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The optical measurement of fruit quality and the insight of light propagation in intact fruit are important to understand the optical detection mechanism and optimize the signals obtained by spectroscopy methods such as diffuse reflectance. To this end, this study measured the optical properties (absorption coefficient (μ a) and reduced scattering coefficient (μ s ')) of melon tissues (exocarp, green mesocarp, and pulp) and the internal qualities (soluble solids content (SSC) and moisture content) for two cultivars ('Golden' and 'Huanghemi') during storage. The μ a spectra showed five distinct absorption peaks near 481, 675, 984, 1195, and 1423 nm for exocarp, green mesocarp, and pulp, while increasing storage time led to decreasing μ a values of melon tissues. Among the observed tissues, the exocarp had the highest scattering level in the observed wavelength ranges. The μ s ′ values of the pulp decreased with the increasing storage time, while these of the exocarp and green mesocarp first decreased and then increased. The μ a and μ s ′ spectra of melon pulp were both positively correlated with moisture content and negatively correlated with SSC. Next, the light propagation in intact melon fruit and optimization of spectral detection in diffuse reflectance mode were investigated by voxel-based Monte Carlo simulations based on the estimated optical properties (OPs) of melon tissues. The contribution of pulp to the detected signals increased gradually with the increase of source-detector distance, while the detected optical diffuse reflectance decreased exponentially. At the source-detector distance of 2–20 mm, 95% of the information about the pulp carried by the detected signals came from the narrow range of pulp with a depth of 7.5–12 mm and a radial width of 10.5–23.5 mm. The measured diffuse reflectance profiles of the detection configuration selected based on the simulation results followed the same trend as the simulated diffuse reflectance profiles. The optimized diffuse reflectance detection obtained considerable results for predicting SSC (R p = 0.86, RMSEP = 0.79%, RPD = 1.93) and moisture content (R p = 0.87, RMSEP = 0.76%, RPD = 2.06) by established partial least squares regression (PLSR) models. Accordingly, this study provides a reference for understanding the relationship between optical properties and internal quality of melons, supports a better insight into the interaction of light with the melon tissues, and helps the development of more effective non-destructive testing methods for melon fruit. • Optical properties (OPs) of melon tissues were measured during 13 d storage. • The OPs were negatively and positively correlated with SSC and moisture content. • Source-detector distance affected the detected signals (contribution and intensity). • Light mainly interacted with the narrow and superficial region of the pulp layer. • The optimized diffuse reflectance detection obtained considerable results. [ABSTRACT FROM AUTHOR]

Visible/near-infrared (Vis/NIR) spectroscopy has been authenticated for quality evaluation of melon fruit. However, since melon is a multi-layered fruit with large size, the optical properties (OPs) of different tissue layers can influence the performance of the quality evaluation. Therefore, the OPs of different tissue layers (exocarp, green mesocarp and pulp) among different fruit positions (stem, equator and calyx) of 36 'Huanghemi' melons were measured using single integrating sphere measurements and the light propagation through melon fruit was investigated by the Monte Carlo (MC) simulation based on the OPs. Moreover, the relationship of the OPs with microstructure and internal quality properties (soluble solids content (SSC) and moisture content) was explored. In the absorption coefficient (μ a) spectra, five obvious absorption peaks for carotenoids (481 nm), chlorophyll (675 nm) and water (984, 1195 and 1423 nm) were observed. The exocarp had the highest μ a values at 481 nm owing to its orange-yellow peel and the lowest μ a values at 1423 nm, while the μ a values of green mesocarp and pulp had no significant differences at all absorption peaks. The differences in reduced scattering coefficient (μ s ') spectra were obvious with a decreasing trend from the outermost (exocarp) to the innermost (pulp) layer and the stem to the calyx position in pulp layer, which mainly related to the different tissue structure. The MC simulation results indicated that the energy along the wavelength was mainly absorbed by the exocarp and green mesocarp, with a 'diagnostic window' appearing in 700–850 nm. As the source-detector distance increased, the mean optical pathlength and attenuation of detected photons in each tissue layer increased, while the contribution fraction to the detected diffuse reflectance signals by the exocarp, green mesocarp and pulp respectively decreased, increased and increased. To acquire more information about the pulp and ensure a good signal-to-noise ratio of the spectral signal, a source-detector distance of 7 mm with a suitable light source power would be a good choice. Furthermore, the best prediction models with good performance for SSC and moisture content were built based on the μ a spectra, with the correlation coefficient of prediction (R p) of 0.78–0.80, 0.76–0.88 and the root mean square error of prediction (RMSEP) of 0.83–0.92%, 0.70–0.93%. This study was the first attempt to measure the OPs of melon tissues and investigate the light propagation through melon fruit, which would provide a reference to develop nondestructive testing techniques or instruments for melon fruit based on Vis/NIR spectroscopy. • Optical properties (μ a and μ s ') of melon tissues were measured for the first time. • Optical properties were compared among tissue layers and fruit positions. • Light propagation in melon fruit was investigated by Monte Carlo simulations. • Exocarp and green mesocarp contributed mostly to the diffuse reflectance signal. • The μ a spectra was most fit for the prediction of SSC and moisture content. [ABSTRACT FROM AUTHOR]

