Development of a multicriteria decision-making model for evaluating hybrid offspring in the sweetpotato (Ipomoea batatas L.) breeding process

Abstract

Sweetpotato variety breeding is always a long process. Screening of hybrid offspring is dominated by empirical judgment in this process. Data analysis and decision fatigue have been troubling breeders. In recent years, the low-efficiency screening mode has been unable to meet the requirements of sweetpotato germplasm innovation. Therefore, it is necessary to construct a high-efficiency method that can screen germplasms for different usages, for mining elite genotypes, and to create dedicated sweetpotato varieties. In this article, the multicriteria decision-making (MCDM) model was constructed based on six agronomic traits, including fresh root yield, vine length, vine diameter, branch number, root number and the spatial distribution of storage roots, and five quality traits, including dry matter content, marketable root yield, uniformity of roots, starch content and the edible quality score. Among these, the edible quality score was calculated by using fuzzy comprehensive evaluation to integrate the sensory scores of color, odor, sweetness, stickiness and fibrous taste. The MCDM model was compared with the traditional screening method via an evaluation in 25 sweetpotato materials. The interference of subjective factors on the evaluation results was significantly reduced. The MCDM model is more overall, more accurate and faster than the traditional screening method in the selection of elite sweetpotato materials. It could be programmed to serve the breeders in combination with the traditional screening method.

Introduction

Sweetpotato (Ipomoea batatas (L.) Lam.), which belongs to the Ipomoea genus of the Convolvulaceae family, is an annual or perennial trailing herb (Ekwealor et al. 2015). It ranks seventh in world food production after wheat, rice, maize, potato, barley, and cassava (Abong et al. 2020). Due to its high yield, wide adaptability and stress resistance (Truong et al. 2018), sweetpotato has been considered an important food crop to alleviate the food crisis for disaster relief and to tide over populations during lean years in poor areas (Iese et al. 2018). Meanwhile, sweetpotato is also a food with abundant nutrients (Kwak 2019). Its storage root is mainly composed of starch (Lu et al. 2020), soluble sugar (Wei et al. 2017), dietary fibre (Liu et al. 2020b), protein (Mu et al. 2009), fat (Rondhi et al. 2020), vitamins (Neela and Fanta 2019) and minerals (Jongstra et al. 2020). It also contains functional components such as polysaccharides (Tang et al. 2019), polyphenols (Makori et al. 2020), polyterpenes (Suematsu et al. 2020) and glycoproteins (Tian et al. 2019), which are beneficial to the human body. Therefore, the usage of sweetpotato has evolved from a food crop to a diversified industrial crop, such as the raw material of industrial processing, food processing and health product processing (Adu-Kwarteng et al. 2021, Ju et al. 2017, Vithu et al. 2019). It is apparent that today’s old sweetpotato cultivars cannot meet the needs of all the new usages. The way to break through the bottleneck problem of raw material supply in the sweetpotato industry is germplasm innovation.

As an allohexaploid with complex genetic information (Yang et al. 2017), sweetpotato improvement is still dominated by conventional breeding (Katayama et al. 2017, Lestari et al. 2019). Currently, sweetpotato crossbreeding is generally divided into two methods: directional hybridization (hand pollination) and designed group hybridization (natural open pollination) (Yi et al. 2018). In China, the five-round screening method is typically used for screening hybrid offspring, which includes primary seed selection, secondary seed selection, line identification, primary line comparison and secondary line comparison (Shen et al. 2020). It can be seen that sweetpotato variety breeding needs at least 5 years for screening hybrid offspring in addition to hybridization tests. This means that the birth of a new sweetpotato variety is a long process. The design of field experiments for seed selection generally requires 5–10 plants in a single row (1.5–3 m²) per material. After two seed selections, approximately 5% of materials will be selected as new lines based on observational methods and simple measurement methods. The design of the field experiment for the line test was generally 70–180 plants in a test plot (15–40 m²) per line. Approximately 10% of new lines will be selected as elite lines after three line tests. As seen above, 95% of materials are eliminated according to several observed phenotypic traits in the stage of seed selection. This could easily cause some valuable genotypes to be ignored due to simple estimates, even though two screenings were performed. Although numerous traits were measured in the stage of line identification, the results of the assessment were generally based on the targeted traits (e.g., fresh root yield, starch yield and edible quality score) due to the limitations of subjective judgement. The same is true for the stage of line comparison. In fact, the full-scale performance of sweetpotato materials has not been comprehensively analyzed in line tests. Therefore, it is particularly important to select an assessment method possessing intellectual rigour in the evaluation of sweetpotato germplasms (Brown et al. 2020). For this purpose, a multicriteria decision-making (MCDM) model that was found to be able to solve the complex problems of multipurpose germplasm evaluation will be introduced into this study to address the problem of sweetpotato usage.

Construction of an MCDM model in general comprises three stages, namely, criteria index selection, criteria index weighting and multicriteria decision analysis. The first stage is selecting the criteria indices according to the purpose of evaluation. Diverse criteria indices are focused on different usages, especially the quality-related criteria indices. In China, sweetpotato is used for industrial development mainly through processing for starch-based products (PSPs), processing for commercial foods (PCFs) and cooking for vegetable foods (CVFs) (Wang et al. 2021a). Except for CVFs (the sales product is the stem tip), the sweetpotato used in PSPs and PCFs shares a set of criteria indices because of the same sales products (storage root). The second stage is weighting the criteria indices. The weighting method includes subjective weighting (e.g., pairwise comparisons (Blanquero et al. 2006), analytic hierarchy process (Nikkhah et al. 2019) and Delphi method (Ahmad and Wong 2019)) and objective weighting (e.g., entropy method (Sudha and Jeba 2015), standard deviation method (Odu 2019), and statistical variance procedure (Vavrek 2019)). To take both expert opinion and data characteristics into consideration, two weighting methods are often integrated (Deepa et al. 2019). The last stage of multicriteria decision analysis (e.g., grey relational analysis (Xu et al. 2018), technique for order preference by similarity to an ideal solution (Seyedmohammadi et al. 2018), and simple multiattribute rating technique (Lavik et al. 2020)) was conducted to select the best alternative through similarity measures in multicriteria systems.

