Measuring Inconsistency in Fuzzy Answer Set Semantics

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Authors

Nicolás Madrid

Manuel Ojeda-Aciego

Published

1 January 2011

Publication details

{IEEE} Trans. Fuzzy Syst. vol. 19 (4), pages 605–622.

Links

Abstract

Recent approaches have shown that the measurement of the amount of inconsistent information contained in a logic theory can be useful to infer positive information. This paper deals with the definition of measures of inconsistency in the residuated-logic-programming paradigm under the fuzzy answer set semantics. This fuzzy framework provides a soft mechanism to control the amount of information inferred and, thus, controlling the inconsistencies by modifying slightly the truth values of some rules.

Citation

Please, cite this work as:

[MO11] N. Madrid and M. Ojeda-Aciego. “Measuring Inconsistency in Fuzzy Answer Set Semantics”. In: IEEE Trans. Fuzzy Syst. 19.4 (2011), pp. 605-622. DOI: 10.1109/TFUZZ.2011.2114669. URL: https://doi.org/10.1109/TFUZZ.2011.2114669.

BibTeX

@Article{Madrid2011,
     author = {Nicol{’a}s Madrid and Manuel Ojeda-Aciego},
     journal = {{IEEE} Trans. Fuzzy Syst.},
     title = {Measuring Inconsistency in Fuzzy Answer Set Semantics},
     year = {2011},
     number = {4},
     pages = {605–622},
     volume = {19},
     bibsource = {dblp computer science bibliography, https://dblp.org},
     biburl = {https://dblp.org/rec/journals/tfs/MadridO11.bib},
     doi = {10.1109/TFUZZ.2011.2114669},
     timestamp = {Mon, 03 Jan 2022 00:00:00 +0100},
     url = {https://doi.org/10.1109/TFUZZ.2011.2114669},
}

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Measuring Inconsistency in Fuzzy Answer Set Semantics

Cites

The following graph plots the number of cites received by this work from its publication, on a yearly basis.

Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

[1] M. Blondeel, S. Schockaert, D. Vermeir, et al. “Complexity of fuzzy answer set programming under Łukasiewicz semantics”. In: International Journal of Approximate Reasoning 55.9 (Dec. 2014), p. 1971–2003. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2013.10.011. URL: http://dx.doi.org/10.1016/j.ijar.2013.10.011.

[2] T. Brys, Y. De Hauwere, M. De Cock, et al. “Solving satisfiability in fuzzy logics with evolution strategies”. In: 2012 Annual Meeting of the North American Fuzzy Information Processing Society (NAFIPS). IEEE, Aug. 2012, p. 1–6. DOI: 10.1109/nafips.2012.6290998. URL: http://dx.doi.org/10.1109/nafips.2012.6290998.

[3] T. Brys, M. M. Drugan, P. A. Bosman, et al. “Solving satisfiability in fuzzy logics by mixing CMA-ES”. In: Proceedings of the 15th annual conference on Genetic and evolutionary computation. GECCO ’13. ACM, Jul. 2013, p. 1125–1132. DOI: 10.1145/2463372.2463510. URL: http://dx.doi.org/10.1145/2463372.2463510.

[4] H. Bustince, N. Madrid, and M. Ojeda-Aciego. “A measure of contradiction based on the notion of N-weak-contradiction”. In: 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, Jul. 2013, p. 1–6. DOI: 10.1109/fuzz-ieee.2013.6622563. URL: http://dx.doi.org/10.1109/fuzz-ieee.2013.6622563.

[5] H. Bustince, N. Madrid, and M. Ojeda-Aciego. “The Notion of Weak-Contradiction: Definition and Measures”. In: IEEE Transactions on Fuzzy Systems 23.4 (Aug. 2015), p. 1057–1069. ISSN: 1941-0034. DOI: 10.1109/tfuzz.2014.2337934. URL: http://dx.doi.org/10.1109/tfuzz.2014.2337934.

[6] M. E. Cornejo, D. Lobo, and J. Medina. “Characterizing Fuzzy y-Models in Multi-adjoint Normal Logic Programming”. In: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications. Springer International Publishing, 2018, p. 541–552. ISBN: 9783319914794. DOI: 10.1007/978-3-319-91479-4_45. URL: http://dx.doi.org/10.1007/978-3-319-91479-4_45.

[7] M. E. Cornejo, D. Lobo, and J. Medina. “Extended multi-adjoint logic programming”. In: Fuzzy Sets and Systems 388 (Jun. 2020), p. 124–145. ISSN: 0165-0114. DOI: 10.1016/j.fss.2019.03.016. URL: http://dx.doi.org/10.1016/j.fss.2019.03.016.

[8] M. E. Cornejo, D. Lobo, and J. Medina. “Measuring the Incoherent Information in Multi-adjoint Normal Logic Programs”. In: Advances in Fuzzy Logic and Technology 2017. Springer International Publishing, Sep. 2017, p. 521–533. ISBN: 9783319668307. DOI: 10.1007/978-3-319-66830-7_47. URL: http://dx.doi.org/10.1007/978-3-319-66830-7_47.

[9] M. E. Cornejo, D. Lobo, and J. Medina. “Selecting the Coherence Notion in Multi-adjoint Normal Logic Programming”. In: Advances in Computational Intelligence. Springer International Publishing, 2017, p. 447–457. ISBN: 9783319591537. DOI: 10.1007/978-3-319-59153-7_39. URL: http://dx.doi.org/10.1007/978-3-319-59153-7_39.

[10] M. E. Cornejo, D. Lobo, and J. Medina. “Syntax and semantics of multi-adjoint normal logic programming”. In: Fuzzy Sets and Systems 345 (Aug. 2018), p. 41–62. ISSN: 0165-0114. DOI: 10.1016/j.fss.2017.12.009. URL: http://dx.doi.org/10.1016/j.fss.2017.12.009.

