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Faced with a fiercely competitive market environment, enterprises are investing huge resources, such as human resource, capital and material resources to research and develop new products. The product conceptual design determines the quality, cost and reliability of the final product and is considered to be the most important stage in the product life cycle. Considering the ambiguity of information in the product conceptual design process and the interactivity of experts in selecting conceptual products, a product conceptual design method based on intuitionistic fuzzy binary semantics group decision making is proposed, and a case is used to illustrate the proposed method.

New product development is a crucial process in maintaining a company’s competitive position and succeeding in dynamic markets. Conceptual design plays an important role in development of new products and redesign of existing products. Brunetti and Golob [

The use of platform-based product family design of assembled products has been reconceptualised into a framework of platform-based design of non-assembled products for the process industries [

Multi-objective optimization is used for the conceptual design of a new industrial process for the production of poly dimethyl ethers [

The uncertainties due to the subjective evaluations from engineers and customers are not considered in most existing conceptual design approaches. For conceptual design of mechatronics system, various tools like fuzzy delphi method, fuzzy interpretive structural modeling, fuzzy analytical network process and fuzzy quality function deployment can be used [

The concept of intuitionistic fuzzy set (IFS) was presented by Atanassov [

Combining the advantages of intuitionistic fuzzy set and binary semantics, intuitionistic fuzzy binary semantics can express the uncertainty and fuzziness in the decision-making process well. The definitions and operation rules of intuitionistic fuzzy binary semantics are given as follows.

Definition 1 Let S = { s i | i = 1 , 2 , ⋯ , g } be a language term set, S ˜ is the intuitionistic fuzzy binary semantic set generated by S, and S ˜ = { ( μ s i , v s i + 1 ) , μ , v ∈ [ 0 , 1 ] , μ + v ≤ 1 , i = 1 , 2 , ⋯ , g − 1 } . Element ( μ s i , v s i + 1 ) indicates that the membership degree of a scheme belongs to s_{i} is μ, and the membership degree belongs to s_{i}_{+1} is v.

Definition 2 Let S ˜ = { ( μ s i , v s i + 1 ) , μ , v ∈ [ 0 , 1 ] , μ + v ≤ 1 , i = 1 , 2 , ⋯ , g − 1 } be an intuitionistic fuzzy binary semantic set. We can define a mapping f, and which can convert S ˜ into corresponding interval values.

f ( μ s i , v s i + 1 ) = [ ( 1 − b ) + i , a + i ] (1)

where, a = 1 − μ , b = 1 − v . The subscript 1 , 2 , ⋯ , g represents the corresponding language variables. Then formula (1) can be further rewritten as:

f ( μ s i , v s i + 1 ) = [ v + i , 1 − μ + i ] = [ μ L , μ R ] (2)

where, u L = v + i , u R = 1 − μ + i .

During the process of group decision making, it is necessary to aggregate the evaluation information on the basis of the weight of each indicator, and also need to summarize the opinions of experts. Therefore, the intuitionistic fuzzy binary semantics should be integrated.

Definition 3 Let S ˜ = ( ( μ 1 s 1 , v 1 s 2 ) , ( μ 2 s 2 , v 2 s 3 ) , ⋯ , ( μ n s n , v n s n + 1 ) ) be an intuitionistic fuzzy binary semantic set, and W = { ω 1 , ω 2 , ⋯ , ω n } is the corresponding weight vector, where ω i ∈ [ 0 , 1 ] , and ∑ i = 1 n ω i = 1 . The weighted average set of intuitionistic fuzzy binary semantics is:

T W A ( s ˜ ) = ∑ i = 1 n ( ω i f ( μ s i , v s i + 1 ) ) = ∑ i = 1 n [ ω i μ L , ω i μ R ] (3)

The membership degrees of the intuitionistic fuzzy binary semantics can be converted into interval values by formula (1). Hence the operation rules of interval values can be adopted. Inspired by the reference [

