Using a fuzzy multiple criteria decision-making method to evaluate personal diversity perception to work in a diverse workgroup

2.1 The personality elements

Research suggests that all personality measures can be categorized under the Big Five model framework, which includes the dimensions of conscientiousness, agreeableness, extraversion, neuroticism, and openness to experience [13, 14]. Rothmann and Coetzer [15] used statistical analysis to investigate the Big Five personality dimensions and job performance. The five dimensions of the five-factor model of personality were described by Rothmann and Coetzer [15] as follows: neuroticism is a dimension of normal behavior relating to adverse effects such as sadness, fear, embarrassment, anger, guilt, and disgust; extraversion refers to sociability, emotionally optimistic, and high level of interaction; openness to experience includes intellectual curiosity, liberal values, aesthetic sensitivity, and independence of judgment; agreeableness indicates that a person is fundamentally altruistic, sympathetic to others, and eager to help them, believing that others will be equally helpful; and conscientiousness, which refers to a person who is purposeful, strong-willed, and determined.

2.2 Value elements and attitude elements

Affective commitment to the workgroup refers to the positive emotional state of sharing beliefs and values. Job satisfaction and attitudinal commitment are treated as specific reflections of a general attitude by Harrison et al. [16] because each is a fundamental evaluation of an individual’s job experiences. They conceptualized both job satisfaction and organizational commitment as indicating an underlying overall job attitude. Meta-analysis and structural equations indicated that overall job attitude strongly predicted desirable contributions made to an individual’s work role. Lourenco et al. [17] indicated that people learn by modifying their behavior and attitudes to meet external requirements.

In contrast, whereas teams learn by adapting their strategies and modes of operating to internal and external demands. Member satisfaction is defined as the satisfaction level exhibited by each member relating to different aspects of group function, such as quality of the relationship or effective acceptance of team decisions [17]. Value is another deep-level trait in diversity that we consider. The value of receiving a good project grade is referred to as outcome importance. The differences in task meaningfulness and outcome importance are related to overall perceived deep-level diversity [12]. Meaningfulness completely mediates the task significance and performance link. If the task is perceived as meaningful, people tend to have better performance at work [18].

2.3 Substantive and affective conflict

Substantive conflict can enhance cognitive tasks’ performance, and affective conflict can promote turnover [10]. Using a middle-ground approach, Pelled ([10], p.620) defined substantive conflict and affective conflict in the following manner: “Substantive conflict is the perception among group members that there are disagreements about task issues, including the nature and importance of task goals and key decision areas, procedures for task accomplishment, and the appropriate choice for action. Affective conflict is the perception among group members that there are interpersonal clashes characterized by anger, distrust, fear, frustration, and other forms of negative affect”. The perceived differences among group members may become a source of conflict in workgroups [9]. Sjöberg [19] studied risk and willingness to work using factor analysis and pointed out that willingness to work was related to work performance in terms of both quality and quantity. Collaboration provides a mechanism for a collective of employees committed to the organization and its goals to work together toward organizational success [20]. The team outcome and successful collaboration are based on four critical components: “right goal, right culture, right leadership, and right people” [21].

Different methods could be applied to deal with personal diversity perception. Mousa et al. [22] applied t-test and structural equation modeling (SEM) to investigate diversity management perceptions at workplaces regarding gender. Lee et al. [5] also used SEM to test the influence of diversity climate on turnover intentions. Rabl et al. [23] studied employees’ perception of diversity and behavior using statistical methods such as confirmatory factor analysis and hierarchical multiple regression. However, according to the analysis mentioned above, it is seen that there are various criteria to consider when evaluating diversity workgroups perception from an individual perspective, including qualitative and quantitative ones. A multiple criteria framework for investigating personal diversity perception can be seen in Fig. 2. The individual’s diversity perception and willingness to work in diverse workgroups have not been evaluated by applying fuzzy MCDM. This study aims to fill this gap by using a proposed fuzzy MCDM method to investigate personal elements, job-related values, attitude, and the willingness to work in different diverse workgroups through a questionnaire survey of 42 participants, including 32 sufficient work experience decision-makers and 10 students.

