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On decision evaluation functions in three-way decision spaces derived from overlap and grouping functions

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Abstract

Overlap and grouping functions, as two kinds of particular binary aggregation functions, have been continuously discussed in the literature for their vast preponderance in some real applications. Meanwhile, after Hu introduced the notion of three-way decision spaces, the decision evaluation functions in three-way decision spaces constructed from the so-called semi-decision evaluation functions have been investigated consistently. This paper continues to consider this research topic and mainly focuses the decision evaluation functions in three-way decision spaces obtained from overlap and grouping functions. Firstly, based on overlap and grouping functions, we give several methods of constructing semi-decision evaluation functions in semi-three-way decision spaces. Secondly, we show some novel semi-decision evaluation functions which are related to fuzzy sets, interval-valued fuzzy sets, fuzzy relations and hesitant fuzzy sets, respectively. Finally, using overlap and grouping functions, we get some ways to construct decision evaluation functions in three-way decision spaces from semi-decision evaluation functions in semi-three-way decision spaces.

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References

  • Afridi M, Azam N, Yao J (2020) Variance based three-way clustering approaches for handling overlapping clustering. Int J Approx Reason 118:47–63

    Article  MathSciNet  MATH  Google Scholar 

  • Bedregal B, Bustince H, Palmeira E, Dimuro G, Fernandez J (2017) Generalized interval-valued OWA operators with interval weights derived from interval-valued overlap functions. Int J Approx Reason 90:1–16

    Article  MathSciNet  MATH  Google Scholar 

  • Bustince H, Fernández J, Mesiar R, Montero J, Orduna R (2009) Overlap index, overlap functions and migrativity. In: Proceedings of IFSA/EUSFLAT conference, pp 300–305

  • Bustince H, Fernandez J, Mesiar R, Montero J, Orduna R (2010) Overlap functions. Nonlinear Anal 72:1488–1499

    Article  MathSciNet  MATH  Google Scholar 

  • Bustince H, Pagola M, Mesiar R, Hüllermeier E, Herrera F (2012) Grouping, overlaps, and generalized bientropic functions for fuzzy modeling of pairwise comparisons. IEEE Trans Fuzzy Syst 20:405–415

    Article  Google Scholar 

  • Cabitza F, Ciucci D, Locoro A (2017) Exploiting collective knowledge with three-way decision theory: cases from the questionnaire-based research. Int J Approx Reason 83:356–370

    Article  MathSciNet  MATH  Google Scholar 

  • Cao M, Hu BQ, Qiao J (2018) On interval \(({\mathbb{G}},{\mathbb{N}})\)-implications and \(({\mathbb{O}},{\mathbb{G}},{\mathbb{N}})\)-implications derived from interval overlap and grouping functions. Int J Approx Reason 100:135–160

    Article  MathSciNet  MATH  Google Scholar 

  • De Miguel L, Gómez D, Rodríguez JT, Montero J, Bustince H, Dimuro GP, Sanz JA (2019) General overlap functions. Fuzzy Sets Syst 372:81–96

    Article  MathSciNet  MATH  Google Scholar 

  • Deng W (2020) An effective improved co-evolution ant colony optimization algorithm with multi-strategies and its application. Int J Bio-Inspired Comput 1–10

  • Deng W, Liu H, Xu J, Zhao H, Song Y (2020) An improved quantum-inspired differential evolution algorithm for deep belief network. IEEE Trans Instrum Meas. https://doi.org/10.1109/TIM.2020.2983233

    Article  Google Scholar 

  • Dimuro GP, Bedregal B (2015) On residual implications derived from overlap functions. Inf Sci 312:78–88

    Article  MathSciNet  MATH  Google Scholar 

  • Dimuro GP, Bedregal B, Santiago RHN (2014) On \((G, N)\)-implications derived from grouping functions. Inf Sci 279:1–17

    Article  MathSciNet  MATH  Google Scholar 

  • Dimuro GP, Bedregal B, Bustince H, Asiáin MJ, Mesiar R (2016) On additive generators of overlap functions. Fuzzy Sets Syst 287:76–96

    Article  MathSciNet  MATH  Google Scholar 

  • Dimuro GP, Bedregal B, Bustince H, Jurio A, Baczyński M, Miś K (2017) \(QL\)-operations and \(QL\)-implication functions constructed from tuples \((O, G, N)\) and the generation of fuzzy subsethood and entropy measures. Int J Approx Reason 82:170–192

