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Distributed Linguistic Representations in Decision Making: Taxonomy, Key Elements and Applications, and Challenges in Data Science and Explainable Artificial Intelligence
Yuzhu Wu, Zhen Zhang, Gang Kou, Hengjie Zhang, Xiangrui Chao, Cong-Cong Li, Yucheng Dong, Francisco Herrera
TL;DR
The paper addresses how distributed linguistic representations model uncertain and complex preference information in linguistic decision making. It reviews their taxonomy, processing elements, applications, and data science and XAI challenges, concluding that these representations offer flexible tools for complex decision contexts while leaving transformation theory insufficiently systematic.
Problem
Decision makers’ uncertain and hesitant linguistic preferences require representations capable of expressing distributed information in complex decision-making contexts.
Method
The paper reviews distributed linguistic representations through their taxonomy, key processing elements, applications, and challenges in data science and explainable artificial intelligence.
Results
Distributed linguistic representations are organized into two origins—proportional linguistic 2-tuples and HFLTS-based extensions—and related forms are classified within a broader taxonomy.
Takeaways & Limitations
Distributed linguistic representations provide flexible tools for modelling uncertain and complex preferences across decision-making problems and applications.
Takeaways & Limitations
Systematic research on transformations among distributed linguistic representations remains lacking, including axiom-based and minimum-information-loss analyses.
Abstract
from arXiv · showhide
Distributed linguistic representations are powerful tools for modelling the uncertainty and complexity of preference information in linguistic decision making. To provide a comprehensive perspective on the development of distributed linguistic representations in decision making, we present the taxonomy of existing distributed linguistic representations. Then, we review the key elements of distributed linguistic information processing in decision making, including the distance measurement, aggregation methods, distributed linguistic preference relations, and distributed linguistic multiple attribute decision making models. Next, we provide a discussion on ongoing challenges and future research directions from the perspective of data science and explainable artificial intelligence.
1. Introduction
Distributed linguistic representations extend linguistic decision-making models to express uncertain, hesitant, and distributed preferences. This paper reviews their taxonomy, processing elements, applications, and challenges in data science and explainable artificial intelligence.
- Origins and representations: Computing with words models process linguistic information, including membership-function and symbolic computational approaches.The 2-tuple linguistic representation is widely used for balanced linguistic information, while other models address unbalanced information and individual semantics.
- Origins and representations: Hesitant fuzzy linguistic term sets represent comparative hesitant preferences, whereas linguistic distributions assign symbolic proportions to linguistic terms.Probabilistic linguistic term sets use a different name for a similar concept to linguistic distributions.
- Motivation: Compared with simple linguistic 2-tuples, HFLTS and LD provide more flexible expressions for complex decision-making problems.Decision makers may be uncertain or hesitant because of time pressure and limited knowledge, producing distributed linguistic preference information.
- Paper scope: The paper reviews distributed linguistic representations through taxonomy, key elements, applications, and challenges from data science and XAI perspectives.The paper is organized around representation taxonomy, decision-making elements and applications, future challenges, and conclusions.
2. Distributed linguistic representations: origin, basic concepts, and taxonomy
Distributed linguistic representations extend linguistic decision-making models to capture hesitant, proportional, distributed, and incomplete preference information. The review organizes these representations around linguistic 2-tuples, HFLTS, LD and related variants, identifying their mathematical relationships.
- Basic representations: HFLTS represents hesitant preferences as an ordered finite subset of consecutive linguistic terms elicited through comparative linguistic expressions.It was introduced to improve the flexibility of linguistic expressions for decision makers’ hesitant necessities.
- Origins: Distributed linguistic representations arise either from individual linguistic preferences with distributed information or from group-level fusion of linguistic terms and HFLTSs.The review identifies proportional linguistic 2-tuple extensions and HFLTS-based distributed preference information as two main origins.
- Distributed representations: LD assigns symbolic proportions to linguistic terms, forming a complete probabilistic distribution whose expectation can support further computation.Each linguistic term has an associated proportion, and the proportions sum to one.
- Incomplete representations: Incomplete distributed information is represented through PLD, PLTS, and ILD, with proportional coefficients expressing partial information or confidence in linguistic evaluations.The review describes incomplete information using coefficients whose total may be below one and interprets these coefficients as confidence levels.