2.4 Fuzzy MCDM

Fuzzy numbers and MCDM techniques have been employed in various studies [24] and prove the advantages. The methods such as Analytic Hierarchy Process (AHP), Technique of Order Preference Similarity to the Ideal Solution (TOPSIS), or FST are powerful to solve multicriteria problems, produce quality decision making, and select best alternatives due to its careful consideration of criteria [25]. Moreover, the FST can address subjectivity in consistently and reliably assessing team integration performance in teamwork projects. Numerous fuzzy MCDM techniques have been developed in recent years. Zhang et al. [26] considered a new type of group decision-making problems in which experts provide interval fuzzy preference relations over alternatives under a social network environment and proposed a new model to help experts reach consensus. Zhang et al. [27] constructed a new fuzzy rough set (FRS) model based on fuzzy α-neighborhood operator and proposed three different sorting decision-making schemes by PROMETHEE II method using fuzzy-valued information systems. Numerical experiments demonstrated the effectiveness of their method. Ye et al. [28] established a probabilistic rough fuzzy set model and MCDM-based 3WD (three-way decisions) model by means of the constructed fuzzy ɛ-neighborhood classes, and a project investment example was used to demonstrate the validity of the proposed method. Zhan et al. [29] proposed a 3WD model based on ELECTRE I and the effectiveness of the proposed 3WD method was demonstrated by solving a problem of enterprise project investment target selections, comparative analysis and two experimental evaluations. Ye et al. [30] expanded the TOPSIS method with FRS based on a fuzzy β-neighborhood operator as a new way to handle MCDM problems. Aiming to explore the 3WD concept under a hesitant fuzzy (HF) environment, Wang et al. [31] applied the 3WD theory and used the ELECTRE method to establish an objective calculation process of the HF conditional probability and the effectiveness of the proposed method was verified by solving an infectious disease diagnosis problem. The 3WD theory research focuses on designing three decision-making options of acceptance, rejection, and non-commitments as an effective way to reduce decision risks.

Personal can be biased, and consequently, it can limit an individual’s ability to make a decision. In Manoharan et al.’s [32] work about employees’ performance, they proved the advantage of fuzzy numbers in reproducing individuals’ subjective thinking by using weight vector or decision matrix to translate linguistic and ill-defined judgments of human beings. Turskis et al. [33] used a new fuzzy hybrid MCDM to solve personnel assessment problems and indicated that crisp values could not model personnel selection because of data uncertainty. Fuzzy MCDM methods are effective in solving uncertain problems. Kazancoglu and Ozan-Ozen [34] revealed that teamwork is another principal concept for organizations transforming to Industry 4.0 and indicated that fuzzy logic helps to represent and deal with impreciseness in the decision-making process. In 2019, Zhang et al. [35] proposed a linguistic distribution based approach to deal with multiattribute large-scale group decision making problems with multigranular unbalanced hesitant fuzzy linguistic information. An example of the selection of subway lines was used to demonstrate the feasibility of the proposed approach. Zhang et al. [36] developed an approach for two-sided matching decision-making (TSMDM) via multi-granular hesitant fuzzy linguistic term sets and incomplete criteria weight information. An example for the matching of green building technology supply and demand was provided to demonstrate the feasibility of the proposed approach. From the literature review, fuzzy MCDM has been proven to be an effective method in evaluating and ranking alternatives under uncertain conditions, especially in relevant human resource problems. However, ranking methods are usually needed to defuzzify the final fuzzy evaluation values from the fuzzy MCDM models for better executing the decision-making procedure.

Ranking fuzzy numbers using the centroid method [37, 38] and the maximizing and minimizing set [39] are important concepts and have been widely studied and applied in fuzzy MCDM models. A review of the centroid applications can be seen in [40]. Chu and Nguyen [41] suggested a ranking method of the relative maximizing and minimizing sets to improve the Chen [39] method. However, Chu and Nguyen’s [41] method can be complicated if applying to rank nonlinear fuzzy numbers. Hence, we suggest using the mean of relative values to rank fuzzy numbers to resolve this limitation. A numerical comparison with some other ranking methods is made to display the advantages of the proposed ranking method. Finally, an empirical example in personal diversity perception practice is conducted to verify the feasibility of the proposed fuzzy MCDM method and some discussions on results are provided.

3.1 Fuzzy sets

A = {(x, f _A  (x)) |x ∈ U} where U is the universe of discourse, x is an element in U, A is a fuzzy set in U, f _A  (x) is the membership function of A at x [42]. The larger f _A  (x), the stronger the grade of membership for x in A.

