliminate the need of having absolute or concrete values, therefore keeping the number of labels down to only the meaningful ones. Thus, relative labels help to increase the interpretability of the fuzzy rules and to reduce the complexity when designing fuzzy rules. One disadvantage of relative linguistic labels is that they are applicable only under conditions where absolute linguistic labels are not required. For example, in the case when several alternatives should be ranked, absolute labels may be preferable. This leads the research to propose the following:
Proposition 1: Relative linguistic labels increase the interpretability of the fuzzy rules. Proposition 2: Relative linguistic labels reduce the complexity when designing fuzzy rules.
The design of fuzzy rules can be realized in different ways (Duţu et al., 2018). It is common to involve domain experts since they have in-depth knowledge of the domain (Liao, 2005). The most common approach is to create all possible combinations of fuzzy rules based on the available linguistic variables and labels (i.e. a complete set of fuzzy rules). However, such an approach soon become unmanageable with an increasing number of required rules (Guillaume, 2001; Gacto et al., 2011; Chen et al., 2018). It is challenge to domain experts, to be aware of the difference between numerous rules and how these differences should be demonstrated in the output. Based on this issue, the concept of high-level rules was applied in this study. This means that only the rules that are relevant to the problem at hand and that is more intuitive to a domain expert are created (i.e. a reduced set of fuzzy rules). One advantage of high-level rules is increased interpretability by keeping the number of rules to a minimum. Another advantage is reduced complexity when designing fuzzy rules by only considering the rules that are most relevant to the problem. Thus, high-level rules help to increase the interpretability of the fuzzy rules and to reduce the complexity when designing fuzzy rules. This leads the research to propose the following:
Proposition 3: High-level rules increase the interpretability of the fuzzy rules. Proposition 4: High-level rules reduce the complexity when designing fuzzy rules.
One possible disadvantage of using a reduced set of fuzzy rules it that inconsistencies between the fuzzy rules may occur (Alcalá et al., 2006; Lughofer, 2013; Gegov et al., 2017). However, as shown in this study, the concept of high-level rules, if implemented correctly, help to create a reduced set of rules without inconsistencies. The set is simply reduced but removing all the rules that are not relevant in the particular decision. This leads the research to propose the following:
Proposition 5: High-level rules reduce the set of fuzzy rules without creating inconsistencies
The approach of using domain experts to assign the consequent to the fuzzy rules is much easier when a reduced set of fuzzy rules have been designed compared to a complete set of fuzzy rules (Cpałka et al., 2016). A reduced set of fuzzy rules increase the interpretability of the rules but also comes with a risk of inconsistencies between them (Casillas et al., 2009; Gegov et al.,
2015). A complete set of fuzzy rules, on the other hand, decreases the interpretability of the rules but eliminates the risk of inconsistencies. Inconsistencies between the rules must be dealt with in order to generate accurate results and thus support the use of a more complete set of fuzzy rules. However, the method of having domain experts evaluating the fuzzy rules becomes unmanageable with a too high number of required fuzzy rules. The required number of rules increase exponentially with the number of linguistic variables and labels. Most domain experts find it complex and time consuming to evaluate plentiful of fuzzy rules (Herrera and Martínez, 2000). Based on these issues, the concept of linguistic variable weights was applied in this study. The advantage of this concept is that the consequent for each fuzzy rule in a complete set rapidly and automatically can be assigned without human interference. This eliminates the arduous task of assigning output values to all of the fuzzy rules. Thus, linguistic variable weights help reduce the complexity when designing fuzzy rules. One disadvantage of this approach is that a complete set of fuzzy rules is required which reduce the interpretability. This leads the research to propose the following:
Proposition 6: Linguistic variable weights reduce the complexity when designing fuzzy rules.
8 Conclusion and further research
The aim of this study was to investigate the possibility to increase the interpretability of fuzzy rules and to reduce the complexity when designing fuzzy rules. To achieve this, three novel fuzzy logic concepts (i.e., relative linguistic labels, high-level rules and linguistic variable weights) were conceived and implemented in a fuzzy logic system for reshoring decision-making. The system was configured in two ways in order to incorporate the novel concepts. The introduced concepts increase the interpretability of fuzzy rules and reduce the complexity when designing fuzzy rules while still providing accurate results. The interpretability of the fuzzy rules is increased when applying relative linguistic labels and high-level rules. The complexity when designing fuzzy rules is reduced by applying relative linguistic labels, high-level rules and linguistic variable weights.
An interesting area for further research would be to study the trade-off between interpretability and accuracy when applying high-level rules and linguistic variable weights. Another area for further research would be to develop a fuzzy logic system that also considers the sub-criteria level. The current set of criteria can also be expanded to include locational and risk factors. Other areas for further research would be to evaluate different types of membership functions in a reshoring context and to use multiple outputs. This study only involved one decision variable with two possible output values (i.e., evaluate/don’t evaluate). In the future it would be realistic to more than two output values. Another interesting area for further research would be to investigate the possibility of creating a script that automatically creates fuzzy rules (using intelligent techniques). A final interesting area for further research would be to compare and evaluate different types of fuzzy logic methods for reshoring decision-making.
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