Definition 4 If the intuitionistic fuzzy binary semantic sets R ˜ k = ( r ˜ 1 , r ˜ 2 , ⋯ , r ˜ n ) generated from the language terms set S = { s i | i = 1 , 2 , ⋯ , g } , where k = 1, 2, then the distance between the two sets R ˜ 1 and R ˜ 2 is:

d ( R ˜ 1 , R ˜ 2 ) = 1 n ( ∑ i = 1 , j = 1 n ( 1 2 ( | μ L ( r ˜ i ) − μ L ( r ˜ j ) | ) θ + 1 2 ( | μ R ( r ˜ i ) − μ R ( r ˜ j ) | ) θ ) 1 θ ) (4)

The reverse distance between R ˜ 1 and R ˜ 2 can be defined as:

T ( R ˜ 1 , R ˜ 2 ) = g − d ( R ˜ 1 , R ˜ 2 ) (5)

For formula (5), the larger the reverse distance T, the closer the set R ˜ 1 and R ˜ 2 are, and the more similar the two sets are. For R ˜ 1 and R ˜ 2 , the following properties hold.

1) 0 ≤ T ( R ˜ 1 , R ˜ 2 ) ≤ g ;

2) T ( R ˜ 1 , R ˜ 2 ) = T ( R ˜ 2 , R ˜ 1 ) ;

3) T ( R ˜ 1 , R ˜ 2 ) = g , if and only if R ˜ 1 and R ˜ 2 are completely similar;

4) T ( R ˜ 1 , R ˜ 2 ) = 0 , if and only if R ˜ 1 and R ˜ 2 are completely different.

Since the proof is simple, hence it is ignored here.

How to determine the weights of decision makers during the group decision process? The technique for order preference by similarity to ideal solution (TOPSIS) method is adopted in this paper. The basic principle is to calculate the distances between different opinions according to formulas (4) and (5). If the decision maker’s opinion differs greatly from the ideal optimal opinion, then a smaller weight is assigned to the decision maker. Otherwise, a larger weight is assigned.

Definition 5 The weight of the kth decision maker can be determined as,

λ k = T ( R ˜ k , R ˜ + ) + d ( R ˜ k , R ˜ − ) ∑ k = 1 l [ T ( R ˜ k , R ˜ + ) + d ( R ˜ k , R ˜ − ) ] , k = 1 , 2 , ⋯ , l . (6)

where, l indicates the number of decision makers; λ k represents the weight of the kth decision maker; T ( R ˜ k , R ˜ + ) denotes the inverse distance between the opinion of the kth decision maker and the ideal optimal opinion; d ( R ˜ k , R ˜ − ) indicates the distance between the opinion of the kth decision maker and the ideal worst opinion; R ˜ + is the ideal optimal opinion and R ˜ − is the ideal worst opinion. The distance and the reverse distance are simultaneously considered because for a cell in a large interval, the cell closest to the left border is not necessarily the farthest from the right border.

In practice, the selection of a conceptual product is generally based on the comprehensive optimal principle, that is, the combination of all aspects of indicators to choose the best comprehensive performance. In this paper, the idea of TOPSIS method is adopted, that is, the conceptual product is selected according to the reverse distance between each alternative and the ideal optimal scheme and also the distance from the ideal worst one. The alternative closest to the ideal optimal solution and the farthest from the ideal worst solution is the best solution.

Definition 6 There are two scheme X 1 and X 2 , if

T ( X 1 , R ˜ + ) + d ( X 1 , R ˜ − ) > T ( X 2 , R ˜ + ) + d ( X 2 , R ˜ − ) (7)

Then, the scheme X 1 is superior to the scheme X 2 .