3.2 Fuzzy numbers

A real fuzzy number A is described as any fuzzy subset of the real line R with a membership function f _A that possesses the following properties [43]

f _A is a continuous mapping from R to [0,1];

In this paper, the triangular fuzzy numbers will be used. The fuzzy number A is a triangular fuzzy number if its membership function f _A is given as follows [44]. f A ( x ) = { ( x - a ) / ( b - a ) , a ⩽ x ⩽ b , ( x - c ) / ( b - c ) , b ⩽ x ⩽ c , 0 , otherwise , where a , b and c are real numbers .(1)

The α-cuts of fuzzy number A can be defined as A ^α  = {x|f _A  (x) ⩾ α} , α ∈ [0, 1], where A ^α is a non-empty bounded closed interval is contained in R and can be denoted by A α = [ A l α , A u α ] , where A l α and A u α are lower and upper bounds, respectively [42].

3.4 Arithmetic operations on fuzzy numbers

Given fuzzy numbers A and B, A, B ∈ R⁺, A α = [ A l α , A u α ] and B α = [ B l α , B u α ] . By the interval arithmetic, some main operations of A and B can be expressed as follows [42]. ( A ⊕ B ) α = [ A l α + B l α , A u α + B u α ](2) ( A ⊖ B ) α = [ A l α - B u α , A u α - B l α ](3) ( A ⊗ B ) α = [ A l α · B l α , A u α · B u α ](4) r ( A ) α = [ r · A l α , r · A u α ] , r ∈ R +(5)

A linguistic variable is a variable whose values are expressed in linguistic terms. A linguistic variable is a beneficial concept for dealing with too complex situations or not well-defined to be reasonably described by traditional quantitative expressions [6, 45]. The present work assumes that decision-makers have reached a consensus in rating alternatives versus qualitative criteria in the proposed fuzzy MCDM model using linguistic values such as Strongly dissimilar (SD)/Strongly not prefer (SNP), Dissimilar (D)/Not prefer (NP), Somewhat dissimilar (SWD)/Somewhat not prefer (SWNP), Moderate (M), Somewhat similar (SWS)/Somewhat prefer (SWP), Similar (S)/Prefer (P), Strongly similar (SS)/Strongly prefer (SP). It also assumes that these linguistic values can be represented by triangular fuzzy numbers such as SD/SNP=(0.1,0.2,0.25), D/NP=(0.2,0.3,0.4), SWD/SWNP=(0.25,0.4,0.5), M=(0.4,0.55,0.7), SWS/ SWP=(0.6,0.7,0.85), S/P=(0.7,0.8,0.9) and SS/SP= (0.85,0.9,1). Moreover, decision-makers are assumed to have agreed to weight each criterion using linguistic values such as Absolutely Unimportant (AU), Unimportant (UI), Less Important (LI), Important (IM), More Important (MI), Very Important (VI) and Absolutely Important (AI), which can also be represented by triangular fuzzy numbers such as AU=(0.1,0.2,0.25), UI=(0.2,0.3,0.4), LI=(0.25,0.4,0.5), IM=(0.4,0.55,0.7), MI=(0.6,0.7, 0.85), VI=(0.7,0.8,0.9) and AI=(0.85,0.9,1). This work’s proposed fuzzy MCDM model assumes that decision-makers are honest in rating alternatives versus qualitative criteria and in weighting those criteria.

4.1 Average weights

Let w _jt  = (o _jt , p _jt , q _jt ), w _jt  ∈ R⁺, j = 1, . . . , n, t = 1, . . . , k, be weights assigned by decision-maker D _t to criterion C _j . w _j  = (o _j , p _j , q _j ) is averaged weight of C_j assessed by k decision-makers. The average operator is used to aggregate fuzzy weights and fuzzy ratings because it is intuitive and easy to calculate. w j = ( 1 k ) ⊗ ( w j 1 ⊕ . . . ⊕ w jt ⊕ . . . . ⊕ w jk )(6) where o j = ∑ t = 1 k o jt k , p j = ∑ t = 1 k p jt k , q j = ∑ t = 1 k q jt k .