    Article  MathSciNet  MATH  Google Scholar 

  • Dimuro GP, Bedregal B, Fernandez J, Sesma-Sara M, Pintor JM, Bustince H (2019) The law of \(O\)-conditionality for fuzzy implications constructed from overlap and grouping functions. Int J Approx Reason 105:27–48

    Article  MathSciNet  MATH  Google Scholar 

  • Elkano M, Galar M, Sanz J, Fernández A, Barrenechea E, Herrera F, Bustince H (2015) Enhancing multi-class classification in FARC-HD fuzzy classifier: on the synergy between n-dimensional overlap functions and decomposition strategies. IEEE Trans Fuzzy Syst 23:1562–1580

    Article  Google Scholar 

  • Elkano M, Galar M, Sanz J, Bustince H (2016) Fuzzy rule-based classification systems for multi-class problems using binary decomposition strategies: on the influence of n-dimensional overlap functions in the fuzzy reasoning method. Inf Sci 332:94–114

    Article  Google Scholar 

  • Elkano M, Galar M, Sanz JA, Schiavo PF, Pereira S Jr, Dimuro GP, Borges EN, Bustince H (2018) Consensus via penalty functions for decision making in ensembles in fuzzy rule-based classification systems. Appl Soft Comput 67:728–740

    Article  Google Scholar 

  • Fan Z (2000) On the convergence of a fuzzy matrix in the sense of triangular norms. Fuzzy Sets Syst 109:409–417

    Article  MathSciNet  MATH  Google Scholar 

  • Gómez D, Rodríguez JT, Montero J, Bustince H, Barrenechea E (2016a) n-dimensional overlap functions. Fuzzy Sets Syst 287:57–75

    Article  MathSciNet  MATH  Google Scholar 

  • Gómez D, Rodríguez JT, Yáñez J, Montero J (2016b) A new modularity measure for Fuzzy Community detection problems based on overlap and grouping functions. Int J Approx Reason 74:88–107

    Article  MathSciNet  MATH  Google Scholar 

  • Goudey R (2007) Do statistical inferences allowing three alternative decision give better feedback for environmentally precautionary decision-making. J Environ Manag 85:338–344

    Article  Google Scholar 

  • He X, Wei L, She Y (2018) L-fuzzy concept analysis for three-way decisions: basic definitions and fuzzy inference mechanisms. Int J Mach Learn Cybern 9:1857–1867

    Article  Google Scholar 

  • Herbert JP, Yao JT (2009) Criteria for choosing a rough set model. J Comput Math Appl 57:908–918

    Article  MATH  Google Scholar 

  • Hu BQ (2014) Three-way decisions space and three-way decisions. Inf Sci 281:21–52

    Article  MathSciNet  MATH  Google Scholar 

  • Hu BQ (2016) Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets. Knowl Based Syst 91:16–31

    Article  Google Scholar 

  • Hu BQ (2017) Three-way decisions based on semi-three-way decision spaces. Inf Sci 382–383:415–440

    Article  MATH  Google Scholar 

  • Hu BQ, Wong H, Yiu KFC (2016) The aggregation of multiple three-way decision space. Knowl Based Syst 98:241–249

    Article  Google Scholar 

  • Hu BQ, Wong H, Yiu KFC (2017) On two novel types of three-way decisions in three-way decision spaces. Int J Approx Reason 82:285–306

    Article  MathSciNet  MATH  Google Scholar 

  • Hu J, Yang Y, Chen X (2018) A novel TODIM method-based three-Way decision model for medical treatment selection. Int J Fuzzy Syst 20:1240–1255

    Article  MathSciNet  Google Scholar 

  • Jiao L, Yang H, Li S (2020) Three-way decision based on decision-theoretic rough sets with single-valued neutrosophic information. Int J Mach Learn Cybern 11:657–665

    Article  Google Scholar 

  • Jurio A, Bustince H, Pagola M, Pradera A, Yager R (2013) Some properties of overlap and grouping functions and their application to image thresholding. Fuzzy Sets Syst 229:69–90

    Article  MathSciNet  MATH  Google Scholar 

  • Klement EP, Mesiar R, Pap E (2000) Triangular norms. Kluwer, Dordrecht

    Book  MATH  Google Scholar 

  • Lang G, Miao D, Cai M (2017) Three-way decision approaches to conflict analysis using decision-theoretic rough set theory. Inf Sci 406–407:185–207

    Article  MATH  Google Scholar 

  • Le VT, Hu BQ (2016) Three-way decisions based on covering rough set. J Intell Fuzzy Syst 30:1763–1772

