Abstract
In formal concept analysis, as a data visualization tool, attribute partial ordered structure diagram can effectively discover the partial order relationship between attributes. Numerous linguistically valued facts from the actual world have been modeled using the fuzzy linguistic approach. To make attribute partial ordered structure diagram more effective in handling fuzzy linguistic information, this paper proposes a fuzzy linguistic attribute partial ordered structure diagram (FL-APOSD) construction approach from the hierarchical and structural perspectives. Firstly, the linguistic truth-valued lattice implication algebra is applied as the fuzzy linguistic representation model to express comparable and incomparable evaluative linguistic expressions. Secondly, to express the complex linguistic relationships between objects and attributes, FL-APOSD is proposed to embed fuzzy linguistic information into an attribute partial ordered structure diagram based on a linguistic-valued formal context. Moreover, a FL-APOSD construction model is developed from the hierarchical and structural perspectives to represent the attribute partial order relation under the linguistic environment. Finally, the comparative analysis shows the effectiveness of the proposed model in expressing the linguistic expressions’ incompleteness, uncertainty, and incomparable characteristics.
Similar content being viewed by others
Data availability
Enquiries about data availability should be directed to the authors.
References
Belohlavek R, Vychodil V (2012) Formal concept analysis and linguistic hedges. Int J Gen Syst 41(5):503–532
Boran FE, Akay D, Yager RR (2016) An overview of methods for linguistic summarization with fuzzy sets. Expert Syst Appl 61:356–377
Chemmalar SG, Lakshmi PG, Joseph RB (2019) A fca-based concept clustering recommender system. In: Context-aware systems and applications, and nature of computation and communication. Springer, pp 178–187
Chen S-M, Hong J-A (2014) Multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets and the aggregation of fuzzy sets. Inf Sci 286:63–74
Cui H, Yue G, Zou L, Liu X, Deng A (2021) Multiple multidimensional linguistic reasoning algorithm based on property-oriented linguistic concept lattice. Int J Approx Reason 131:80–92
Dong Q, Sheng Q, Martínez L, Zhang Z (2022) An adaptive group decision making framework: Individual and local world opinion based opinion dynamics. Inf Fusion 78:218–231
Hao F, Yang Y, Min G, Loia V (2021) Incremental construction of three-way concept lattice for knowledge discovery in social networks. Inf Sci 578:257–280
Herrera F, Alonso S, Chiclana F, Herrera-Viedma E (2009) Computing with words in decision making: foundations, trends and prospects. Fuzzy Optim Decis Mak 8(4):337–364
Hong W, Li S, Yu J (2012) A new approach of generation of structural partial-ordered attribute diagram. ICIC Express Lett Int J Res Surv Part B Appl 3(4):823–830
Hong W, Pang J, Yu J (2013) Knowledge reduction in Chinese medical diagnosis based on structural partial-ordered attribute diagram. ICIC Express Lett Part B Appl Int J Res Surv 4(4):959–965
Kumar CA, Srinivas S (2010) Concept lattice reduction using fuzzy k-means clustering. Expert Syst Appl 37(3):2696–2704
Kuznetsov SO, Makhazhanov N, Ushakov M (2017) On neural network architecture based on concept lattices. In: International symposium on methodologies for intelligent systems. Springer, pp 653–663
Lan N, Yang S, Yin L, Gao Y (2021) Research on knowledge graphs with concept lattice constraints. Symmetry 13(12):2363
Liang H, Li C-C, Dong Y, Herrera F (2020) Linguistic opinions dynamics based on personalized individual semantics. IEEE Trans Fuzzy Syst 29(9):2453–2466
Liu Y, Rodriguez RM, Hagras H, Liu H, Qin K, Martinez L (2019) Type-2 fuzzy envelope of hesitant fuzzy linguistic term set: a new representation model of comparative linguistic expression. IEEE Trans Fuzzy Syst 27(12):2312–2326
Luan J, Wang C, Yan E, Song J, Yu J, Hong W (2013) The classification of Hayes-Roth dataset based on structural partial-ordered attribute diagram. ICIC Express Lett 7(B):965–970
Luan J, Liu X, Hong W, Song J (2019) Generating syndrome name based on partial-ordered attributes theory. In: 2019 12th international congress on image and signal processing, BioMedical engineering and informatics (CISP-BMEI). IEEE, pp 1–6
Malhotra T, Gupta A (2020) A new 2-tuple linguistic approach for unbalanced linguistic term sets. IEEE Trans Fuzzy Syst 29(8):2158–2168
Martinez L, Ruan D, Herrera F (2010) Computing with words in decision support systems: an overview on models and applications. Int J Comput Intell Syst 3(4):382–395
Mendel JM (2016) A comparison of three approaches for estimating (synthesizing) an interval type-2 fuzzy set model of a linguistic term for computing with words. Granul Comput 1(1):59–69
Meng H, Hong W, Yu C, Ding W, Song J, Li S, Yan E (2021) Symptom-herb knowledge discovery based on attribute partial ordered structure diagrams. Granul Comput 6(2):229–240
