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Information is a key factor that influences the performance of decision makers. With the explosive proliferation of Web 2.0, the volume of online textual reviews has been sharply increasing. However, how to use this type of unstructured data and utilize the valuable information hidden behind are still problems to be solved. This study aims to provide a multi-attributes decision analysis (MADA) framework based on incomplete online textual reviews to aid in decision making. First, online textual reviews are obtained by data crawling. Attributes information is determined by textual analysis and the attitudes of assessors toward each attribute is discriminated by the sentiment analysis. Then, some new rules are developed in encoding incomplete online textual reviews into interval-valued linguistic distribution assessment (ILDA) to better characterize the evaluators’ attitudes. Next, evidential reasoning (ER) algorithm is extended to the ILDA environment to combine the information with multiple attributes, and the utility interval of each alternative is constructed by solving a pair of nonlinear optimization models. Given that the interval data cannot be directly compared, an enhanced minimax regret approach is proposed to compare and rank them. Finally, a real case study about online commodity evaluation is examined to show the implementation process of the proposed framework, and a discussion is also conducted to systematically analyze its superiority.

Interval type-2 fuzzy sets (IT2 FS) have played a prominent role in the development of type-2 (T2) fuzzy logic and fuzzy systems for application to linguistic approximation transformations. Although there have been a number of studies of individual linguistic perception understanding based on T2 fuzzy logic, few of these have paid attention to the computational manipulation of group linguistic perceptions based on IT2 FS theory and methods. Proportional hesitant fuzzy linguistic term sets (PHFLTSs) allow conceptualization of group linguistic perceptions with the inclusion of generalized linguistic terms and their associated proportions. Interpreting PHFLTSs from the viewpoint of T2 fuzzy logic instead of its type-1 counterpart has the potential to provide useful results because of the ability of IT2 FSs to accurately model individual comprehension in the presence of linguistic uncertainty. This paper brings a novel perspective to encoding PHFLTSs based on the concept of a proportional interval T2 hesitant fuzzy set (PIT2 HFS). PIT2 HFSs combine IT2 FSs translated from generalized linguistic terms together with their proportional information. To facilitate computing with PIT2 HFSs, basic operations satisfying the closure property are defined for PIT2 HFSs based on Archimedean t-norms and s-norms. Information measurements such as a distance and a score function for PIT2 HFS are also defined. Two instrumental aggregation operators for PIT2 HFSs, namely, the Hamacher proportional interval T2 hesitant fuzzy power weighted average (Ham-PIT2HPWA) operator and the Hamacher proportional interval T2 hesitant fuzzy power weighted geometric (Ham-PIT2HPWG) operator, are investigated, and their limiting cases with respect to various parameters are discussed. Furthermore, two andness optimization models with the andness measure being the attitudinal character are constructed in a bid to determine reasonable parameter values associated with the Ham-PIT2HPWA and Ham-PIT2HPWG operators. On the basis of the Hamacher aggregation operators and the andness optimization models, a proportional interval T2 hesitant fuzzy TOPSIS approach is developed to provide linguistic decision making under uncertainty. The proposed approach represents a novel paradigm for linguistic group decision making under the umbrella of T2 fuzzy logic and systems for computing with words that has potential for application in real-life scenarios.

Possibility distribution provides an alternative explanation of linguistic terms in an hesitant fuzzy linguistic term set (HFLTS). It is generated from a given HFLTS based on the assumption that all linguistic terms in an HFLTS follow a uniform distribution. In decision making contexts, linguistic terms in each HFLTS are assumed to exhibit the same possibility to represent the decision-maker(DM)s assessment rating. However, DMs may give ratings based on different assessing attitudes because of individual differences in cognitive styles. In practice, comparative linguistic expressions are generally converted into HFLTSs through the transformation process as DMs usually use comparative linguistic expressions instead of HFLTSs when giving ratings. The transformed HFLTSs likewise exclude the DMs assessing attitudes. To enhance the interpretability of generated possibility distributions, this paper relaxes the original assumption of uniform distribution and incorporates an attitudinal dimension into the transformation process that converts comparative linguistic expressions to HFLTSs. With these modified conditions for possibility distribution generation, an assessing attitude-driven approach is proposed based on probability density functions (PDFs) to generate HFLTS possibility distributions. The proposed PDF-based HFLTS possibility distributions personalize individual semantics and further facilitate the process of computing with words to obtain assessing attitude-embedded accurate linguistic results that are easy for individuals to interpret and understand.