    Article  MATH  Google Scholar 

  • Li Y, Zhang C, Swan JR (2000) An information filtering model on the Web and its application in JobAgent. Knowl Based Syst 13:285–296

    Article  Google Scholar 

  • Li H, Zhang L, Huang B, Zhou X (2016) Sequential three-way decision and granulation for cost-sensitive face recognition. Knowl Based Syst 91:241–251

    Article  Google Scholar 

  • Li X, Sun B, She Y (2017a) Generalized matroids based on three-way decision models. Int J Approx Reason 90:192–207

    Article  MathSciNet  MATH  Google Scholar 

  • Li X, Yi H, She Y, Sun B (2017b) Generalized three-way decision models based on subset evaluation. Int J Approx Reason 83:142–159

    Article  MathSciNet  MATH  Google Scholar 

  • Liang D, Liu D, Kobina A (2016) Three-way group decisions with decision-theoretic rough sets. Inf Sci 345:46–64

    Article  Google Scholar 

  • Liu H, Zhao B (2019) On distributivity equations of implications over overlap functions and contrapositive symmetry equations of implications. J Intell Fuzzy Syst 36:283–294

    Article  Google Scholar 

  • Liu P, Yang H (2019) Three-way decisions with intuitionistic uncertain linguistic decision-theoretic rough sets based on generalized maclaurin symmetric mean operators. Int J Fuzzy Syst. https://doi.org/10.1007/s40815-019-00718-7

    Article  Google Scholar 

  • Liu D, Yao YY, Li TR (2011) Three-way investment decisions with decision-theoretic rough sets. Int J Intell Syst 4:66–74

    Article  Google Scholar 

  • Liu D, Liang D, Wang C (2016) A novel three-way decision model based on incomplete information system. Knowl Based Syst 91:32–45

    Article  Google Scholar 

  • Lucca G, Dimuro GP, Mattos V, Bedregal B, Bustince H, Sanz JA (2015) A family of Choquet-based nonassociative aggregation functions for application in fuzzy rule-based classification systems. In: 2015 IEEE international conference on fuzzy systems (FUZZ-IEEE), Los Alamitos, pp 1–8

  • Paternain D, Bustince H, Pagola M, Sussner P, Kolesárová A, Mesiar R (2016) Capacities and overlap indexes with an application in fuzzy rule-based classification systems. Fuzzy Sets Syst 305:70–94

    Article  MathSciNet  MATH  Google Scholar 

  • Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11:341–356

    Article  MATH  Google Scholar 

  • Peters JF, Ramanna S (2016) Proximal three-way decisions: theory and applications in social networks. Knowl Based Syst 91:4–15

    Article  Google Scholar 

  • Qiao J (2019a) On binary relations induced from overlap and grouping functions. Int J Approx Reason 106:155–171

    Article  MathSciNet  MATH  Google Scholar 

  • Qiao J (2019b) On distributive laws of uninorms over overlap and grouping functions. IEEE Trans Fuzzy Syst 27:2279–2292

    Article  Google Scholar 

  • Qiao J, Hu BQ (2017) On interval additive generators of interval overlap functions and interval grouping functions. Fuzzy Sets Syst 323:19–55

    Article  MathSciNet  MATH  Google Scholar 

  • Qiao J, Hu BQ (2018a) On the migrativity of uninorms and nullnorms over overlap and grouping functions. Fuzzy Sets Syst 346:1–54

    Article  MathSciNet  MATH  Google Scholar 

  • Qiao J, Hu BQ (2018b) On the distributive laws of fuzzy implication functions over additively generated overlap and grouping functions. IEEE Trans Fuzzy Syst 26:2421–2433

    Article  Google Scholar 

  • Qiao J, Hu BQ (2018c) On transformations from semi-three-way decision spaces to three-way decision spaces based on triangular norms and triangular conorms. Inf Sci 432:22–51

    Article  MathSciNet  MATH  Google Scholar 

  • Qiao J, Hu BQ (2018d) On multiplicative generators of overlap and grouping functions. Fuzzy Sets Syst 332:1–24

    Article  MathSciNet  MATH  Google Scholar 

  • Qiao J, Hu BQ (2018e) The distributive laws of fuzzy implications over overlap and grouping functions. Inf Sci 438:107–126

    Article  MathSciNet  MATH  Google Scholar 

  • Qiao J, Hu BQ (2019) On generalized migrativity property for overlap functions. Fuzzy Sets Syst 357:91–116

    Article  MathSciNet  MATH  Google Scholar 

  • Qiao J, Hu BQ (2020) On decision evaluation functions in generalized three-way decision spaces. Inf Sci 507:733–754