Mezni H, Abdeljaoued T (2018) A cloud services recommendation system based on fuzzy formal concept analysis. Data Knowl Eng 116:100–123
Novák V (2008) A comprehensive theory of trichotomous evaluative linguistic expressions. Fuzzy Sets Syst 159(22):2939–2969
Novak V (2015) Evaluative linguistic expressions vs. fuzzy categories. Fuzzy Sets Syst 281:73–87
Pang K, Liu P, Li S, Zou L, Lu M, Martínez L (2023) Concept lattice simplification with fuzzy linguistic information based on three-way clustering. Int J Approx Reason 154:149–175
Pei Z, Ruan D, Liu J, Xu Y (2010) Linguistic values based intelligent information processing: theory, methods, and applications, vol 259. Springer, Berlin
Pei Z, Ruan D, Meng D, Liu Z (2013) Formal concept analysis based on the topology for attributes of a formal context. Inf Sci 236:66–82
Ramos-Soto A, Martin-Rodilla P (2021) Enriching linguistic descriptions of data: a framework for composite protoforms. Fuzzy Sets Syst 407:1–26
Rodriguez RM, Martinez L, Herrera F (2011) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 20(1):109–119
Singh PK (2018) Concept learning using vague concept lattice. Neural Process Lett 48(1):31–52
Wan S-P, Zou W-C, Dong J-Y, Martínez L (2022) A consensual method for multi-criteria group decision-making with linguistic intuitionistic information. Inf Sci 582:797–832
Wang Z-C, Ran Y, Chen Y, Yang X, Zhang G (2022) Group risk assessment in failure mode and effects analysis using a hybrid probabilistic hesitant fuzzy linguistic MCDM method. Expert Syst Appl 188:116013
Wille R (2009) Restructuring lattice theory: an approach based on hierarchies of concepts. In: International conference on formal concept analysis. Springer, pp 314–339
Xu Y, Ruan D, Qin K, Liu J (2003) Lattice-valued logic. Stud Fuzziness. Soft Comput 132:27–57
Xu Y, Chen S, Ma J (2006) Linguistic truth-valued lattice implication algebra and its properties. In: The proceedings of the multiconference on computational engineering in systems applications, vol 2. IEEE, pp 1413–1418
Yan E, Song J, Liu C, Hong W (2017) A research on syndrome element differentiation based on phenomenology and mathematical method. Chin Med 12(1):1–18
Yan E, Song J, Ren Y, Zheng C, Mi B, Hong W (2020) Construction of three-way attribute partial order structure via cognitive science and granular computing. Knowl Based Syst 197:105859
Yan E, Yu C, Lu L, Hong W, Tang C (2021) Incremental concept cognitive learning based on three-way partial order structure. Knowl Based Syst 220:106898
Yu J, Hong W, Qiu C, Li S, Mei D (2016) A new approach of attribute partial order structure diagram for word sense disambiguation of english prepositions. Knowl Based Syst 95:142–152
Zadeh LA (1999) Fuzzy logic computing with words. In: Zadeh LA, Kacprzyk J (eds) Computing with words in information/intelligent systems, vol 1. Springer, pp 3–23
Zhang T, Li H-H, Liu M-Q, Rong M (2020) Incremental concept-cognitive learning based on attribute topology. Int J Approx Reason 118:173–189
Zhang T, Rong M, Shan H, Liu M (2021) Causal asymmetry analysis in the view of concept-cognitive learning by incremental concept tree. Cogn Comput 13(5):1274–1286
Zhang T, Rong M, Shan H, Liu M (2022) Stability analysis of incremental concept tree for concept cognitive learning. Int J Mach Learn Cybern 13(1):11–28
Zhang T, Lin L, Xue Z (2023a) A voice feature extraction method based on fractional attribute topology for Parkinson’s disease detection. Expert Syst Appl 219:119650
Zhang T, Lin L, Tian J, Xue Z, Guo X (2023b) Voice feature description of Parkinson’s disease based on co-occurrence direction attribute topology. Eng Appl Artif Intell 122:106097
Zou C, Zhang D, Wan J, Hassan MM, Lloret J (2015) Using concept lattice for personalized recommendation system design. IEEE Syst J 11(1):305–314
Zou L, Pang K, Song X, Kang N, Liu X (2020) A knowledge reduction approach for linguistic concept formal context. Inf Sci 524:165–183
Zou L, Kang N, Che L, Liu X (2022) Linguistic-valued layered concept lattice and its rule extraction. Int J Mach Learn Cybern 13(1):83–98
Acknowledgements
This work is supported by the National Natural Science Foundation of China (nos. 61976124, 62176142), the National Key R &D Program (no. 2018YFC1707703), and Special Foundation for Distinguished Professors of Shandong Jianzhu University.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Conflict of interest
The authors have no relevant financial or non-financial interests to disclose.
Ethics approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Pang, K., Zou, L., Kang, N. et al. The construction of fuzzy linguistic attribute partial ordered structure diagram. Comp. Appl. Math. 42, 240 (2023). https://doi.org/10.1007/s40314-023-02360-4
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40314-023-02360-4
Keywords
- Formal concept analysis
- Attribute partial ordered structure diagram
- Linguistic truth-valued lattice implication algebra
- Fuzzy linguistic information
- Granular computing