Due to the high subjectivity of traditional screening methods, the introduction of MCDM models is undoubtedly a supplement and improvement to sweetpotato germplasm evaluation. Moreover, for the comprehensive score (e.g., edible quality score) of some sensory criteria indices, a mathematical model (e.g., fuzzy comprehensive evaluation) is also needed to ensure stability and consistency. Finally, a high-efficiency evaluation system will be developed to provide assistance for the optimization of sweetpotato breeding programs. Currently, MCDM is widely used in biology-related fields, such as performance evaluation of herbaceous peonies (Zhang et al. 2019), land suitability evaluation for citrus cultivation (Tercan and Dereli 2020), and energy potential evaluation of miscanthus (Xiang et al. 2018). The present work aimed to develop an MCDM model to evaluate sweetpotato germplasms for improving the efficiency of breeding.

Materials and Methods

As shown in Fig. 1, an MCDM model, which was supplemented by fuzzy comprehensive evaluation, was constructed to improve the sweetpotato breeding evaluation system in the study. The MCDM model was constructed based on six agronomic traits, including fresh root yield, vine length, vine diameter, branch number, root number and the spatial distribution of storage roots, and five quality traits, including dry matter content, marketable root yield, uniformity of roots, starch content and the edible quality score. The weights were calculated by integrating analytic hierarchy process (AHP) and the entropy weight method. Grey relational analysis was performed to screen the elite genotypes and select parental materials. In the following section, the detailed procedure of above-mentioned model construction for screening the hybrid offspring of sweetpotato is described.

Fig. 1.

The procedure to establish a multicriteria decision-making model.

Multicriteria decision-making

Selection of criteria indices

To accurately screen sweetpotato species with superior marketable value or select potential breeding materials with highlighted traits, the MCDM model was designed. The criteria indices of evaluation model are usually focused on the phenotypic traits or functional genes closely related to marketable requirements. Currently, phenotypic traits suitable for rapid testing are used as criteria indices for mass screening of sweetpotato germplasms due to the heavy workload of breeding and lagging genomic research.

The criteria indices, as the core traits, are generally selected through the following three steps: 1. to select promising traits, the literature on sweetpotato in fields of the above two commercial applications was analyzed and various reported traits connected with the marketable value of sweetpotato were screened; 2. to clarify the necessity of selected traits, researchers, farmers and operators working in sweetpotato production and processing-related fields were surveyed; and 3. to select core traits, citation ratio and importance of the traits were taken into consideration.

AHP-based weighting

AHP is a subjective weighting method that combines qualitative and quantitative analysis. Its high credibility comes from a deep mathematical foundation. The weighting processes of AHP are expounded as follows:

Step 1: Construct a decision hierarchy structure

The hierarchical structure commonly consists of three layers: the goal layer, criteria indices layer and solution layer (Cobuloglu and Büyüktahtakın 2015). The goal layer is the top level, which represents an objective to select the best alternative; the criteria indices layer is the medium level, which represents the core traits (second-level criteria indices) and their categories (first-level criteria indices); and the solution layer is the bottom level, which represents the alternatives.

Step 2: Build a pairwise comparison matrix

As shown in Eq. (1), the relative importance of the core traits in the square matrix will be pairwise compared (Borkar and Sarode 2017). The basic judgement standard of pairwise comparison refers to Table 1 (Saaty 2004).

Table 1. Judge rule of the relative significance of second-level criteria indices in pairwise comparisons

Significance score	Criteria
1	It denotes two indices having equal importance
3	It denotes the previous index being moderately more significant than the latter index
5	It denotes the previous index being significantly more significant than the latter index
7	It denotes the previous index being very significantly more significant than the latter index
9	It denotes the previous index being extremely more significant than the latter index
2, 4, 6, 8	They denote the medians of the above adjacent judgement
Reciprocal	If ratio of the importance of trait i to trait j is aij, ratio of the importance of trait j to trait i is aji = 1/aij

  

$$A=\begin{array}{c}\left[\begin{array}{cccccc}{w}_{11}& w_{12}& \dots & w_{1k}& \dots & w_{1m}\\ w_{21}& w_{22}& \dots & w_{2k}& \dots & w_{2m}\\ ⁝& ⁝& & ⁝& & ⁝\\ w_{j1}& w_{j2}& \dots & w_{\mathit{jk}}& \dots & w_{\mathit{jm}}\\ ⁝& ⁝& & ⁝& & ⁝\\ w_{m1}& w_{m2}& \dots & w_{\mathit{mk}}& \dots & w_{\mathit{mm}}\end{array}\right]\end{array}$$(1)

where j represents the sequence number of the previous criteria index; k represents the sequence number of the subsequent criteria index; m denotes the aggregate of criteria indices in matrix A; and w_jk refers to the specific value of the significance of the j^th criteria index compared with the k^th criteria index, which is scored by specialists in terms of Table 1.

Step 3: Standardize the pairwise comparison matrix by Eq. (2)

  

$$w_{\mathit{jk}}\text{'}=\frac{w_{\mathit{jk}}}{{\displaystyle \sum _{j=1}^m}{w}_{\mathit{jk}}}$$(2)

where w_jk is the rank element of pairwise comparison and w_jkʹ denotes the rank element of the pairwise comparison after standardizing (Lukić et al. 2021).

Step 4: Calculate the weight value and eigenvector by Eq. (3) to Eq. (5)

  

$${\omega }_j=\frac{{\displaystyle \sum _{k=1}^m}{w}_{\mathit{jk}}\text{'}}{m}$$(3)

  

$$W=\left[\begin{array}{c}{\omega }_1\\ {\omega }_2\\ ⁝\\ {\omega }_j\\ ⁝\\ {\omega }_m\end{array}\right]$$(4)

  

$${\lambda }_{\text{max}}\frac{1}{m}\sum _{j=1}^m{\left(\mathit{AW}\right)}_j/{\omega }_j$$(5)

where ω_j represents the weight value of the j^th criteria index; W represents the eigenvector of matrix A; λ_max refers to the biggest eigenvalue of matrix A (Saha et al. 2020).

Step 5: Evaluate the consistency level by Eq. (6) to Eq. (8)

The consistency level in the pairwise comparison is expressed by consistency ratio (CR). When CR < 0.10, it means that the consistency level is acceptable (Ren et al. 2016). If CR ≥ 0.10, it implies that there is a contradiction in the pairwise comparison matrix.