Let X = { X 1 , X 2 , ⋯ , X m } be the set of alternative conceptual products, C = { C 1 , C 2 , ⋯ , C n } indicates the evaluation indicators, C_{j} denotes the jth indicator, j = 1 , 2 , ⋯ , n . Suppose l decision makers are invited to evaluate conceptual products, and E_{k} indicates the evaluation opinion of the kth decision maker, marked as E = { E 1 , E 2 , ⋯ , E l } . λ_{k} represents the weight of the kth decision maker, where ∑ k = 1 l λ k = 1 , k = 1 , 2 , ⋯ , l , and λ_{k} is a normalized weight vector. The evaluation opinions of decision makers about the indicators of the alternative conceptual products are expressed by intuitionistic fuzzy binary semantics. The framework of intuitionistic fuzzy binary semantic group decision process is shown in

The optimal conceptual product selection process is as follows.

Step 1: According to the attribute types of evaluation indices, the corresponding comment sets are selected. The linguistic variables in the comment sets represent the evaluation opinions of decision makers. For instance, a five-level comment set is defined as below:

For benefit-based indicators: the comment set is {s_{1} (very low), s_{2} (low), s_{3} (medium), s_{4} (high), s_{5} (very high)}. For cost-based indicators: the comment set is {s_{1} (very high), s_{2} (high), s_{3} (medium), s_{4} (low), s_{5} (very low)}.

It should be pointed out that different levels of comment sets, such as seven-level or nine-level, can be used according to actual conditions.

Step 2: The decision makers evaluate alternative conceptual products and thus the corresponding judgment matrices are formed. Assume that there are C j ( j = 1 , 2 , ⋯ , n ) indicators of X i ( i = 1 , 2 , ⋯ , m ) conceptual product need to be evaluated by E k ( k = 1 , 2 , ⋯ , l ) decision makers, and the evaluation opinion r ˜ i j k is denoted by intuitionistic fuzzy binary semantics, that is, r ˜ i j k = ( μ s i ( x i j ) , v s i + 1 ( x i j ) ) , x_{ij} represents the C_{j} attribute of the product X_{i}. The decision opinion of each decision maker constitutes an intuitionistic fuzzy binary semantic decision matrix R ˜ k = ( r ˜ i j k ) m × n .

R ˜ k = [ r ˜ 11 k r ˜ 12 k ⋯ r ˜ 1 m k r ˜ 21 k r ˜ 22 k ⋯ r ˜ 2 m k ⋮ ⋮ ⋱ ⋮ r ˜ n 1 k r ˜ n 2 k ⋯ r ˜ n m k ]

The intuitionistic fuzzy binary semantic decision matrix can be rewritten according to formulas (1) and (2), and the corresponding interval evaluation values are obtained. The opinions of decision makers are assembled according to formula (3).

Step 3: According to formulas (4) and (5), the distances and reverse distances between the opinions of decision makers and the virtual optimal/worst scheme are calculated.

Step 4: According to formula (6), the weights of decision makers can be achieved. The formula (3) is used to aggregate the opinions of the various decision makers, and the evaluation interval values of alternative conceptual products are acquired.

Step 5: Select the best conceptual product on the basis of formula (7).

Assume that there are four types of conceptual products have been selected through the process of product conceptual design, as shown in

A total of four decision makers further evaluated the four kinds of alternative conceptual products: product function C_{1}, product structure C_{2}, operation behavior C_{3}, and product cost C_{4}. The weights of indicators can be acquired by methods such as analytic network process, entropy method, and principal component analysis. This paper does not focus on the weights of indicators. Suppose these four indicators have the same weights:

W T = ( ω 1 , ω 2 , ω 3 , ω 4 ) T = ( 0.25 , 0.25 , 0.25 , 0.25 ) T

1) Determining the comment sets, as shown in

2) Assume that the evaluation information given by the four decision makers are as follows.