    Article  MathSciNet  Google Scholar 

  • Savchenko A (2019) Sequential three-way decisions in multi-category image recognition with deep features based on distance factor. Inf Sci 489:18–36

    Article  MathSciNet  Google Scholar 

  • Shen W, Wei Z, Li Q, Zhang H, Miao D (2020) Three-way decisions based blocking reduction models in hierarchical classification. Inf Sci 523:63–76

    Article  MathSciNet  Google Scholar 

  • Xu J, Miao D, Zhang Y, Zhang Z (2017) A three-way decisions model with probabilistic rough sets for stream computing. Int J Approx Reason 88:1–22

    Article  MathSciNet  MATH  Google Scholar 

  • Yao JT, Azam N (2015) Web-based medical decision support systems for three-way medical decision making with game-theoretic rough sets. IEEE Trans Fuzzy Syst 23:3–15

    Article  Google Scholar 

  • Yao JT, Herbert JP (2007) Web-based support systems based on rough set analysis. In: Kryszkiewicz M, Peters JF, Rybiński H, Skowron A (eds) RSEISP 2007, LNCS (LNAI), vol 4585. Springer, Heidelberg, pp 360–370

    Google Scholar 

  • Yao YY (2009) Three-way decision: an interpretation of rules in rough set theory. In: Wen P, Li Y, Polkowski L, Yao Y, Tsumoto H, Wang G (eds) RSKT, vol 5589. LNCS (LNAI). Springer, Heidelberg, pp 642–649

    Google Scholar 

  • Yao YY (2010) Three-way decisions with probabilistic rough sets. Inf Sci 180:341–353

    Article  MathSciNet  Google Scholar 

  • Yao YY (2011) The superiority of three-way decisions in probabilistic rough set models. Inf Sci 181:1080–1096

    Article  MathSciNet  MATH  Google Scholar 

  • Yao Y, Wang S, Deng X (2017) Constructing shadowed sets and three-way approximations of fuzzy sets. Inf Sci 412–413:132–153

    Article  MathSciNet  MATH  Google Scholar 

  • Yao YY, Wong SKM, Lingras P (1990) A decision-theoretic rough set model. In: Ras ZW, Zemankova M, Emrich ML (eds) Methodologies for intelligent systems. North-Holland, New York, pp 17–24

    Google Scholar 

  • Yu H, Jiao P, Yao Y, Wang G (2016) Detecting and refining overlapping regions in complex networks with three-way decisions. Inf Sci 373:21–41

    Article  MATH  Google Scholar 

  • Yu H, Chen L, Yao J, Wang X (2019) A three-way clustering method based on an improved DBSCAN algorithm. Phys A 535:1222289

    Article  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  • Zhang S, Li S, Yang H (2020) Three-way convex systems and three-way fuzzy convex systems. Inf Sci 510:89–98

    Article  MathSciNet  Google Scholar 

  • Zhao XR, Hu BQ (2015) Fuzzy and interval-valued fuzzy decision-theoretic rough set approaches based on fuzzy probability measure. Inf Sci 298:534–554

    Article  MathSciNet  MATH  Google Scholar 

  • Zhao XR, Hu BQ (2016) Fuzzy probabilistic rough sets and their corresponding three-way decisions. Knowl Based Syst 91:126–142

    Article  Google Scholar 

  • Zhao XR, Yao YY (2019) Three-way fuzzy partitions defined by shadowed sets. Inf Sci 497:23–37

    Article  Google Scholar 

  • Zhao XR, Hu BQ (2020) Three-way decisions with decision-theoretic rough sets in multiset-valued information tables. Inf Sci 507:684–699

    Article  MathSciNet  Google Scholar 

  • Zhou H, Yan X (2019) Migrativity properties of overlap functions over uninorms. Fuzzy Sets Syst. https://doi.org/10.1016/j.fss.2019.11.011

    Article  Google Scholar 

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Acknowledgements

The authors would like to give their sincere thanks to the Editors and anonymous reviewers for their most valuable comments and suggestions in improving this paper greatly.

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Correspondence to Junsheng Qiao.

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This work was supported by the National Natural Science Foundation of China (11901465), the Scientific Research Fund for Young Teachers of Northwest Normal University (NWNU-LKQN-18-28) and the Doctoral Research Fund of Northwest Normal University (6014/0002020202).

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Jia, Z., Qiao, J. On decision evaluation functions in three-way decision spaces derived from overlap and grouping functions. Soft Comput 24, 15159–15178 (2020). https://doi.org/10.1007/s00500-020-05283-y

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