With respect to multi-attribute group decision-making (MAGDM) problems in which the attribute values take form of intuitionistic trapezoid fuzzy linguistic numbers, some new aggregation operators are proposed, such as intuitionistic trapezoid fuzzy linguistic weighted geometric operator, intuitionistic trapezoid fuzzy linguistic ordered weighted geometric operator, intuitionistic trapezoid fuzzy linguistic hybrid weighted geometric operator, intuitionistic trapezoid fuzzy linguistic generalized weighted averaging operator, intuitionistic trapezoid fuzzy linguistic generalized ordered weighted averaging operator and intuitionistic trapezoid fuzzy linguistic generalized hybrid weighted averaging operator are proposed at first. Then, some desirable properties of these proposed operators are discussed, including monotonicity, idempotency, commutativity and boundedness. Furthermore, based on the proposed operators, some novel methods are developed to solve MAGDM problems with intuitionistic trapezoid fuzzy linguistic information under different cases. Finally, an illustrative example of emergency response capability evaluation is provided to illustrate the applicability and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Dual hesitant fuzzy set (DHFS), which permits the possible membership degrees and non-membership degrees of an element having sets of values in [0,1], is considered as a powerful tool to express uncertain information in the process of multiple attribute group decision making (MAGDM). In this paper, we study the MAGDM problems in which the attribute values take the form of dual hesitant fuzzy elements and the weights of attributes and decision makers take the form of real numbers. Firstly, the normalized Hamming distance of the dual hesitant fuzzy elements is defined. Then, a new method for dealing MAGDM problems under dual hesitant fuzzy environment is proposed on the basis of grey relational analysis (GRA) theory. For the incompletely known and completely unknown information of attribute weight, some optimization models are established to determine the weights of attributes. Finally, a numerical example of investment alternative selection is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

With respect to multiple attribute decision making (MADM) problems in which the attributes are inter-dependent and take the form of dual hesitant fuzzy elements, a new MADM method with dual hesitant fuzzy information is investigated in this paper. Firstly, by using the Choquet integral, some new aggregation operators are developed for aggregating the dual hesitant fuzzy information, such as the dual hesitant fuzzy Choquet ordered average (DHFCOA) operator, the dual hesitant fuzzy Choquet ordered geometric (DHFCOG) operator, the generalized dual hesitant fuzzy Choquet ordered average (GDHFCOA) operator and the generalized dual hesitant fuzzy Choquet ordered geometric (GDHFCOG) operator. Then, some special cases, desirable properties of these operators and the relationships between them are discussed. Furthermore, based on the DHFCOA operator, an approach to MADM is proposed under dual hesitant fuzzy environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

This paper studies the multi-attribute decision making (MADM) problems under two situations that the attributes are independent and correlative, respectively, in which the attribute values take the form of dual hesitant fuzzy linguistic elements and the weights of attributes take the form of real numbers. Firstly, the concept, operational laws, score function and accuracy function of dual hesitant fuzzy linguistic element (DHFLE) are defined. For the situation that the attributes are independent, some dual hesitant fuzzy linguistic geometric aggregation operators are proposed. Considering that there exists prioritization among the attributes, we propose several dual hesitant fuzzy linguistic prioritized aggregation operators based on the prioritized average (PA) operator. Moreover, some desirable properties and special cases of these operators are investigated in detail. Based on the proposed operators, two novel approaches to MADM with dual hesitant fuzzy linguistic information are proposed. Finally, a numerical example for investment alternative selection is given to illustrate the application of the proposed methods. [ABSTRACT FROM AUTHOR]