The advantages and applications of rule-based systems have caused them to be widely recognized as one of the most popular systems in human decision-making, due to their accuracy and efficiency. To improve the performance of rule-based systems, there are several issues proposed to be focused. First, it is unnecessary to take the entire rule base into consideration during each decision-making process. Second, there is no need to visit the entire rule base to search for the key rules. Last, the key rules for each decision-making process should be different. This paper focuses on an advanced extended belief rule base (EBRB) system and proposes a multi-attribute search framework (MaSF) to reconstruct the relationship between rules in the EBRB to form the MaSF-based EBRB. MaSFs can be divided into k-dimensional tree (KDT)-based MaSFs and Burkhard-Keller (BKT)-based MaSFs. The former is targeted at decision-making problems with small-scale attribute datasets, while the latter is for those with large-scale attribute datasets. Based on the MaSF-based EBRB, the k-neighbor search and the best activated rule set algorithms are further proposed to find both the unique and the desired rules for each decision-making process without visiting the entire EBRB, especially when handling classification problems with large attribute datasets. Two sets of experiments based on benchmark datasets with different numbers of attributes are performed to analyze the difference between KDT-based MaSFs and BKT-based MaSFs, and to demonstrate how to use MaSFs to improve the accuracy and efficiency of EBRB systems. MaSFs and their corresponding algorithms are also regarded as a general optimization framework that can be used with other rule-based systems.

We propose the general concept of PHFLTS.We define the negation, union, and intersection operations on PHFLTSs.We present the PHFLWA and PHFLOWA operators.A transformation algorithm is proposed to convert the proportional comparative linguistic pairs into PHFLTSs.We develop a proportional hesitant fuzzy linguistic MCGDM model. The theory of hesitant fuzzy linguistic term sets (HFLTSs) is a powerful technique used to describe hesitant situations, which are typically assessed by experts using several possible linguistic values or rich expressions instead of a single term. The union of HFLTSs with respect to each expert, that is, an extended HFLTS (EHFLTS), further facilitates the elicitation of linguistic assessments for addressing group decision-making problems because EHFLTSs can deal with generalized (either consecutive or non-consecutive) linguistic terms. In this study, we propose proportional HFLTSs (PHFLTSs), which include the proportional information of each generalized linguistic term. The mathematical form for a PHFLTS is consistent with that for a linguistic distribution assessment. However, the underlying meanings of the proportions associated with generalized linguistic terms are different. PHFLTSs can be viewed as a special method for performing linguistic distribution assessments. PHFLTSs are recognized as a useful extension of HFLTSs and a possibility distribution for HFLTSs under different assumptions. We define the basic operations with closed properties among PHFLTSs on the basis of t-norms and t-conorms. We then propose a probability theory-based outranking method for PHFLTSs by providing possibility degree formulas. We also study two fundamental aggregation operators for PHFLTSs, namely, the proportional hesitant fuzzy linguistic weighted averaging operator and the proportional hesitant fuzzy linguistic ordered weighted averaging operator. Several important properties of these aggregation operators are investigated. Finally, we use the proposed multiple criteria group decision-making model in practical applications.

The article Proportional hesitant fuzzy linguistic term set for multiple criteria group decision making (Information Sciences, vol. 357, 6187, 2016) contains some computational errors that hinder the validation of the proposed method. The computational errors are corrected, and the pertinent analysis descriptions are revised accordingly.