  

$$\mathit{\text{CR}}=\frac{\mathit{\text{CI}}}{\mathit{\text{RI}}}$$(6)

  

$$\mathit{\text{CI}}=\frac{{\lambda }_{\text{max}}-m}{m-1}$$(7)

  

$$\mathit{\text{RI}}=\frac{-5.739303+4.303993m-1.281630m^2+0.241633m^3}{1.771704m-0.540019m^2+0.137736m^3}$$(8)

where CI is the consistency index (Tadesse and Negese 2020); RI is the random consistency index which is calculated by the empirical equation established by Tang (2010).

Entropy-based weighting

The entropy weight method calculates the objective weights in terms of the information of criteria indices, and it represents the relative significance of the criteria indices and how they are associated with the dispersion degree of trait values (Zhu et al. 2020). For a trait, a higher dispersion degree indicates a lower entropy, which illustrates that the weight of the trait should be set correspondingly high (Zou et al. 2006). The weighting processes of the entropy weight method are shown below:

Step 1: Build an evaluation matrix

To show the performance of all tested materials, the measurement data of each criteria index were inputted into Eq. (9) as matrix elements (Li et al. 2019).

  

$$x_{s\times c}=\begin{array}{cc}& \begin{array}{ccccccccccc}{c}_1& & & c_2& \dots & & c_j& & \dots & & c_m\end{array}\\ \begin{array}{c}{s}_1\\ s_2\\ ⁝\\ s_i\\ ⁝\\ s_n\end{array}& \left(\begin{array}{cccccc}{x}_1\left(1\right)& x_1\left(2\right)& \dots & x_1\left(j\right)& \dots & x_1\left(m\right)\\ x_2\left(1\right)& x_2\left(2\right)& \dots & x_2\left(j\right)& \dots & x_2\left(m\right)\\ ⁝& ⁝& & ⁝& & ⁝\\ x_i\left(1\right)& x_i\left(2\right)& \dots & x_i\left(j\right)& \dots & x_i\left(m\right)\\ ⁝& ⁝& & ⁝& & ⁝\\ x_n\left(1\right)& x_n\left(2\right)& \dots & x_n\left(j\right)& \dots & x_n\left(m\right)\end{array}\right)\end{array}$$(9)

where c refers to the core traits; s refers to the tested materials; m denotes the total number of core traits; n denotes the total number of tested materials; i represents the sequence number of a tested material; j represents the sequence number of a core trait; and x_i(j) is the measured value of the j^th core trait in the i^th tested material.

Step 2: Standardize the evaluation matrix

One of the after-mentioned three equations was used to standardize the aforesaid matrix in terms of the characteristics of the core traits (Xue et al. 2013).

For a larger-is-better change, the standardization equation of former sequence is ruled as Eq. (10).

  

$$y_i\left(j\right)=\frac{x_i\left(j\right)-\underset{i}{\text{min}}{x}_i\left(j\right)}{\underset{i}{\text{max}}{x}_i\left(j\right)-\underset{i}{\text{min}}{x}_i\left(j\right)}$$(10)

For a smaller-is-better change, the standardization equation of former sequence is ruled as Eq. (11).

  

$$y_i\left(j\right)=\frac{\underset{i}{\text{max}}{x}_i\left(j\right)-x_i\left(j\right)}{\underset{i}{\text{max}}{x}_i\left(j\right)-\underset{i}{\text{min}}{x}_i\left(j\right)}$$(11)

For a nominal-is-better change, the standardization equation of former sequence is ruled as Eq. (12).

  

$$y_i\left(j\right)=1-\frac{\left|x_i\left(j\right)-x_0\left(j\right)\right|}{\underset{i}{\max }\left|x_i\left(j\right)-x_0\left(j\right)\right|}$$(12)

where x_i(j) refers to former sequence; y_i(j) refers to the standardized sequence; max_ix_i(j) represents the maximum value of x_i(j); min_ix_i(j) represents the minimum value of x_i(j); x₀(j) is the desired value; and max_i|x_i(j) – x₀(j)| refers to the maximum value of |x_i(j) – x₀(j)|.

Step 3: Calculate the entropy of core traits

Entropy is calculated by Eq. (13) (Cui et al. 2019).

  

$$e_i\left(j\right)=-\frac{{\displaystyle \sum _{i=1}^n}\frac{y_i\left(j\right)}{{\displaystyle \sum _{i=1}^n}{y}_i\left(j\right)}\ln \frac{y_i\left(j\right)}{{\displaystyle \sum _{i=1}^n}{y}_i\left(j\right)}}{\ln n}$$(13)

where e_i(j) denotes the entropy of the j^th core trait.

Step 4: Calculate the entropy-based weight of core traits

The entropy-based weight is computed by Eq. (14) (Zhong et al. 2017).

  

$$W_j=\frac{1-e_i\left(j\right)}{{\displaystyle \sum _{j=1}^m}(1-e_i(j\left)\right)}$$(14)

where W_j denotes the entropy-based weight of the j^th core trait.

Integrating the weights

In this article, the AHP-based weight (ω_j) and the entropy-based weight (W_j) were integrated to calculate the comprehensive weight (W_jʹ) using additive synthesis method. The subjective weight coefficient (σ) was set to a high value of 0.7 due to the importance of specialist experience in the sweetpotato breeding process (Wang et al. 2021b).

  

$$W_j\text{'}=\sigma {\omega }_j+(1-\sigma )W_j$$(15)

Grey relational analysis

The relational grades between tested materials are calculated using grey relational analysis based on the level of similarity and difference in variation tendency. The procedures of grey relational analysis are described as follows (Deng 1989).

Step 1: Establish the relational matrix and ideal species

The relational matrix is established according to the above-mentioned evaluation matrix (Zhou et al. 2019). The ideal species (reference sequence) is established based on the features of three types of core traits (Han et al. 2021). The core trait of ideal species is set to the maximum/minimum/optimum value of the tested materials when it belongs to the larger-is-better/smaller-is-better/nominal-is-better type.

Step 2: Standardize the dataset

There is a need to preprocess the data (i.e., data standardization) before the grey relational analysis because of the diverse data features of the different core traits (Du et al. 2020b). The standardization method is identical to that introduced in the entropy weight method by Eq. (10), Eq. (11) and Eq. (12) (Tan et al. 2019).