We investigate the multi-attribute group decision making (MAGDM) problems in which the attribute values provided by the decision makers take the form of intuitionistic trapezoid fuzzy linguistic (ITrFL) information considering the uncertainty and inaccuracy of input arguments. Some new power aggregation operators called intuitionistic trapezoid fuzzy linguistic power average (ITrFLPA) operator, intuitionistic trapezoid fuzzy linguistic power weighted average (ITrFLPWA) operator, intuitionistic trapezoid fuzzy linguistic power ordered weighted average (ITrFLPOWA) operator, intuitionistic trapezoid fuzzy linguistic power hybrid weighted average (ITrFLPHWA) operator, intuitionistic trapezoid fuzzy linguistic power geometric (ITrFLPG) operator, intuitionistic trapezoid fuzzy linguistic power weighted geometric (ITrFLPWG) operator, intuitionistic trapezoid fuzzy linguistic power ordered weighted geometric (ITrFLPOWG) operator and intuitionistic trapezoid fuzzy linguistic power hybrid weighted geometric (ITrFLPHWG) operator are proposed. Then, we study some desirable properties of the proposed operators, such as idempotency, commutativity and boundedness. In addition, two novel approaches based on the proposed operators are developed to solve MAGDM problems with intuitionistic trapezoid fuzzy linguistic information. Finally, a numerical example is provided to verify the feasibility of the proposed approaches. [ABSTRACT FROM AUTHOR]

With respect to multiple attribute group decision making (MAGDM) problems in which the assessment values of attributes take the form of interval-valued hesitant uncertain linguistic elements, a novel MAGDM method is proposed in this paper. Firstly, the concept, operational laws and score function of interval-valued hesitant uncertain linguistic elements (IVHULEs) are introduced. Then, based on the operational laws of IVHULEs, some generalized aggregation operators are proposed for aggregating the interval-valued hesitant uncertain linguistic information, including the generalized interval-valued hesitant uncertain linguistic weighted aggregation operators, the generalized interval-valued hesitant uncertain linguistic ordered weighted aggregation operators and the generalized interval-valued hesitant uncertain linguistic hybrid aggregation operators. Furthermore, some desirable properties of these operators and the relationships between them are discussed. Based on the proposed operators, an approach to multiple attribute group decision making with unknown weight information is developed under interval-valued hesitant uncertain linguistic environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Hamacher operations to aggregate the dual hesitant fuzzy elements (DHFEs). Firstly, operational rules of DHFEs based on Hamacher t-norm and t-conorm are proposed. Then, we develop some dual hesitant fuzzy Hamacher aggregation operators based on the operational rules of DHFEs, such as dual hesitant fuzzy Hamacher weighted averaging (DHFHWA) operator, dual hesitant fuzzy Hamacher weighted geometric (DHFHWG) operator, dual hesitant fuzzy Hamacher ordered weighted averaging (DHFHOWA) operator, dual hesitant fuzzy Hamacher ordered weighted geometric (DHFHOWG) operator, dual hesitant fuzzy Hamacher hybrid averaging (DHFHHA) operator and dual hesitant fuzzy Hamacher hybrid geometric (DHFHHG) operator are proposed. Some desirable properties of these operators such as idempotency and boundedness are discussed, and some special cases of these operators are analyzed. Furthermore, a method to multiple attribute decision making (MADM) based on the proposed operators is developed. Finally, a practical example is given to illustrate the developed method and a comparison analysis is also conducted, which further demonstrates the practicality and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates multiple attribute decision making (MADM) problems in which the attribute values take the form of interval-valued dual hesitant fuzzy elements (IVDHFEs). Firstly, motivated by the concepts of dual hesitant fuzzy set (DHFS) and interval number, the concept, operational laws and comparison laws of interval-valued dual hesitant fuzzy elements are proposed. Then, based on the operational laws of IVDHFEs, some aggregation operators are developed for aggregating the interval-valued dual hesitant fuzzy information, such as the interval-valued dual hesitant fuzzy weighted aggregation operators, the interval-valued dual hesitant fuzzy ordered weighted aggregation operators, the generalized interval-valued dual hesitant fuzzy weighted aggregation operators, the generalized interval-valued dual hesitant fuzzy ordered weighted aggregation operators and the interval-valued dual hesitant fuzzy hybrid aggregation operators. Furthermore, some desirable properties of these operators and the relationships between them are discussed in detail. Based on the interval-valued dual hesitant fuzzy weighted average (IVDHFWA) operator, an approach to multiple attribute decision making is proposed under interval-valued dual hesitant fuzzy environment. Finally, a numerical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

