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Linguistic probabilities: theory and application

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Abstract

Over the past two decades a number of different approaches to “fuzzy probabilities” have been presented. The use of the same term masks fundamental differences. This paper surveys these different theories, contrasting and relating them to one another. Problems with these existing approaches are noted and a theory of “linguistic probabilities” is developed, which seeks to retain the underlying insights of existing work whilst remedying its technical defects. It is shown how the axiomatic theory of linguistic probabilities can be used to develop linguistic Bayesian networks which have a wide range of practical applications. To illustrate this a detailed and realistic example in the domain of forensic statistics is presented.

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References

  • Aitken C, Taroni F, Garbolino P (2003) A graphical model for the evaluation of cross-transfer evidence in DNA profiles. Theo Popul Biol 63(3): 179–190

    Article  MATH  Google Scholar 

  • Balding DJ, Donnelly P (1995) Inference in forensic identification. J R Stat Soc Ser A 158: 21–53

    Article  Google Scholar 

  • Budescu DV, Wallsten TS (1985) Consistency in interpretation of probabilistic phrases. Organ Behav Hum Decis Process 36: 391–405

    Article  Google Scholar 

  • Cook R, Evett I, Jackson G, Jones P, Lambert J (1998) A hierarchy of propositions: deciding which level to address in casework. Sci Justice 38: 231–239

    Article  Google Scholar 

  • Cook R, Evett I, Jackson G, Jones P, Lambert J (1998) A model for case assessment and interpretation. Sci Justice 38: 151–156

    Article  Google Scholar 

  • Cook R, Evett I, Jackson G, Jones P, Lambert J (1999) Case pre- assessment and review in a two-way transfer case. Sci Justice 39: 103–111

    Article  Google Scholar 

  • Dawid AP, Mortera J, Pascali VL, van Boxel DW (2002) Probabilistic expert systems for forensic inference from genetic markers. Scand J Stat 29: 577–595

    Article  MATH  Google Scholar 

  • de Cooman G (2005) A behavioural model for vague probability assessments. Fuzzy Sets Syst 154(3): 305–358

    Article  MATH  Google Scholar 

  • Evett I, Jackson G, Lambert J (2000a) More on the hierarchy of propositions: exploring the distinction between explanations and propositions. Sci Justice 40: 3–10

    Article  Google Scholar 

  • Evett I, Jackson G, Lambert J, McCrossan S (2000b) The impact of the principles of evidence interpretation on the structure and content of statements. Sci Justice 40: 233–239

    Article  Google Scholar 

  • Gómez Marin-Blazquez J, Shen Q (2002) From approximative to descriptive fuzzy classifiers. IEEE Trans Fuzzy Syst 10(4): 487–497

    Article  Google Scholar 

  • Grimmet G, Welsh D (1986) Probability: an introduction. Oxford University Press, Oxford

    Google Scholar 

  • Halliwell J, Keppens J, Shen Q (2003) Linguistic bayesian networks for reasoning with subjective probabilities in forensic statistics. In: Proceedings of the 9th international conference on AI and law. ACM, pp 42–50

  • Halliwell J, Shen Q (2002) Towards linguistic probability theory. In: Proceedings of the 11th international conference on fuzzy systems, pp 596–601

  • Jain P, Agogino AM (1990) Stochastic sensitivity analysis using fuzzy influence diagrams. In: Schachter RD, Levitt TS, Kanal LN, Lemmer JF(eds) Uncertainty in artificial intelligence, vol 4. North-Holland, Amsterdam, pp 79–92

    Google Scholar 

  • Kahneman D, Slovic P, Tversy A (1985) Judgement under uncertainty: heuristics and biases. Cambridge University Press, Cambridge

    Google Scholar 

  • National Research Council Governing Board Commitee on the Assessment of Risk (1981) The handling of risk assessments in NRC reports, Washington DC

  • Okuda T, Tanaka H, Asai K (1978) A formulation of fuzzy decision problems with fuzzy information, using probability measures of fuzzy events. Inf Control 38: 135–147

    Article  MATH  MathSciNet  Google Scholar 

  • Pearl J (1988) Probabilistic reasoning in intelligent systems. Morgan Kaufmann, San Mateo

    Google Scholar 

  • Russell B (1923) Vagueness. Australas J Psychol Philos 1: 84–92

    Article  Google Scholar 

  • Tanaka H, Okuda T, Asai K (1979) Fuzzy information and decision in statistical model. In: Gupta M, Rage P, Yager R(eds) Advances in fuzzy sets theory and applications. North Holland, Amsterdam, pp 303–320

    Google Scholar 

  • Wallsten TS, Budescu DV, Rapoport A, Zwick R, Forsyth B (1986) Measuring the vague meanings of probability terms. J Exp Psychol Gen 115(4): 348–365

    Article  Google Scholar 

  • Zadeh L (1975) The concept of a linguistic variable and its application to approximate reasoning. Part 2. Inf Sci 8: 301–353

    Article  MathSciNet  Google Scholar 

  • Zadeh L (1984) Fuzzy probabilities. Inf Process Manag 20: 363–372

    Article  MATH  Google Scholar 

  • Zadeh L (1996) Fuzzy logic = computing with words. IEEE Trans Fuzzy Syst 2: 103–111

    Article  MathSciNet  Google Scholar 

  • Zimmer AC (1983) Verbal vs. numerical processing of subjective probabilities. In: Scholz RW(eds) Decision making under uncertainty. North-Holland, Amsterdam

    Google Scholar 

  • Zimmer AC (1986) What uncertainty judgements can tell about the underlying subjective probabilities. In: Kanal LN, Lemmer JF(eds) Uncertainty in artificial intelligence. North-Holland, Amsterdam

    Google Scholar 

Download references

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Authors and Affiliations

  1. School of Informatics, University of Edinburgh, Edinburgh, UK

    Joe Halliwell

  2. Department of Computer Science, University of Wales, Aberystwyth, UK

    Qiang Shen

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  1. Joe Halliwell
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  2. Qiang Shen
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Correspondence to Joe Halliwell.

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Halliwell, J., Shen, Q. Linguistic probabilities: theory and application. Soft Comput 13, 169–183 (2009). https://doi.org/10.1007/s00500-008-0304-1

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