Step 3: Calculate the grey relational coefficients

After data standardization, the grey relation coefficients ε_i(j) are computed by Eq. (16) (Qin et al. 2021a):

  

$$\begin{array}{}{\displaystyle {\epsilon }_i\left(j\right)=\\ \frac{\underset{i}{\text{min}}\underset{j}{\text{min}}\left|y_0\left(j\right)-y_i\left(j\right)\right|+\rho \underset{i}{\text{max}}\underset{j}{\text{max}}\left|y_0\left(j\right)-y_i\left(j\right)\right|}{\left|y_0\left(j\right)-y_i\left(j\right)\right|+\rho \underset{i}{\text{max}}\underset{j}{\text{max}}\left|y_0\left(j\right)-y_i\left(j\right)\right|}}\end{array}$$(16)

where y₀(j) represents the reference sequence; y_i(j) represents the comparability sequence (tested material); and ρ denotes the identification coefficient which is usually set to 0.5 (Wang et al. 2019).

Step 4: Produce the grey relational grade

The grey relational grade (GRG) reflects the closeness of the tested materials to the ideal species, which is calculated by Eq. (17) (Qazi et al. 2021):

  

$${\gamma }_i=\sum _{j=1}^m{W}_j\text{'}{\epsilon }_i\left(j\right)$$(17)

where γ_i denotes the GRG of the i^th tested material and W_jʹ means the comprehensive weight of the j^th core trait.

Fuzzy comprehensive evaluation

The evaluation of the edible quality of sweetpotato is being conducted with the traditional sensory evaluation method (Nwosisi et al. 2017). However, the lack of a standard protocol makes the traditional evaluation method subjective and imprecise (Lado et al. 2021). To address this problem, this study intended to establish a sensory evaluation model by using fuzzy mathematics. The evaluation team is then formed to score each sensory criteria index of each tested material.

Construction of factor set

Factor set U refers to a set composed of sensory criteria indices of edible quality and is expressed as U = {u₁, u₂, ..., u_ι, u_α} (Sun et al. 2018).

Construction of weight set and weighting

Weight set D refers to a set that reflects the degree of influence of the sensory criteria indices on the edible quality and is expressed as D = {d₁, d₂, ..., d_ι, d_α}, where d_ι represents the weight value of the corresponding sensory criteria index u_ι (Wei et al. 2020). The weighting method is the same as that used in the AHP method by Eqs. (1) to (8).

Construction of comment set and sensory scoring

Comment set V refers to a set composed of feedback information and its grade of valuators on sensory criteria indices. It is expressed as V = {v₁, v₂, ..., v_χ, v_τ} (Liu et al. 2020a).

Construction of fuzzy relation matrix and normalizing

The sensory scores of various sensory criteria indices of all tested materials marked by valuators were used as the rank elements to construct a fuzzy relationship matrix, which is shown in Eq. (18) (Xiang et al. 2021):

  

$$R=\begin{array}{c}\left[\begin{array}{cccccc}{r}_{11}& r_{12}& \dots & r_{1\kappa }& \dots & r_{1\beta }\\ r_{21}& r_{22}& \dots & r_{2\kappa }& \dots & r_{2\beta }\\ ⁝& ⁝& & ⁝& & ⁝\\ r_{\iota 1}& r_{\iota 2}& \dots & r_{\mathit{\iota \kappa }}& \dots & r_{\mathit{\iota \beta }}\\ ⁝& ⁝& & ⁝& & ⁝\\ r_{\alpha 1}& r_{\alpha 2}& \dots & r_{\mathit{\alpha \kappa }}& \dots & r_{\mathit{\alpha \beta }}\end{array}\right]\end{array}$$(18)

where r_ικ is the sensory score assigned to the ι^th sensory criteria index of the κ^th tested material; α is the number of sensory criteria indices; and β is the number of tested materials.

  

$$r_{\iota \kappa }^{\text{'}}=\frac{r_{\mathit{\iota \kappa }}}{{\displaystyle \sum _{\kappa =1}^{\beta }}{r}_{\mathit{\iota \kappa }}}$$(19)

where r_ικ represents the sensory score marked by valuators and r_ικʹ denotes the sensory score after normalizing (Zhang and Zhang 2011).

Synthesizing the resultant vector of fuzzy comprehensive evaluation using Eq. (20) and Eq. (21)

  

$$f_{\kappa }=\text{min}(1,\sum _{\iota =1}^{\alpha }{d}_{\iota }{r}_{\mathit{\iota \kappa }}^{\text{'}})$$(20)

  

$$F=D◦R^{\text{'}}=\left(f_1,f_2,\dots ,f_{\kappa },\dots ,f_{\beta }\right)$$(21)

where F denotes the resultant vector of fuzzy comprehensive evaluation; “○” refers to the fuzzy operator; D is the weight set of the sensory criteria indices; Rʹ is the standardized fuzzy relation matrix; d_ι represents the weight of the ι^th sensory criteria index; and f_κ represents the fuzzy comprehensive evaluation result of the κ^th tested material (Lu et al. 2017, Peng et al. 2008, Zhang et al. 2017).

Analysis of fuzzy comprehensive evaluation results

The edible quality score is calculated using Eq. (22). The score is divided into four levels: very palatable (90 < S_κ ≤ 100) for superior edible products, palatable (80 < S_κ ≤ 90) for dedicated edible products, mediocre (70 < S_κ ≤ 80) for dual-purpose products and unpalatable (S_κ ≤ 70) for dedicated starch-based products.

  

$$S_{\kappa }=\delta +\mu \times \frac{f_{\kappa }-f_0}{\sqrt{\frac{{\displaystyle \sum _{\kappa =1}^{\beta }}{(f_{\kappa }-\bar{f})}^2}{\beta -1}}}$$(22)

where S_κ represents the edible quality score of the κ^th tested material; f₀ is the fuzzy comprehensive evaluation result of the reference cultivar; $\stackrel{-}{f}$ denotes the average value of the fuzzy comprehensive evaluation results of β tested materials; δ is the edible quality score of the reference cultivar; and μ is a coefficient of standard deviation for adjusting the range of edible quality scores.