Let x _ijt  = (a _ijt , b _ijt , c _ijt ) , i = 1, . . . , m, j = 1, . . . , h, t = 1, . . . , k, be the rating assigned to an alternative A _i under criterion C _j by a decision-maker D _t . Aggregated rating x _ij  = (a _ij , b _ij , c _ij ) is: x ij = ( 1 k ) ⊗ ( x ij 1 ⊕ . . . ⊕ x ijt ⊕ . . . . ⊕ x ijk )(7) where a ij = ∑ t = 1 k a ijt k , b ij = ∑ t = 1 k b ijt k , c ij = ∑ t = 1 k c ijt k .

Suppose r _ijt  = (d _ijt , e _ijt , f _ijt ) is the value of an alternative A _i ,  i = 1, 2, . . . , m, versus a quantitative criterion C _j , j = h + 1, . . . , n, by a decision-maker D _t . The average value of an alternative A _i ,  i = 1, 2, . . . , m, versus a benefit (B) criterion or a cost (C) criterion can be produced r _ij  = (d _ij , e _ij , f _ij ) by Equation (7). The normalization is completed by approach from Chu and Le [46], which preserves the property where the ranges of normalized triangular fuzzy numbers belong to [0,1]. The normalized value x_ij can be as x ij = ( d ij - d j * s j * , e ij - d j * s j * , f ij - d j * s j * ) , j ∈ B ,(8) x ij = ( f j * - f ij s j * , f j * - e ij s j * , f j * - d ij s j * ) , j ∈ C ,(9) where d j * = min i d ij , f j * = max i f ij , s j * = f j * - d j * , i = 1, . . . , m, j = h + 1, . . . , n, x _ij  = (a _ij , b _ij , c _ij ).

The membership function of the final fuzzy evaluation value of each alternative can be denoted as: G i = 1 h ∑ j = 1 h ( w j ⊗ x ij ) + 1 g - h ∑ j = h + 1 g ( w j ⊗ x ij ) + 1 n - g ∑ j = g + 1 n ( w j ⊗ x ij )(10)

By Equations (2)–(5), 1 h ∑ j = 1 h ( w j α ⊗ x ij α ) can be as: [ ] 1 h ∑ j = 1 h ( p j - o j ) ( b ij - a ij ) α 2 + 1 h ∑ j = 1 h [ a ij ( p j - o j ) + o j ( b ij - a ij ) ] α + 1 h ∑ j = 1 h a ij o j , 1 h ∑ j = 1 h ( p j - q j ) ( b ij - c ij ) α 2 + 1 h ∑ j = 1 h [ c ij ( p j - q j ) + q j ( b ij - c ij ) ] α + 1 h ∑ j = 1 h c ij q j [ ](11)

Similarly, 1 g - h ∑ j = h + 1 g ( w j α ⊗ x ij α ) , 1 n - g ∑ j = g + 1 n ( w j α ⊗ x ij α ) can also be derived the same to Equation (11).

The assumption symbols A _i , B _i , C _i , D _i , O _i , P _i , Q _i , which are used to shorten the Equations (10)–(11), can be seen in Appendix I.

Then, the following equation is obtained: [ A i α 2 + B i α + O i , C i α 2 + D i α + Q i ](12)

The membership function G _i can be derived from Equation (12) as follows [46]: f G i L ( x ) = - B i + [ B i 2 + 4 A i ( x - O i ) ] 1 / 2 2 A i , O i ⩽ x ⩽ P i ,(13) f G i R ( x ) = - D i - [ D i 2 + 4 C i ( x - Q i ) ] 1 / 2 2 C i , P i ⩽ x ⩽ Q i .(14) For convenience , G i = ( A i , B i , C i , D i , O i , P i , Q i ) , i = 1 ∼ m .(15)

Chu and Nguyen [41] proposed a method to improve Chen’s [39] maximizing and minimizing set in ranking fuzzy numbers. However, the procedure of their method becomes complicated if applying to rank nonlinear fuzzy numbers. To resolve this limitation, we suggest a simpler method by using the mean of relative values to rank fuzzy numbers. First, Chu and Nguyen’s [41] relative maximizing and minimizing sets are introduced as follows.

Suppose there are n fuzzy numbers A _i  = (a _i , b _i , c _i ) , i = 1, . . , n, n ⩾ 2, f _{A i}  ∈ R. Suppose there are n fuzzy numbers A _i  = (a _i , b _i , c _i ) , i = 1, . . , n, n ⩾ 2, f _{A i}  ∈ R. x_min = inf S, x_max = sup S, S = U i = 1 n S i , S i = { x | f A i ( x ) > 0 } .