This paper investigates the multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant intuitionistic fuzzy linguistic elements (HIFLEs). Firstly, motivated by the idea of hesitant fuzzy linguistic elements and intuitionistic fuzzy numbers, the concept, operational laws and comparison laws of HIFLEs are defined. Then, some aggregation operators are developed for aggregating the hesitant intuitionistic fuzzy linguistic information, such as hesitant intuitionistic fuzzy linguistic weighted aggregation operators, hesitant intuitionistic fuzzy linguistic ordered weighted aggregation operators and hesitant intuitionistic fuzzy linguistic hybrid aggregation operators. Some desirable properties of these operators and the relationships between them are discussed. Furthermore, the hesitant intuitionistic fuzzy linguistic set is extended to hesitant intuitionistic fuzzy uncertain linguistic set, and some hesitant intuitionistic fuzzy uncertain linguistic aggregation operators are developed. Based on the hesitant intuitionistic fuzzy linguistic weighted average (HIFLWA) operator, an approach to MADM is proposed under hesitant intuitionistic fuzzy linguistic environment. Finally, a practical example is given to illustrate the application of the proposed method and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making (MADM) problems in which the attribute values take the form of trapezoid fuzzy 2-tuples. Firstly, we develop some trapezoid fuzzy 2-tuple linguistic aggregation operators based on the operational laws of trapezoid fuzzy 2-tuples, such as the trapezoid fuzzy 2-tuple weighted geometric (TFTWG) operator, the trapezoid fuzzy 2-tuple ordered weighted geometric (TFTOWG) operator, the generalized trapezoid fuzzy 2-tuple weighted average (GTFTWA) operator and the generalized trapezoid fuzzy 2-tuple ordered weighted average (GTFTOWA) operator. Then, we study some desirable properties of the developed operators, such as idempotency, monotonicity, commutativity and boundedness, and analyze some special cases of these operators. Furthermore, we propose an approach to multiple attribute decision making under trapezoid fuzzy linguistic environment based on the GTFTWA and TFTWG operators. Finally, an illustrative example is given to verify the proposed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

Present studies have shown that near-infrared spectroscopy (NIRS) could be used to identify the producing area of apple. However, we still do not know whether the producing area affects the optical properties of apple, whether it affects the relationship between optical properties and internal qualities, and whether the optical parameters could be used to predict the apple-producing area. To answer these questions, the apples produced in three areas with different temperatures, precipitations, and altitudes in the Loess Plateau region, China, were used as samples to obtain the optical properties of apple pulp by a single integrating sphere system, analyze the differences in optical properties of apples produced in different areas, analyze the correlations between optical properties (absorption coefficient (μ a) and reduced scattering coefficient (μ s ')) and internal quality indices (soluble solids content (SSC), moisture content and firmness), and investigate the feasibility of discriminating the apples produced in different areas and predicting the internal qualities using NIRS. The results showed that the apples produced in Luochuan had the highest SSC while Yangling apples had the highest moisture content. The μ a had three absorption peaks at around 985, 1200, and 1430 nm, and the μ s ' of apples from three areas showed a similar trend with wavelength. The best correlation of μ a with SSC and moisture content was found in Yangling apples with a correlation coefficient of −0.90 and 0.79, respectively. The built linear discriminant analysis based on μ a spectra performed better in discriminating producing area. The established partial least squares regression models based on μ a spectra had the best prediction performance for SSC and moisture content, while the model built with μ s ' had the best prediction performance for firmness. This study is helpful to understand the differences in optical property of 'Fuji' apple produced in different areas and offers information for identifying the producing area of fruit using NIRS technology. • The internal qualities of apple produced in three areas had significant difference. • The apples produced in three areas had three absorption peaks at 980, 1200, and 1430 nm. • The best correlation of μ a with SSC and moisture content was found in Yangling apples. • μ a spectra performed better in discriminating the apple-producing area. • μ a and μ s ' spectra had the best prediction performance for SSC and firmness, respectively. [ABSTRACT FROM AUTHOR]