Comparison between the MCDM model and traditional screening method

In the present study, 23 advanced sweetpotato lines with their corresponding merits and demerits that were difficult to choose were evaluated to identify elite lines by the MCDM model and traditional screening method. Two sweetpotato cultivars, Xushu 22 (applied to PSPs) and Xiangshu 99 (applied to PCFs), were used as the control group. They were planted in the Gaoqiao Experimental Station (N28.48°, E113.36°) of Hunan Academy of Agricultural Science in China. This experiment was in the stage of line comparison, and these tested materials were planted in a continuous cropping field for adaptability testing. The experimental design was a random block arrangement with three repetitions, and each experimental plot area was 30 m². The planting pattern was a small ridge (row spacing 0.9 m, ridging height 0.3 m) in a single row, and the planting density was 110 plants per experimental plot. The compound fertilizer (N-P₂O₅-K₂O: 17-17-17) was used as base-fertilizer and its rate of application was 0.6 t·hm^–2. The tested materials (vine cuttings) were planted on 28 May 2020 and watered initially, with no subsequent watering. These materials were weeded (integrating haloxyfop-methyl and hand weeding) before the ridges were sealed with vines. The growth period of the tested materials lasted 150 days.

Traits such as vine length, vine diameter and branch number were measured about 90 days after planting. In harvest time, fresh root yield, root number, spatial distribution of storage roots, marketable root yield and uniformity of roots were determined. Dry matter content, starch content and edible quality score were detected within seven days after harvest. To perform sensory scoring, three-point method (difference test) and scoring method (scale test) were adopted to train the evaluators and 11 evaluators were singled out. The median scores of these evaluators were counted as sensory scores for five sensory criteria indices.

Results

Application of the MCDM model

Establishment of the criteria indices system for MCDM model construction

In this study, the criteria indices used to construct the MCDM model were selected from agronomic and quality traits, which are the main factors affecting the market potential of sweetpotato in starch-based products and commercial food processing. The agronomic traits include the yield-related traits of fresh root yield and root number, and the harvest-related traits of vine length, vine diameter, branch number and spatial distribution of storage roots. The quality traits included the dry matter content, marketable root yield, uniformity of roots, starch content and edible quality score. These traits (second-level criteria indices) and their measurement methods are shown in Table 2. The decision hierarchy system used in this study was built as shown in Fig. 2. The evaluation of marketable value is the main objective; market-related agronomic and quality traits are the first-level criteria indices; 11 specific traits (e.g., fresh root yield, dry matter content) are the second-level criteria indices; and two commercial usages, i.e., PSPs and PCFs are the alternatives.

Table 2. Definitions of the second-level criteria indices for evaluating the marketable value of sweetpotato

Traits	Definition	PSPs	PCFs	References
	Market-related agronomic traits
FRY	Total fresh storage root weight per hectare (t·hm–2)	L	L	(Gurmu et al. 2017, 2018)
VL	Length from the ground to the terminal bud of the longest branch (cm)	S	S	(Du et al. 2019)
VD	Diameter at the middle of the longest branch (mm)	N	N	(Ngailo et al. 2015)
BN	Number of branches 10 cm above the ground counted	N	N	(Hetharie et al. 2021, Mukhtar et al. 2010)
RN	Number of storage roots per plant	L	L	(Ma et al. 2015)
SDR	Spatial distribution characteristics of storage roots per plant	L	L	(Lewthwaite and Triggs 2009)
	Market-related quality traits
DMC	Percentage of dry matter weight of the fresh sample weight by drying at 70°C until constant weight (%)	L	N	(Rukundo et al. 2013, Wang et al. 2020)
MRY	Percentage of marketable storage root weight of the total storage root weight per 10 plants (%)	L	L	(Laurie et al. 2017, Wang et al. 2010)
UR	Uniformity of size and shape of storage roots	L	L	(Delgado-Paredes et al. 2017)
SC	Weight of starch of dry sample (%)	L	N	(Qin et al. 2021b, Yang et al. 2018)
EQS	Integrated score of the edible quality of sensory evaluation	L	L	(Adebisi et al. 2020, Nwosisi et al. 2017)

PSPs: processing for starch-based products. PCFs: processing for commercial foods. FRY: fresh root yield. VL: vine length. VD: vine diameter. BN: branch number. RN: root number. SDR: spatial distribution of storage roots. DMC: dry matter content. MRY: marketable root yield. UR: uniformity of roots. SC: starch content. EQS: edible quality score. L: larger-the-better. S: smaller-the-better. N: nominal-is-better.

Fig. 2.

Decision hierarchy system of the multicriteria decision-making model for assessing sweetpotato.

Weights of the second-level criteria indices

In this study, the pairwise comparison of second-level criteria indices were carried out by experts for different usages. The overall consistency levels (i.e., CR values ) for PSPs and PCFs were assessed to be acceptable at 0.07 and 0.06, respectively. The weights of the second-level criteria indices for each commercial usage are shown in Table 3. Higher weight values represent more important effects of the second-level criteria indices during the evaluation of sweetpotato.

Table 3. Weight coefficients of the 11 second-level criteria indices for evaluating sweetpotato in two commercial usages

Second-level criteria indices	Processing for starch-based products						Processing for commercial foods
	SW	Order	OW	Order	CW	Order	SW	Order	OW	Order	CW	Order
FRY	0.2331	1	0.1041	5	0.1944	1	0.2331	1	0.1109	5	0.1965	1
VL	0.0249	10	0.1382	2	0.0588	7	0.0249	10	0.1472	2	0.0615	7
VD	0.0190	11	0.0406	9	0.0255	11	0.0190	11	0.0432	9	0.0263	11
BN	0.0311	8	0.0257	11	0.0295	10	0.0311	8	0.0273	11	0.0300	10
RN	0.1053	4	0.1366	3	0.1147	4	0.1053	4	0.1455	3	0.1174	4
SDR	0.0866	5	0.1001	6	0.0906	5	0.0866	6	0.1066	6	0.0926	5
DMC	0.2290	2	0.0660	8	0.1801	2	0.0405	7	0.0459	7	0.0421	8
MRY	0.0512	6	0.0302	10	0.0449	9	0.1184	3	0.0321	10	0.0925	6
UR	0.0396	7	0.1708	1	0.0790	6	0.0931	5	0.1820	1	0.1198	3
SC	0.1510	3	0.0790	7	0.1294	3	0.0263	9	0.0435	8	0.0314	9
EQS	0.0292	9	0.1087	4	0.0531	8	0.2217	2	0.1158	4	0.1899	2
Color							0.165	3
Odor							0.127	4
Sweetness							0.385	1
Stickiness							0.229	2
Fibrous taste							0.095	5

SW: Subjective weight. OW: Objective weight. CW: Comprehensive weight. Order is the rank of weight. FRY: fresh root yield. VL: vine length. VD: vine diameter. BN: branch number. RN: root number. SDR: spatial distribution of storage roots. DMC: dry matter content. MRY: marketable root yield. UR: uniformity of roots. SC: starch content. EQS: edible quality score.