- Taxonomy: The taxonomy identifies FLE as a generalization of most reviewed representations and classifies LD, PDHFLTS, PHFLTS, PLTS, PLD, and ILD as special HLDs.It also reports that PLD is approximately equivalent to PLTS and ILD, PHFLTS is mathematically consistent with LD, PDHFLTS is a special case of LD, and INLD generalizes LD.
3. Key elements and applications of distributed linguistic representations in decision making
This section reviews how distributed linguistic representations support decision making through distance measurement, aggregation, preference relations, MADM models, and applications. It summarizes representative methods for comparing and combining distributed linguistic information and its use in uncertain assessments and practical decision support.
- 3.1. Distributed linguistic distance measurements: Distance measurements compare distributed linguistic representations using symbolic proportions, linguistic-term scales, uncertainty, or incomplete-information parameters.Reviewed measures include LD, PDHFLTS, PLTS, ILD, and FLE distances.
- 3.2. Aggregation approaches of distributed linguistic representations: Aggregation methods combine distributed linguistic information through weighted, ordered weighted, power-average, and weighted power-average operators.The reviewed operators include LDWA, LDOWA, LDPA, LDWPA, INLDWA, and INLDOWA.
- 3.5. Some real-life applications: Applications include tourism-product and hotel-selection decision support, including a sentiment-analysis and LD-VIKOR model for hotel selection.The reviewed applications address practical decision contexts such as online tourism services and hotels.
4. Summary, critical discussion and challenges from the perspective of decision making and data science/XAI
The review organizes distributed linguistic representations by their origins, taxonomy, decision-making applications, and unresolved challenges for data science and XAI. It highlights concept confusion, incomplete transformation frameworks, and the need for interpretable data-driven processing.
- Origin and taxonomy: Distributed linguistic representations originate from extensions of proportional linguistic 2-tuples or HFLTS-based representations, formed individually or through group information fusion.The reviewed representations include LD, INLD, PLD, and ILD in the first family, and PDHFLTS, PHFLTS, PLTS, HLD, and FLE in the second.
- Origin and taxonomy: FLE generalizes the reviewed distributed linguistic representations, while several LD variants have stated special-case or mathematical-consistency relationships.The review identifies LD, PDHFLTS, PHFLTS, PLTS, PLD, and ILD as special HLDs, and describes INLD as a generalization of LD.
- Applications: Applications span distance measurement and aggregation, distributed linguistic preference relations, distributed linguistic MADM, and real-life decision problems.Most distance and aggregation methods build on classical measurements and aggregation operators, with optimization methods addressing some accuracy problems.
- Limitations and research needs: The literature lacks systematic, axiom-based transformations among distributed linguistic representations and rational minimum-information-loss transformation models.Existing normalization methods for transforming incomplete PLTSs into LDs are described as questionable, motivating further study of reasonable PLTS-to-LD normalization.
- Limitations and research needs: Similar concepts and parallel research have produced repeated discussions and confusion, making attention to original formulations and meaningful comparisons necessary.The review identifies FLE as a potential tool for forming a unified framework.
- Data science and XAI: Data science and XAI challenges include extracting linguistic assessments with NLP, fusing large heterogeneous data, learning preferences, and developing interpretable linguistic models.Open problems include analyzing distributed linguistic data at scale, learning word encodings and personalized semantics, and obtaining insights from fused data without relying solely on difficult-to-interpret black models.
5. Conclusion
The conclusion reviews distributed linguistic representations through taxonomy, key elements and applications, and ongoing challenges. It connects their decision-making uses with future directions in data science and XAI.
- Conclusion: The paper reviews distributed linguistic representations through taxonomy, key elements and applications, and ongoing challenges.Its scope is explicitly organized around these three perspectives.
- Conclusion: The review classifies existing representations by proportional linguistic 2-tuple extensions and HFLTS-based extended representations.It also distinguishes individual linguistic preference expressions from group information fusion.
- Conclusion: It summarizes distance measurements, aggregation methods, preference relations, distributed linguistic MADM, and real-life applications.These are presented as key elements and applications in decision problems.
- Conclusion: The paper critically discusses concept confusion and proposes data science and XAI challenges and future directions.The conclusion frames these issues as ongoing research directions.