Uncertain probabilities I: the discrete case

Buckley, James J.; Eslami, Esfandiar

doi:10.1007/s00500-002-0234-2

Cited by 45 publications

(47 citation statements)

References 22 publications

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“…We present a general definition, through stochastic vectors, for the approach proposed by Buckley to calculate fuzzy probabilities [10,22], which does not consider the standard probability theory [23]. Let X = {x 1 , .…”

Section: Fuzzy Probabilitiesmentioning

confidence: 99%

“…When several experts provide these values, then a i and b i are obtained by calculating the variance of all the pessimistic and optimistic estimates, respectively, on the occurrence of x i , and u i is the result of the arithmetic mean of all "most likely" estimates about the analyzed event [10,22]. Hardly the obtained triangular fuzzy number is going to be symmetric, then one should transform this fuzzy number in order to obtain a new symmetric triangular fuzzy number denoted by…”

Section: Fuzzy Probabilitiesmentioning

confidence: 99%

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An Approach to Interval Fuzzy Probabilities

Asmus

Dimuro

Bedregal

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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Fuzzy sets and logic have been largely used for the treatment of the uncertainty, vagueness and ambiguity found in the modeling of real problems. However, there may exist also the case when there is uncertainty related to the membership functions to be used in the modeling of fuzzy sets and fuzzy numbers, as there are many ways to define the shape of this kind of number. Thus, one can use, for example, the theory of interval fuzzy sets to address this uncertainty, considering different modelings of fuzzy numbers into a single interval fuzzy number. In this paper, we use interval fuzzy numbers to represent probabilities that are difficult to be estimated and where the modeling of fuzzy numbers is not trivial. To elaborate the calculation of interval fuzzy probabilities, we introduce an approach based on the one used by Buckley and Eslami for fuzzy probabilities, where the probabilities respect an arithmetic restriction. We discuss several properties of the proposed approach.

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Section: Fuzzy Probabilitiesmentioning

confidence: 99%

Section: Fuzzy Probabilitiesmentioning

confidence: 99%

An Approach to Interval Fuzzy Probabilities

Asmus

Dimuro

Bedregal

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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“…The concept of FRVs was first introduced by Zadeh [7] and further developed by Kwakernaak [8] and Kratschmer [9] according to different requirements of measurability. Buckley [10][11][12] defined fuzzy probability using fuzzy numbers as parameters in probability density function and probability mass function. These fuzzy numbers are obtained from the set of confidence intervals.…”

Section: Introductionmentioning

confidence: 99%

On Solving Multiobjective Quadratic Programming Problems in a Probabilistic Fuzzy Environment

Biswas

De²

2014

Advances in Intelligent Systems and Computing

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In this paper, a fuzzy goal programming (FGP) approach for solving fuzzy multiobjective quadratic chance-constrained programming (CCP) problem involving exponentially distributed fuzzy random variables (FRVs) is developed. In the proposed methodology, the problem is first converted into interval-valued quadratic programming problem using CCP technique and a-cut of fuzzy numbers. Then, using fuzzy partial order relations, the problem is converted into its equivalent deterministic form. The individual optimal value of each objective is found in isolation to construct the quadratic fuzzy membership goals of each of the objective. The quadratic membership goals are transferred into linear goals by applying piecewise linear approximation technique. A minsum goal programming (GP) method is then applied to both the linearized and quadratic model to achieve the highest membership degree of each of the membership goals in the decision-making context. Finally, a comparison is made on the two different approaches with the help of distance function. An illustrative numerical example is provided to demonstrate the applicability of the proposed methodology.

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“…Some works devoted to this proposal are [11,12,13,14,15]. It is interesting to note that all the classic probability theory can be fuzzified this way.…”

Section: Introductionmentioning

confidence: 99%

Towards fuzzy linguistic Markov chains

Villacorta¹,

Verdegay²,

Pelta³

2013

Proceedings of the 8th Conference of the European Society for Fuzzy Logic and Technology

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In this contribution we deal with the problem of doing computations with a Markov chain when the information about transition probabilities is expressed linguistically. This could be the case, for instance, if the process we are modeling is described by a human expert, for whom the use of linguistic labels is easier than being forced to give inexact numerical probabilities which, in turn, may yield an unstable chain. We address the uncertainty of linguistic judgments by introducing fuzzy probabilities, and carry on the calculation of the linguistic stationary distribution of the chain by resorting to an existing fuzzy approach with restricted matrix multiplication. Preliminary results are very promising and deserve further research.

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Uncertain probabilities I: the discrete case

Cited by 45 publications

References 22 publications

An Approach to Interval Fuzzy Probabilities

An Approach to Interval Fuzzy Probabilities

On Solving Multiobjective Quadratic Programming Problems in a Probabilistic Fuzzy Environment

Towards fuzzy linguistic Markov chains

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