Generally, the comprehensive weight ratio of yield/harvest/quality-related traits was approximately 3:2:5 in both PSPs and PCFs. This result indicates that quality-related traits are the most important criteria indices in terms of assessing the marketable value of sweetpotato in both usages, followed by yield-related traits and harvest-related traits. In both usages, the comprehensive weights of the agronomic traits were in the following order: fresh root yield (1/11 representing no. 1 in the 11 second-level criteria indices), root number (4/11), spatial distribution of storage roots (5/11), vine length (7/11), branch number (10/11) and vine diameter (11/11). Nevertheless, the ranking trends of the comprehensive weights of the quality traits were quite different. In the PSPs usage, the ranking trend was in the following order: dry matter content (2/11), starch content (3/11), uniformity of roots (6/11), edible quality score (8/11) and marketable root yield (9/11). In the usage for PCFs, the ranking trend was in the following order: edible quality score (2/11), uniformity of roots (3/11), marketable root yield (6/11), dry matter content (8/11) and starch content (9/11). These results could be because the subjective weights of quality traits in PSPs and PCFs were considerably different.

To screen promising germplasms and select breeding parental materials for different usages, the weights of second-level criteria indices could provide a reference to analyze the marketable value components of sweetpotato. For usage in PSPs, fresh root yield, dry matter content and starch content were the three most important second-level criteria indices, and they contributed more than 50% of the weight. The high comprehensive weight ranking of fresh root yield, dry matter content and starch content are mainly contributed by their high subjective weights of 0.2331 (1/11), 0.2290 (2/11) and 0.1510 (3/11), respectively. For usage in PCFs, fresh root yield, edible quality score and uniformity of roots were the three most important second-level criteria indices, and more than 50% of the weight was contributed by them. The high comprehensive weight ranking of fresh root yield and edible quality score are mainly contributed by their high subjective weights of 0.2331 (1/11) and 0.2217 (2/11), respectively. The third highest comprehensive weight of uniformity of roots was attributed to its highest objective weight value, which was 0.1820 (1/11).

Results of the multi-criteria decision analysis

During grey relational analysis, the GRG is used to express the relationship between the ideal species and individual candidate materials, where a higher GRG value indicates a higher comprehensive performance of traits of marketable value. In this article, sweetpotato cultivars for the corresponding usages were used as reference genotypes for germplasm screening. The results of the analysis of the 25 materials are shown in Table 4. For the marketable usage of PSPs, there were eight genotypes surpassing Xushu 22 (reference cultivar) in GRG value. In terms of the usage of PCFs, 13 genotypes surpassed Xiangshu 99 (reference cultivar) in GRG value.

Table 4. Results comparison between the multicriteria decision-making (MCDM) model and the traditional screening method (TSM)

no.	Lines name	Processing for starch-based products				Processing for commercial foods
		MCDM results		TSM results		MCDM results		TSM results
		GRG	Order	SY	Order	GRG	Order	FRY	Order	EQS	Order
1	12–27–2	0.4416	25	2.694	18	0.4645	24	14.136	15	68.4	21
2	12–27–11	0.4859	19	3.865	10	0.4665	22	16.964	10	67.1	22
3	12–27–14	0.4822	20	2.686	19	0.4628	25	14.091	16	69.6	19
4	16–3–8	0.5528	11	4.626	4	0.6013	7	23.591	2	72.4	16
5	17–2–13	0.5132	15	3.150	14	0.6233	6	14.709	12	87.7	1
6	17–16–3	0.7028	1	4.124	6	0.7333	1	20.409	6	72.0	17
7	17–108–17	0.6913	2	2.912	17	0.5092	21	9.855	25	68.8	20
8	17–Z6–11	0.4821	21	2.401	22	0.5224	17	14.145	14	76.7	8
9	17–Z6–18	0.5893	7	3.278	13	0.5655	12	13.336	20	74.5	12
10	17–hua 3	0.6142	6	3.380	12	0.6851	2	13.727	17	87.7	1
11	18–D2–15	0.5024	17	2.654	20	0.5144	18	12.295	22	67.1	24
12	18–D6–4	0.6398	5	4.047	8	0.6849	3	19.818	7	72.7	15
13	18–D6–5	0.6464	4	5.308	2	0.6394	5	22.509	3	73.8	13
14	18–D9–4	0.5636	8	5.157	3	0.5706	11	22.182	4	75.5	11
15	18–Z2–6	0.6660	3	5.579	1	0.6556	4	24.045	1	76.5	9
16	18–Z3–19	0.5242	14	2.272	23	0.5480	13	10.145	24	77.3	7
17	18–Z5–4	0.5097	16	3.514	11	0.5114	20	15.318	11	72.8	14
18	18–Z5 + 11	0.4466	24	2.201	25	0.5124	19	13.636	18	82.3	3
19	S16–1	0.5019	18	2.206	24	0.5717	10	11.364	23	80.1	5
20	X165	0.4784	23	3.005	16	0.4661	23	13.136	21	65.5	25
21	Jinjingzi 011	0.4787	22	2.578	21	0.5248	16	14.182	13	75.6	10
22	Jinjingzi 012	0.5435	12	4.083	7	0.5796	8	18.136	9	81.1	4
23	Jinjingzi 034	0.5533	10	4.001	9	0.5770	9	21.136	5	67.1	23
24	Xiangshu 99	0.5356	13	4.139	5	0.5408	14	18.427	8	78.8	6
25	Xushu 22	0.5537	9	3.134	15	0.5382	15	13.545	19	70.0	18

GRG: grey relational grade. Order is the rank of GRG. SY: starch yield (t·hm^–2). FRY: fresh root yield (t·hm^–2). EQS: edible quality score. The basic indicator values of the usage of PSPs and PCFs were calculated based on the formula “starch yield = fresh root yield × dry matter content × starch content” and the fuzzy comprehensive evaluation, respectively.