R ˜ 1 = ( 0.8 s 4 , 0.1 s 5 0.3 s 3 , 0.4 s 4 0.6 s 2 , 0.2 s 3 0.2 s 2 , 0.5 s 3 0.6 s 3 , 0.2 s 4 0.7 s 4 , 0.2 s 5 0.5 s 3 , 0.3 s 4 0.2 s 2 , 0.6 s 3 0.8 s 2 , 0.2 s 3 0.8 s 2 , 0.2 s 3 0.7 s 2 , 0.2 s 3 0.2 s 4 , 0.6 s 5 0.3 s 3 , 0.4 s 4 0.3 s 3 , 0.6 s 4 0.5 s 3 , 0.3 s 4 0.2 s 3 , 0.7 s 4 )

R ˜ 2 = ( 0.2 s 4 , 0.5 s 5 0.2 s 3 , 0.7 s 4 0.6 s 2 , 0.2 s 3 0.6 s 2 , 0.3 s 3 0.3 s 2 , 0.6 s 3 0.3 s 4 , 0.7 s 5 0.5 s 3 , 0.2 s 4 0.5 s 2 , 0.2 s 3 0.3 s 2 , 0.6 s 3 0.7 s 2 , 0.2 s 3 0.6 s 2 , 0.3 s 3 0.8 s 4 , 0.2 s 5 0.3 s 3 , 0.5 s 4 0.4 s 3 , 0.5 s 4 0.4 s 3 , 0.5 s 4 0.2 s 3 , 0.5 s 4 )

R ˜ 3 = ( 0.2 s 4 , 0.5 s 5 0.2 s 3 , 0.8 s 4 0.5 s 2 , 0.2 s 3 0.7 s 3 , 0.2 s 4 0.5 s 2 , 0.3 s 3 0.5 s 4 , 0.3 s 5 0.8 s 3 , 0.2 s 4 0.3 s 2 , 0.5 s 3 0.3 s 2 , 0.6 s 3 0.8 s 2 , 0.2 s 3 0.6 s 2 , 0.4 s 3 0.6 s 4 , 0.2 s 5 0.3 s 3 , 0.5 s 4 0.4 s 3 , 0.5 s 4 0.4 s 3 , 0.5 s 4 0.3 s 3 , 0.5 s 4 )

R ˜ 4 = ( 0.3 s 4 , 0.5 s 5 0.7 s 3 , 0.1 s 4 0.2 s 2 , 0.6 s 3 0.7 s 2 , 0.1 s 3 0.4 s 3 , 0.4 s 4 0.5 s 4 , 0.4 s 5 0.4 s 2 , 0.5 s 3 0.2 s 2 , 0.6 s 3 0.6 s 2 , 0.1 s 3 0.5 s 2 , 0.4 s 3 0.4 s 2 , 0.4 s 3 0.8 s 4 , 0.2 s 5 0.3 s 3 , 0.5 s 4 0.6 s 3 , 0.2 s 4 0.8 s 3 , 0.1 s 4 0.4 s 3 , 0.4 s 4 )

where, each row denotes the opinions of decision makers about a conceptual product, and each column represents the opinions of decision makers about an indicator.

Product Category | Product Characteristics |
---|---|

Class A Class B Class C Class D | Focus on functional design and improving functional innovation Focus on improving product structure performance Focus on cost savings Not specializing, but considering many aspects |

Evaluation indicators | Indicator type | Comment set |
---|---|---|

Product function C_{1} | Income type | S = {s_{1} (very low), s_{2} (low), s_{3} (medium), s_{4} (high), s_{5} (very high)} |

Product structure C_{2} | Income type | S = {s_{1} (very low), s_{2} (low), s_{3} (medium), s_{4} (high), s_{5} (very high)} |

Operation behavior C_{3} | Income type | S = {s_{1} (very low), s_{2} (low), s_{3} (medium), s_{4} (high), s_{5} (very high)} |

Product cost C_{4} | Cost type | S = {s_{1} (very high), s_{2} (high), s_{3} (medium), s_{4} (low), s_{5} (very low)} |