The relative maximizing and minimizing sets method is presented as follows. Suppose fuzzy numbers A _p  = (a _p , b _p , c _p ) and A _q  = (a _q , b _q , c _q ) are added to the right and left sides of the above n fuzzy numbers A _i  = (a _i , b _i , c _i ) , i = 1, . . , n, , respectively. Suppose x_min = a₁, x_max = c _n , c _p  ⩾ x_max and a _q  ⩽ x_min. Let δ _R  = c _p  - x_max and δ _L  = x_min - a _q , where x_max = c _n , x_min = a₁, δ _R  ⩾ 0, δ _L  ⩾ 0. The new supremum element is obtained as x max ′ = x max + δ where δ = max {δ _L , δ _R }. The new infimum element is obtained as x min ′ = x min - δ where δ = max {δ _L , δ _R }.

The relative maximizing set M′ is defined as: f M ′ ( x ) = { ( x R i - ( x min - δ ) ( x max + δ ) - ( x min - δ ) ) k 0 , otherwise , ( x min - δ ) ⩽ x R i ⩽ ( x max + δ )(16)

The relative minimizing set N′ is defined as: f N ′ ( x ) = { ( x L i - ( x max + δ ) ( x min - δ ) - ( x max + δ ) ) k 0 , otherwise , ( x min - δ ) ⩽ x L i ⩽ ( x max + δ )(17)

The value of k can be varied to suit the application. Herein, k is set to 1.

The first right relative utility U _{R i1}  (A _i ) is defined in Equation (18); the first left relative utility U _{L i1}  (A _i ) is defined in Equation (19), the second left relative utility U _{L i2}  (A _i ) is defined in Equation (20), and the second right relative utility U _{R i2}  (A _i ) is defined in Equation (21). Finally, the total relative utility of each A _i is defined as Equation (22) to rank fuzzy numbers. A fuzzy number is larger if its total relative utility is larger. U R i 1 ( A i ) = sup ( f M ′ ( x ) ∧ f A i R ( x ) ) , i = 1 , . . , ( n + 2 )(18) U L i 1 ( A i ) = sup ( f N ′ ( x ) ∧ f A i L ( x ) ) , i = 1 , . . . , ( n + 2 )(19) U L i 2 ( A i ) = sup ( f M ′ ( x ) ∧ f A i L ( x ) ) , i = 1 , . . , ( n + 2 )(20) U R i 2 ( A i ) = sup ( f N ′ ( x ) ∧ f A i R ( x ) ) , i = 1 , . . . , ( n + 2 )(21) U T ′ ( A i ) = 1 4 [ U R i 1 ( A i ) + ( 1 - U L i 1 ( A i ) ) + U L i 2 ( A i ) + ( 1 - U R i 2 ( A i ) ) ] , i = 1 , . . . , ( n + 2 )(22)

The relative maximizing and minimizing sets method is very complicated if used to rank nonlinear fuzzy numbers such as the one in Equations (13)–(14). In this work, we suggest the mean of relative values to reduce the computational procedure.