Application of the fuzzy mathematics method

Establishment of the factor set and the comment set for sensory scoring

As shown in Table 5, the factor set was composed of five sensory criteria indices of color, odor, sweetness, stickiness and fibrous taste, which are currently the most frequently used sensory criteria indices in sweetpotato edible quality evaluation. The comment set was divided into five levels by the five-point scoring system and the sensory criteria indices of all levels were described in detail.

Table 5. Evaluation standard of sensory quality for the edible tuberous root of sweetpotato

Rating score	Color	Odor	Sweetness	Stickiness	Fibrous taste
4 < v5 ≤ 5 Score = 4.5 or 5	Extremely attractive: the flesh color is orange or deep purple; the main color is bright and uniform, and no secondary color.	Extremely fragrant: the fragrance is very strong and stable.	Extremely sweet: it has a very strong sweetness and a long aftertaste.	Extremely sticky: the flesh gives a high soft feeling, a high sticky feeling and no powdery feeling.	No fibrous: there is no residue or graininess in the mouth after chewing.
3 < v4 ≤ 4 Score = 3.5 or 4	Strongly attractive: the flesh color is yellow or purple; the main color is bright and uniform, and no secondary color.	Strongly fragrant: the fragrance is rich and deep.	Strongly sweet: it has a strong sweetness and a lasting aftertaste.	Strongly sticky: the flesh gives a soft feeling, a sticky feeling and a slight powdery feeling.	Less fibrous: there is no residue in the mouth after chewing except for a little graininess.
2 < v3 ≤ 3 Score = 2.5 or 3	Moderately attractive: the flesh color is pale yellow or light purple; the main color is uniform and the secondary color is unconspicuous.	Moderately fragrant: the fragrance is obvious but short.	Moderately sweet: it has an obvious sweetness and a short aftertaste.	Moderately sticky: the flesh gives a soft feeling and a powdery feeling.	Moderately fibrous: there is a bit of residue in the mouth after chewing but does not affect the taste.
1 < v2 ≤ 2 Score = 1.5 or 2	Not attractive: the flesh color is white; the secondary color is obvious.	Slightly fragrant: the fragrance is light.	Slightly sweet: it has a slight sweetness.	Slightly sticky: the flesh gives a slight tough feeling, a powdery feeling and a slight dry feeling.	More fibrous: there is some residue in the mouth after chewing and it affects the taste.
v1 ≤ 1 Score = 0.5 or 1	Aversive: the flesh color is dim; the secondary color is obvious.	Not fragrant: there is no fragrance or there is an unpleasant odor.	Not sweet: it does not have sweetness.	Not sticky: the flesh gives a tough feeling, a powdery feeling and a dry feeling.	Large fibrous: there is much residue in the mouth after chewing and it has a strong impact on the taste.

Weights of the sensory quality factors

The sensory criteria index weights of the edible quality of sweetpotato were in the following order: sweetness (0.385), stickiness (0.229), color (0.165), odor (0.127) and fibrous taste (0.095). Among them, the sum of weights of sweetness and stickiness accounts for 61.4% of the total weight. This result indicated that sweetness and stickiness were the main factors affecting the edible quality of eating-type sweetpotato.

Results of the fuzzy comprehensive evaluation

Currently, Xushu 22 is a general control group for various sweetpotato tests in China. In this study, we set its δ value to 70. Xiangshu 99 was taken as a reference cultivar for comparison. The value of μ was set to 6. As shown in Table 4, there were 5 lines (80 < S_κ ≤ 90) surpassing Xiangshu 99, which had the potential to become dedicated edible products, namely, 17–2–13, 17–hua 3, 18–Z5 + 11, Jinjingzi 012 and S16–1. The other 11 lines (70 < S_κ ≤ 80) with edible quality scores between Xushu 22 and Xiangshu 99 were expected to become dual-purpose products.

Comparison results of the MCDM model and traditional screening method

For usage in PSPs and PCFs, the targeted traits of 25 materials were analyzed via the traditional screening method and then compared with the comprehensive performance calculated by the MCDM model. The results (shown in Table 4) showed that the marketable values of the materials assessed by the traditional screening method were different from those calculated by the MCDM method. Some low-ranking/high-ranking genotypes in the results of the traditional screening method had a high/low ranking in the results of the MCDM model. This may be due to the terrible/outstanding performance of certain traits of tested materials, but the excellent/poor performance of other traits. After all, in the traditional screening, the targeted trait (e.g., starch yield, edible quality score and fresh root yield) value is used to express one aspect of the marketable value of individual candidate materials. For example, for the usage of PSPs, the starch yield of 17–108–17 ranked 17th because of low fresh root yield, and its GRG value ranked second due to high dry matter content and starch content.

The results of traditional screening methods and MCDM model were combined for analysis. For use in PSPs, except for 17–108–17, the starch yield of the other seven genotypes surpassed Xushu 22, namely, 17–16–3, 18–Z2–6, 18–D6–5, 18–D6–4, 17–hua 3, 17–Z6–18 and 18–D9–4. In the usage for PCFs, among the above 13 genotypes that surpassed Xiangshu 99, there were four genotypes surpassing Xiangshu 99 in edible quality score, namely, 17–hua 3, 17–2–13, Jinjingzi 012 and S16–1. Furthermore, there were seven genotypes that surpassed Xiangshu 99 in fresh root yield, namely, 17–16–3, 18–D6–4, 18–Z2–6, 18–D6–5, 16–3–8, Jinjingzi 034 and 18–D9–4.