According to formulas (1) and (2), the above intuitionistic fuzzy binary semantic sets can be converted into:

f ( R ˜ 1 ) = ( [ 4.1 , 4.2 ] [ 3.4 , 3.7 ] [ 2.2 , 2.4 ] [ 2.5 , 2.8 ] [ 3.2 , 3.4 ] [ 4.2 , 4.3 ] [ 3.3 , 3.5 ] [ 2.6 , 2.8 ] [ 2.2 , 2.2 ] [ 2.2 , 2.2 ] [ 2.2 , 2.3 ] [ 4.6 , 4.8 ] [ 3.4 , 3.7 ] [ 3.6 , 3.7 ] [ 3.3 , 3.5 ] [ 3.7 , 3.8 ] )

f ( R ˜ 2 ) = ( [ 4.5 , 4.8 ] [ 3.7 , 3.8 ] [ 2.2 , 2.4 ] [ 2.3 , 2.4 ] [ 2.6 , 2.7 ] [ 4.7 , 4.7 ] [ 3.2 , 3.5 ] [ 2.2 , 2.5 ] [ 2.6 , 2.7 ] [ 2.2 , 2.3 ] [ 2.3 , 2.4 ] [ 4.2 , 4.2 ] [ 3.5 , 3.7 ] [ 3.5 , 3.6 ] [ 3.5 , 3.6 ] [ 3.5 , 3.8 ] )

f ( R ˜ 3 ) = ( [ 4.5 , 4.8 ] [ 3.8 , 3.8 ] [ 2.2 , 2.5 ] [ 3.2 , 3.3 ] [ 2.3 , 2.5 ] [ 4.3 , 4.5 ] [ 3.2 , 3.2 ] [ 2.5 , 2.7 ] [ 2.6 , 2.7 ] [ 2.2 , 2.2 ] [ 2.4 , 2.4 ] [ 4.2 , 4.4 ] [ 3.5 , 3.7 ] [ 3.5 , 3.6 ] [ 3.5 , 3.6 ] [ 3.5 , 3.7 ] )

f ( R ˜ 4 ) = ( [ 4.5 , 4.7 ] [ 3.1 , 3.3 ] [ 2.6 , 2.8 ] [ 2.1 , 2.3 ] [ 3.4 , 3.6 ] [ 4.4 , 4.5 ] [ 2.5 , 2.6 ] [ 2.6 , 2.8 ] [ 2.1 , 2.4 ] [ 2.4 , 2.5 ] [ 2.4 , 2.6 ] [ 4.2 , 4.2 ] [ 3.5 , 3.7 ] [ 3.2 , 3.4 ] [ 3.1 , 3.2 ] [ 3.4 , 3.6 ] )

According to formula (3), the information of evaluation indices are assembled, and the comprehensive evaluation intervals of the four types of conceptual products are obtained:

f ( R ˜ 1 ) = ( [ 3.05 , 3.28 ] [ 3.33 , 3.50 ] [ 2.80 , 2.88 ] [ 3.50 , 3.68 ] ) ,

f ( R ˜ 2 ) = ( [ 3.18 , 3.35 ] [ 3.18 , 3.35 ] [ 2.83 , 2.90 ] [ 3.50 , 3.68 ] ) ,

f ( R ˜ 3 ) = ( [ 3.43 , 3.60 ] [ 3.08 , 3.23 ] [ 2.85 , 2.93 ] [ 3.50 , 3.65 ] ) ,

f ( R ˜ 4 ) = ( [ 3.08 , 3.28 ] [ 3.23 , 3.38 ] [ 2.78 , 2.93 ] [ 3.30 , 3.48 ] ) ,

The virtual optimal and worst comprehensive evaluation interval values of the four types of conceptual products are:

f ( R ˜ + ) = ( [ 5.00 , 5.00 ] [ 5.00 , 5.00 ] [ 5.00 , 5.00 ] [ 5.00 , 5.00 ] ) , f ( R ˜ − ) = ( [ 1.00 , 1.00 ] [ 1.00 , 1.00 ] [ 1.00 , 1.00 ] [ 1.00 , 1.00 ] ) .