The first right relative value x _{R i1} can be obtained by Equation (18) as follows. x R i 1 - ( x min - δ ) ( x max + δ ) - ( x min - δ ) = - D i - [ D i 2 + 4 C i ( x R i - Q i ) ] 1 / 2 2 C i ⇒ 4 C i 2 x R i 1 2 + 4 C i x R i 1 { - 2 C i ( x min - δ ) + D i [ ( x max + δ ) - ( x min - δ ) ] - [ ( x max + δ ) - ( x min - δ ) ] 2 } + 4 C i 2 ( x min - δ ) 2 - 4 C i D i ( x min - δ ) [ ( x max + δ ) - ( x min - δ ) ] + 4 C i Q i [ ( x max + δ ) - ( x min - δ ) ] 2 = 0(23) Let E i 1 = - 2 C i ( x min - δ ) + D i [ ( x max + δ ) - ( x min - δ ) ] - [ ( x max + δ ) - ( x min - δ ) ] 2(24) F i 1 = 4 C i 2 ( x min - δ ) 2 - 4 C i D i ( x min - δ ) [ ( x max + δ ) - ( x min - δ ) ] + 4 C i Q i [ ( x max + δ ) - ( x min - δ ) ] 2(25) The first right relative value x _{R i1} can be obtained by applying Equations (24)–(25) to Equation (23) as shown in Equation (26). x R i 1 = - E i 1 ± [ E i 1 2 - F i 1 ] 1 / 2 2 C i ( negative value is not allowed . )(26) Similarly, the first left relative value x _{L i1} can be obtained by Equation (19) as follows. x L i 1 − ( x m a x + δ ) ( x min − δ ) − ( x m a x + δ ) = − B i + [ B i 2 + 4 A i ( x L i − O i ) ] 1 / 2 2 A i ⇒ 4 A i 2 x L i 1 2 + 4 A i x L i 1 { - 2 A i ( x max + δ ) + B i [ ( x min - δ ) - ( x max + δ ) ] - [ ( x min - δ ) - ( x max + δ ) ] 2 } + 4 A i 2 ( x max + δ ) 2 - 4 A i B i ( x max + δ ) [ ( x min - δ ) - ( x max + δ ) ] - 4 A i O i [ ( x min - δ ) - ( x max + δ ) ] 2 = 0(27) Let M i 1 = - 2 A i ( x max + δ ) + B i [ ( x min - δ ) - ( x max + δ ) ] - [ ( x min - δ ) - ( x max + δ ) ] 2(28) N i 1 = 4 A i 2 ( x max + δ ) 2 - 4 A i B i ( x max + δ ) [ ( x min - δ ) - ( x max + δ ) ] - 4 A i O i [ ( x min - δ ) - ( x max + δ ) ] 2(29) The first left relative value x _{L i1} can be obtained by applying Equations (28)–(29) to Equation (27) as shown in Equation (30). x L i 1 = - M i 1 ± [ M i 1 2 - N i 1 ] 1 / 2 2 A i ( Negative value is not allowed . )(30) Similarly, the second left relative value x _{L i2} can be obtained as in Equation (34), and the second right relative value x _{R i2} can be obtained as shown in Equation (38). The detailed derivations of x _{L i2} and x _{R i2} can be seen in Appendix II. x L i 2 = - M i 2 ± [ M i 2 2 - N i 2 ] 1 / 2 2 A i ( Negative value is not allowed . )(34) x R i 2 = - E i 2 ± [ E i 2 2 - F i 2 ] 1 / 2 2 C i ( Negative value is not allowed . )(38) Finally, the mean of relative values A _i can be obtained by averaging Equations (26), (30), (34), and (38) as shown in Equation (39). The fuzzy number A _i is larger if its mean of relative values MR (A _i ) is larger. MR ( A i ) = 1 4 ( x R i 1 + x L i 1 + x L i 2 + x R i 2 )(39)

A flowchart in Fig. 1 is provided to clearly present the procedure of the proposed method.

OPEN IN VIEWER

Fig. 1

Procedure of the proposed method.

6.1 Participants

Data was collected through online and offline surveys in Taiwan and Estonia. The first pilot study was conducted online with participants (in-program students or alumni) from the Global Master of Business Administration program at a university in Taiwan to test the feasibility of the fuzzy MCDM method in measuring diversity perception. The second survey was implemented in three of Estonia’s startup programs with different workgroups through an online questionnaire. The survey decision-makers were diverse in terms of nationality, gender, working field, and working experience. They come from various countries, including Vietnam, Indonesia, Iran, Estonia, Sweden, France, etc. There were 10 students and 32 participants who have sufficient work experience. Among these 32 decision-makers, 6 of them are managers (18.75%), 2 are trained professionals (6.25%), 13 are skilled employees (40.625%), 6 are support staffs (18.75%), 3 are self-employed (9.375%), and other (6.25%). The highest percentage of the years of experience is 1–5 years (18 people, accounts for 56.25%), followed by 11-15 years (6 people, represents 18.75%) and 6–10 years (4 people, represents 12.5%), then 1–12 months and over-15-year account for 6.25% each.

Participants were asked about their perception of diversity and willingness to work in four diverse workgroups, in which positive triangular fuzzy numbers represented ratings for qualitative and quantitative criteria. The four groups were as follows: Group A₁ included people from the same country and same working field; Group A₂ included people from different countries but the same working field; Group A₃ included people from the same country but different working fields; Group A₄ included people from different countries and different working fields. For the perception of diversity at a deep level, the selected criteria are structured as shown in Fig. 2. In quantitative criteria, collaboration numbers of group members and group tenure are defined as Benefit (B). Substantive conflict and Affective conflict are defined as Cost (C).

