Single value simulation of fuzzy variable. (English) Zbl 0633.65144

Let V be a fuzzy variable with possibility distribution \(\mu_ G\). The authors suggest the following procedure for generating a single value of the fuzzy variable V:
Step 1. Generate a value t of the uniform variable T over (0,1]. Step 2. Generate a value x of the uniform variable U over the t-level set \(G_ t:=\{x| \mu_ G(x)\geq t\}\) of the fuzzy set G.
Viewing x as a single value of the fuzzy variable V, like this, an approach to the so-called fuzzy-numerical simulation is presented. We may be interested in this paper on the relation between random sets and fuzzy ones.
Reviewer: Wang Peizhuang


65C99 Probabilistic methods, stochastic differential equations
65C20 Probabilistic models, generic numerical methods in probability and statistics
60D05 Geometric probability and stochastic geometry
03E72 Theory of fuzzy sets, etc.
54D05 Connected and locally connected spaces (general aspects)
Full Text: DOI


[1] Dubois, D.; Prade, H., On several representations of an uncertain body of evidence, () · Zbl 0512.94031
[2] Goodman, I.R., Fuzzy sets as equivalence class of random sets, () · Zbl 0552.60007
[3] Kickert, W.J.M., An example of linguistic modelling: the case of mulders theory of power, () · Zbl 0364.93022
[4] Leung, Y., Maximum entropy estimation with inexact information, ()
[5] Nguyen, W.T., On random sets and belief functiosn, J. math. anal. appl., 65, 531-541, (1978)
[6] Papoulis, A., Probability, random variables, and stochastic processes, (1965), McGraw-Hill New York · Zbl 0191.46704
[7] Prade, H., Approximate and plausible reasoning: the state of art, (), Marseille
[8] Rubinstein, R.Y., Generating random vectors uniformly distributed inside and on the surface of different regions, European J. oper. res., 10, 205-209, (1982) · Zbl 0491.65006
[9] Shafer, G., A mathematical theory of evidence, (1975), Princeton Univ. Press Princeton, NJ
[10] Wenstopp, F., Deductive verbal models of organizations, Internat. J. man-machine stud., 8, 293-311, (1978)
[11] Yager, R.R., Some questions related to linguistic variables, () · Zbl 0524.94037
[12] Yager, R.R., Level set for membership evaluation of fuzzy subsets, () · Zbl 0457.04004
[13] Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
[14] Zadeh, L.A., Fuzzy sets as a basis for theory of possibility, Fuzzy sets and systems, 1, 3-29, (1978) · Zbl 0377.04002
[15] Zadeh, L.A., Fuzzy sets and information granularity, () · Zbl 0139.24606
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