1) According to formulas (4) and (5), the distances between each alternative conceptual product and the virtual worst scheme and their reverse distances from the virtual optimal scheme were calculated, where θ = 2.

d ( R ˜ 1 , R ˜ ) = ( [ 1.84 , 2.17 ] [ 1.59 , 2.41 ] [ 2.16 , 1.84 ] [ 1.42 , 2.59 ] ) ,

d ( R ˜ 2 , R ˜ ) = ( [ 1.74 , 2.26 ] [ 1.74 , 2.26 ] [ 2.14 , 1.86 ] [ 1.42 , 2.59 ] ) ,

d ( R ˜ 3 , R ˜ ) = ( [ 1.49 , 2.51 ] [ 1.85 , 2.15 ] [ 2.11 , 1.89 ] [ 1.43 , 2.58 ] ) ,

d ( R ˜ 4 , R ˜ ) = ( [ 1.83 , 2.18 ] [ 1.70 , 2.30 ] [ 2.15 , 2.85 ] [ 1.61 , 2.39 ] ) ,

where, the first column denotes the reverse distances from the optimal scheme, and the second column represents the distances from the worst scheme, and each row indicates a type of conceptual product. Since the maximum distance of the semantic set elements is s 5 − s 1 = 4 in this paper, the distance and reverse distance should be ranged between 0 and 4. That is, for formula (5), it could be modified as:

T ( R ˜ 1 , R ˜ 2 ) = 4 − d ( R ˜ 1 , R ˜ 2 ) .

2) Calculating the weights of each decision maker on the basis of formula (6):

λ = ( 0.24 0.25 0.27 0.24 0.27 0.25 0.23 0.25 0.25 0.25 0.25 0.25 0.26 0.26 0.25 0.23 ) .

In the above matrix, each row denotes the weights of a conceptual product, and each column indicates the weights of a decision maker. That is to say, each alternative conceptual product has its own weight, and each decision maker has different weights for different alternative conceptual products. The reason is that each decision maker has a preference for each candidate conceptual product. This preference is reflected by the evaluation weight for different schemes. The distances between the comprehensive evaluation interval values and the ideal optimal/worst scheme are different. For each type of alternative conceptual product, the process of determining the weight of each decision maker in line with formula (6) is actually the process of gathering opinions of decision makers.

According to formula (3), the final comprehensive evaluation interval values of the four types of alternative conceptual products are obtained:

f ( X ) = ( [ 3.19 , 3.38 ] [ 3.20 , 3.37 ] [ 2.81 , 2.91 ] [ 3.45 , 3.62 ] )

3) According to formulas (4) and (5), the distances between each candidate conceptual product and the virtual optimal/worst scheme are calculated respectively. The results are as follows:

d ( X , R ˜ ) = ( [ 1.71 , 2.29 ] [ 1.72 , 2.29 ] [ 2.14 , 1.86 ] [ 1.47 , 2.54 ] )

where, the first column denotes the distance from the optimal scheme, and the second column represents the distance from the worst scheme. The sum of distance between each alternative conceptual product and the ideal optimal/worst conceptual product can be calculated:

T ( X , R ˜ + ) + d ( X , R ˜ − ) = ( 4.58 4.57 3.72 5.07 )

According to formula (7), the ranking of the four alternative conceptual products is: D > A > B > C, then the kind of conceptual product D is the optimal one. This is in line with the actual situation. Product D is not specialized, however, various factors are comprehensive considered.

The conceptual product is the prototype of the final product, which is expected to improve people’s consumption experience. The conceptual product design is based on the evaluation of the current product and on the assumption of future demand. Therefore, it is important to choose the best conceptual product. This paper proposes a conceptual product selection method based on intuitionistic fuzzy binary semantics group decision making, which can better deal with the fuzziness and uncertainty in the decision making process, and can integrate the opinions of various decision makers to select the optimal conceptual product as well. The case study shows that the proposed method can solve this kind of problem well.

This work was supported by “the National Natural Science Foundation of China (No. 71771023)”.

The authors declare no conflicts of interest.

Zhou, X.G., Wu, Y.P. and Polochova, V. (2019) Product Conceptual Design Method Based on Intuitionistic Fuzzy Binary Semantics Group Decision Making. Journal of Service Science and Management, 12, 742-754. https://doi.org/10.4236/jssm.2019.126050