Denoeux proposed an operator called the cautious conjunctive rule (CCR) to combine non-dogmatic belief functions (i.e., the frame is considered a focal element) from reliable dependent sources, which can occur in practice. However, in cases such as uncertain multiple attribute and group decision analyses, belief functions may denote data that vary in importance. This paper extends CCR as a weighted CCR (WCCR) to combine belief functions in consideration of their relative weights in such situations. Properties of WCCR are analyzed, proven, and demonstrated using numerical examples. In particular, the consideration of relative weights enables WCCR to combine dogmatic belief functions. The normalized WCCR is further constructed and used to assess the trustworthiness of a hospital information system employed in many hospitals in Anhui Province, China.

Quality function deployment (QFD) provides a planning and problem-solving methodology that is widely renowned for translating customer requirements (CRs) into engineering characteristics (ECs) for new product development. As the first phase of QFD, product planning house of quality (PPHOQ) plays a very important role in this process. The degrees and directions of the relationship measures between CRs and ECs have serious effects on the special planning of ECs, modeling the relationship measures is an important step in constructing PPHOQ. The current paper presents a rough set (RS)-based approach for modeling relationship measures by determining the knowledge and experience of the QFD team, aided by the introduction of the type factor of a relationship used to express the effects of the relationship types. A study of general cases is used to demonstrate the performances and limitations of the proposed RS-based approach. The results show that the novel approach effectively determines the relative knowledge of the QFD team and facilitates decision-making in new product development.

Quality function deployment (QFD) is a planning and problem-solving methodology used to translate customer requirements (CRs) into engineering characteristics (ECs) in the course of new product development (NPD). Estimating the correlation measures among ECs is a crucial step in the product planning house of quality (PPHOQ) construction process because these measures seriously affect the planning of development efforts. This study presents a rough set-based approach used to estimate the correlation measures by revealing the knowledge of a QFD team. The approach involves introducing the category factor of a correlation to express the influences of the correlation categories on the corresponding correlation measures. A case study of a two-cylinder washing machine is used to illustrate the proposed approach. The result shows that the novel approach is effective in revealing the related knowledge of the QFD team and facilitating NPD decision making.

Quality function deployment (QFD) is a planning tool used in new product development and quality management. It aims at achieving maximum customer satisfaction by listening to the voice of customers. To implement QFD, customer requirements (CRs) should be identified and assessed first. The current paper proposes a linear goal programming (LGP) approach to assess the relative importance weights of CRs. The LGP approach enables customers to express their preferences on the relative importance weights of CRs in their preferred or familiar formats, which may differ from one customer to another but have no need to be transformed into the same format, thus avoiding information loss or distortion. A numerical example is tested with the LGP approach to demonstrate its validity, effectiveness and potential applications in QFD practice.

Eigenvector method (EM) is a well-known approach to deriving priorities from pairwise comparison matrices in the analytic hierarchy process (AHP), which requires the solution of a set of nonlinear eigenvalue equations. This paper proposes an approximate solution approach to the EM to facilitate its computation. We refer to the approach as a linear programming approximation to the EM, or LPAEM for short. As the name implies, the LPAEM simplifies the nonlinear eigenvalue equations as a linear programming for solution. It produces true weights for perfectly consistent pairwise comparison matrices. Numerical examples are examined to show the validity and effectiveness of the proposed LPAEM and its significant advantages over a recently developed linear programming method entitled LP-GW-AHP in rank preservation.

This paper investigates the issues of combination and normalization of interval-valued belief structures within the framework of Dempster-Shafer theory (DST) of evidence. Existing approaches are reviewed, examined and critically analysed. They either ignore the normalization or separate it from the combination process, leading to irrational or suboptimal interval-valued belief structures. A new logically correct optimality approach is developed, where the combination and the normalization are optimised together rather than separately. Numerical examples are provided throughout the paper.

Rough set data analysis is one of the main application techniques arising from rough set theory. In this paper we introduce a concept of inclusion degree into rough set theory and establish several important relationships between the inclusion degree and measures on rough set data analysis. It is shown that the measures on rough set data analysis can be reduced to the inclusion degree.