[11] M. E. Cornejo, J. Medina, and E. Ramírez-Poussa. “Adjoint negations, more than residuated negations”. In: Information Sciences 345 (Jun. 2016), p. 355–371. ISSN: 0020-0255. DOI: 10.1016/j.ins.2016.01.038. URL: http://dx.doi.org/10.1016/j.ins.2016.01.038.

[12] C. V. Damásio, N. Madrid, and M. Ojeda-Aciego. “On the Notions of Residuated-Based Coherence and Bilattice-Based Consistence”. In: Fuzzy Logic and Applications. Springer Berlin Heidelberg, 2011, p. 115–122. ISBN: 9783642237133. DOI: 10.1007/978-3-642-23713-3_15. URL: http://dx.doi.org/10.1007/978-3-642-23713-3_15.

[13] G. De Bona, J. Grant, A. Hunter, et al. “Classifying Inconsistency Measures Using Graphs”. In: Journal of Artificial Intelligence Research 66 (Dec. 2019), p. 937–987. ISSN: 1076-9757. DOI: 10.1613/jair.1.11852. URL: http://dx.doi.org/10.1613/jair.1.11852.

[14] C. V. Glodeanu. “Exploring Users’ Preferences in a Fuzzy Setting”. In: Electronic Notes in Theoretical Computer Science 303 (Mar. 2014), p. 37–57. ISSN: 1571-0661. DOI: 10.1016/j.entcs.2014.02.003. URL: http://dx.doi.org/10.1016/j.entcs.2014.02.003.

[15] J. Grant and A. Hunter. “Semantic inconsistency measures using 3-valued logics”. In: International Journal of Approximate Reasoning 156 (May. 2023), p. 38–60. ISSN: 0888-613X. DOI: 10.1016/j.ijar.2023.02.008. URL: http://dx.doi.org/10.1016/j.ijar.2023.02.008.

[16] J. Lee and Y. Wang. “Stable Models of Fuzzy Propositional Formulas”. In: Logics in Artificial Intelligence. Springer International Publishing, 2014, p. 326–339. ISBN: 9783319115580. DOI: 10.1007/978-3-319-11558-0_23. URL: http://dx.doi.org/10.1007/978-3-319-11558-0_23.

[17] D. Lobo, M. E. Cornejo Piñero, and J. Medina. “Abductive reasoning in normal residuated logic programming via bipolar max-product fuzzy relation equations”. In: Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (EUSFLAT 2019). eusflat-19. Atlantis Press, 2019. DOI: 10.2991/eusflat-19.2019.81. URL: http://dx.doi.org/10.2991/eusflat-19.2019.81.

[18] N. Madrid, J. Medina, and E. Ramírez-Poussa. “Rough sets based on Galois connections”. In: International Journal of Applied Mathematics and Computer Science 30.2 (2020). ISSN: 2083-8492. DOI: 10.34768/amcs-2020-0023. URL: http://dx.doi.org/10.34768/amcs-2020-0023.

[19] N. Madrid and M. Ojeda-Aciego. “Functional degrees of inclusion and similarity between L-fuzzy sets”. In: Fuzzy Sets and Systems 390 (Jul. 2020), p. 1–22. ISSN: 0165-0114. DOI: 10.1016/j.fss.2019.03.018. URL: http://dx.doi.org/10.1016/j.fss.2019.03.018.

[20] N. Madrid and M. Ojeda-Aciego. “Multi-adjoint lattices from adjoint triples with involutive negation”. In: Fuzzy Sets and Systems 405 (Feb. 2021), p. 88–105. ISSN: 0165-0114. DOI: 10.1016/j.fss.2019.12.004. URL: http://dx.doi.org/10.1016/j.fss.2019.12.004.

[21] N. Madrid and M. Ojeda-Aciego. “On the measure of incoherent information in extended multi-adjoint logic programs”. In: 2013 IEEE Symposium on Foundations of Computational Intelligence (FOCI). IEEE, Apr. 2013, p. 30–37. DOI: 10.1109/foci.2013.6602452. URL: http://dx.doi.org/10.1109/foci.2013.6602452.

[22] N. Madrid and M. Ojeda-Aciego. “The f-index of inclusion as optimal adjoint pair for fuzzy modus ponens”. In: Fuzzy Sets and Systems 466 (Aug. 2023), p. 108474. ISSN: 0165-0114. DOI: 10.1016/j.fss.2023.01.009. URL: http://dx.doi.org/10.1016/j.fss.2023.01.009.

[23] N. Madrid and M. Ojeda‐Aciego. “A measure of consistency for fuzzy logic theories”. In: Mathematical Methods in the Applied Sciences 46.15 (May. 2021), p. 15982–15995. ISSN: 1099-1476. DOI: 10.1002/mma.7470. URL: http://dx.doi.org/10.1002/mma.7470.

[24] M. Mushthofa, S. Schockaert, and M. De Cock. “Solving Disjunctive Fuzzy Answer Set Programs”. In: Logic Programming and Nonmonotonic Reasoning. Springer International Publishing, 2015, p. 453–466. ISBN: 9783319232645. DOI: 10.1007/978-3-319-23264-5_38. URL: http://dx.doi.org/10.1007/978-3-319-23264-5_38.

[25] M. Ulbricht, M. Thimm, and G. Brewka. “Measuring Inconsistency in Answer Set Programs”. In: Logics in Artificial Intelligence. Springer International Publishing, 2016, p. 577–583. ISBN: 9783319487588. DOI: 10.1007/978-3-319-48758-8_42. URL: http://dx.doi.org/10.1007/978-3-319-48758-8_42.