Discussion

Importance of the selected traits for evaluating marketable value

While screening the agronomic traits of criteria indices, the storage root is the sales product and its yield determines the marketable value of sweetpotato varieties. Therefore, fresh root yield is the principal index for selecting elite varieties regardless of the usage of sweetpotato (Shumbusha et al. 2019). Furthermore, the yield performance of sweetpotato is dominated by the quantity of storage roots per plant (Mekonnen et al. 2021), which are affected by multiple factors of genes (Tang et al. 2020), fertilization (Du et al. 2020a, Si et al. 2018) and planting density (Szarvas et al. 2019). The spatial distribution of storage roots is an important trait for sweetpotato production. To avoid being exposed to light, pathogens, pests, or damage by harvesting, storage roots within the soil ridge should be concentrated rather than widely dispersed (Lewthwaite and Triggs 2009). The traits of vine length, vine diameter and branch number are closely related to field management. Long vine length and high branch number varieties compete better than weeds, which have the effect of suppressing weeds. Nonetheless, commercial farmers prefer short vine lengths and low branch numbers for easy mechanization during harvest and suitable intercropping modes. A thick vine diameter produces strong vines as planting material that are well established at planting, whereas weevils damage thick vines more severely than thin vines. Meanwhile, adequate water and dry matter for withstanding long periods of drought are also considered, so medium vine diameters between 4.0 and 6.0 mm are regarded as acceptable (Nwankwo 2015).

For the utilization of PCFs, a higher edible quality score indicates higher consumer acceptance (Abdou et al. 2018). In general, consumers prefer high dry matter varieties of sweetpotato (Tomlins et al. 2012). Nevertheless, the concentration of fructose, glucose and total sugar within storage roots of sweetpotato are negatively correlated with dry matter content (Shumbusha et al. 2014). To take sweetness into account, the dry matter content of sweetpotato for fresh eating should be between 32% and 34%. In any case, the income of commercial farmers is calculated based on marketable products. Therefore, high marketable root yield is a necessary quality-related trait for the cultivated varieties of sweetpotato (Afuape et al. 2011). In addition, the uniformity of the size and shape of marketable storage roots is also an important influencing factor for pricing the sweetpotato variety (Traynor 2006), which determines the income of commercial farmers. If the tested material also has a high starch content in addition to the aforementioned attributes, it can be recommended as a dual-purpose sweetpotato cultivar.

In the usage of PSPs, a high starch yield is essential for sweetpotato dedicated varieties (Santa-Maria et al. 2009), which is affected by both starch content (SC ≥ 65%) and dry matter content (DMC ≥ 35%). High marketable root yield and high uniformity of the size and shape of those roots are also required for sweetpotato starch processing. Unlike sweetpotato for PCFs, these requirements are met for raw material processing equipment, not consumers. Similarly, if the tested sweetpotato material has a high edible quality score, it can be used as a dual-purpose raw material for PCFs. Alternatively, starch is extracted after completing a certain amount of food processing.

Necessity and effectiveness of application of the MCDM model

The evaluation of the marketable value by the traditional screening method takes the targeted trait values of sweetpotato into consideration, while that of the MCDM method takes comprehensive performance into consideration. The marketable values of sweetpotato are generally evaluated according to product yield and taste in traditional screening methods (Kays and Wang 2002, Rahman et al. 2003). In these cases, the fresh root yield, starch yield and edible quality score are mainly taken into consideration in the expert ratings, and other traits are often neglected. Compared with the traditional screening method, the MCDM model is more comprehensive and most lines carrying beneficial alleles will be retained, but these retained lines may also carry some non-beneficial alleles. Integration of the two methods can take both high comprehensive performance of all traits and the complementation of improved traits into consideration. If the tested materials, which have a higher GRG value than that of the reference cultivar, are inferior to the reference cultivar in targeted traits, they are then classified as subelite lines to be used for parental materials. Those high-ranking genotypes, which surpass the reference cultivar in both the results of the MCDM model and the traditional screening method, can be considered for direct utilization in sweetpotato production and are called elite lines.

For sweetpotato crossbreeding, the subelite lines screened out via the MCDM model are potential parental materials, which conform to the basic principle of high comprehensive performance of traits (Ma et al. 2009) and complementation of improved traits (Bar-Zvi et al. 2017). Moreover, parental selection still needs to take distant relationships (Hwang et al. 2002), high combining ability (Rukundo et al. 2017), genetic effects (additive and non-additive) (Ngailo et al. 2019) and different cross-incompatible groups (Baafi et al. 2016) into consideration. For sweetpotato variety registration, the elite lines screened out via the MCDM model are promising cultivated genotypes. Before formal variety registration, it is necessary to carry out experiments on stress resistance (Gitore et al. 2021), disease resistance (Lee et al. 2019), insect resistance (Kagimbo et al. 2020) and regional adaptation (Felistus et al. 2018).

Improved method based on the MCDM model for screening sweetpotato hybrid offspring

The evaluation of genetic resources is an essential task throughout the entire breeding process. A suitable evaluation system can improve the efficiency of breeding programs. The time spent screening hybrid offspring of sweetpotato may be shortened from 5 to 3 years by constructing an MCDM model. The improved method (three-round screening method) recommended in this study has the following three steps: 1. in the stage of seed selection, the top 15% of materials with superior performance were selected directly as new lines according to sensory traits (e.g., germinability, growth vigor, and the ability to form storage roots); 2. core traits (e.g., storage root number, dry matter content, and edible quality score) were then used to evaluate the marketable value of sweetpotato lines during the stage of line identification, and the top 5% of lines were selected as the elite lines; and 3. the elite lines to be registered were selected according to the targeted traits (e.g., stress resistance, disease resistance, and insect resistance) in the stage of line comparison. The MCDM model is generally used in the stage of line identification and line comparison. The core traits and targeted traits are selected as criteria indices according to the characteristics of the tested materials (e.g., flesh color and leaf color) and the purpose of evaluation (e.g., PSPs, PCFs, and planting in marginal land).

Author Contribution Statement

WX and CZ designed this study. FD and YZ contributed the field trial. DZ and YH contributed the component testing. QZ and LJ contributed the data analysis. WX, KL and ZZ contributed the writing—original draft. WX and LX contributed the writing—review and editing. All authors read and approved the final manuscript.

Acknowledgments

This study was financially co-supported by the Hunan Provincial Natural Science Foundation of China [grant number 2021JJ30432]; the Hunan Agricultural Science and Technology Innovation Fund Project [grant number 2020CX32]; the China Agricultural Research System of MOF and MARA [grant number CARS-10-C14-2021]; the Hunan Key Technology R&D Program [grant number 2020NK2042]; and the Survey, Protection and Utilization of Agricultural Germplasm Resources in Hunan Province [grant number Xiangnongcaizhi 2022 No.1].

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