OPEN IN VIEWER

Fig. 2

Criteria in structure.

After eliminating incomplete responses, the study was first implemented considering 42 valid samples, then the comparison between a group of students and participants working in the industry was examined. The comparison aims to gain a deeper understanding of the diversity perception from different categories and assist the decision-making process; thenceforth, the better choice will be made based on the differentiation when grouping people for more excellent performance in workgroups.

The ratings of alternatives in terms of qualitative and quantitative criteria by 42 decision-makers are shown in Tables 2 and 4, respectively (see Appendix III and Appendix IV, respectively, for details). The average ratings of alternatives in Tables 3 and 5 are obtained via Equation (7). The normalized ratings of alternatives versus quantitative criteria are then obtained by Equations (8)–(9) as shown in Table 6. The weights given by decision-makers (see Table 7 in Appendix V for details) are averaged by Equation (6) and shown in Table 8. Through Equations (10)–(15), the membership functions of the final fuzzy evaluation values are obtained and displayed in Table 9.

Through Equations (26), (30), (34), and (38), the values of x _{R i1} , x _{L i1} , x _{L i2} and x _{R i2} of alternatives (U _T  (A _i ) , i=1,  ...  , 4) can be obtained, shown in Table 10. The ranking values of four alternatives A₂ > A₁ > A₃ > A₄ are produced by Equation (39).

To further test the proposed method’s consistency and applicability, the concept of four relative utilities from Chu and Nguyen [41] is applied to obtain the ranking as displayed in Table 11. The ranking orders of the two methods are the same as A₂ > A₁ > A₃ > A₄. The proposed ranking method is as effective as that of Chu and Nguyen [41] in ranking the alternatives under the proposed fuzzy MCDM method; however, the proposed ranking method has a simpler algorithm, making decision-making more efficient. Because A₂has the highest value, participants are more willing to work in Group A₂, followed by Groups A₁and A₃. Participants had the slightest willingness to work in Group A₄.

The result indicates that decision-makers prefer to work in a group with people from different countries but with the same working field, such as A₂. This result is consistent with Ayub and Jehn’s [9] result that diversity is desirable if multiple dissimilar nationalities are included. At least for their performance, the participants may feel challenged to prove themselves superior to other members. Our result also reveals that decision-makers are less willing to work in groups with people from different countries with different working fields, such as A₄. This result is in line with Velten and Lashley’s [47] result that deep-level dissimilarities, such as different values, mentality, or attitudes, can generate conflict and demotivation in the workplace. In contrast, cultural diversity can make the workplace more challenging and exciting.

In addition, the comparison between 10 students and 32 industrial experienced working people is as shown in Table 12. The ranking values of four alternatives from students is A₂ > A₃ > A₁ > A₄ while the ranking from experienced participants is A₂ > A₁ > A₃ > A₄. Both groups have the same highest and lowest preference of working in group A₂ and group A₄, respectively. The main difference is that students preferentially choose to work in Group A₃ with team members from the different working sectors over Group A₁. In contrast, people working in the industry prefer to work in Group A₁over Group A₃. With different working fields and functional backgrounds, team members can share their knowledge and exchange information. However, having a diverse functional background can lead to conflict because of a different specialization perspective. As indicated in Brodbeck et al. [48] research, a diverse functional background group can broaden member’s knowledge. However, it is not censorious and adequate to the group’s decision quality. A study of top management team diversity and firm performance from Boone and Hendriks [49] corroborated that the collaboration costs are likely more substantial than the advantages from knowledge distribution. Therefore, people with more experience in the industry will understand this situation better than students, which supports our result that the ranking of A₁ is higher than A₃ for employees with working experience. However, the ranking of A₁ is lower than A₃ for students who do not have sufficient work experience. Nevertheless, forming a group depends on specific tasks and circumstances; hence the group ranking is slightly different. The results in this study from 42 decision-makers and 32 experienced decision-makers are consistent with decision-making literature.

From the survey, 32 experienced decision-makers mostly prefer to work in a group of 1–4 members or 5–7 members, no matter whom they work with. Regarding group tenure, working from 4 to 10 months is the highest rated compared to other tenures ()40.625% to Group A1, 46.875% to Group A2, 53.125% to Group A3, and 50% to Group A4. More details of the number of group members and project tenure reference can be seen in Table 13.