The general theory of decisions

Aliev, R. A.; Pedrycz, Witold; Kreinovich, Vladik; Huseynov, Oleg H.

doi:10.1016/j.ins.2015.07.055

Cited by 44 publications

(7 citation statements)

References 43 publications

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“…The use of the Kullback-Leibler information for defining such a probability distribution is justified by the Shore-Jonson theorem [49] stating that there exists only one distribution satisfying consistency conditions, and this distribution is uniquely defined by the minimum of the Kullback-Leibler information, under given constraints. The role of the constraints here are played by the normalization conditions (16) and (26). Then the information functional reads as…”

Section: General Definition Of Utility Factorsmentioning

confidence: 99%

“…When the choice is between just two prospects, whose utility factors are normalized according to condition (16), hence when f (π 1 ) + f (π 2 ) = 1, then the relative difference simplifies to…”

Section: B Choice Between Two Prospectsmentioning

confidence: 99%

“…For instance, there can exist an unknown stochastic environment [14] or a varying context [15]. It may also happen that the provided information is imprecise and only partially reliable [16] or preference relations are incomplete [17] requiring the use of fuzzy logic [18]. In such situations, any prediction is likely to be only partial and often merely qualitative.…”

Section: Introductionmentioning

confidence: 99%

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Quantitative Predictions in Quantum Decision Theory

Yukalov

Sornette

2018

IEEE Trans. Syst. Man Cybern, Syst.

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Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the theory of quantum measurements, which makes this approach relevant both for the description of decision making of humans and the creation of artificial quantum intelligence. General rules are formulated allowing for the explicit calculation of quantum probabilities representing the fraction of decision makers preferring the considered prospects. This provides a method to quantitatively predict decision-maker choices, including the cases of games with high uncertainty for which the classical expected utility theory fails. The approach is applied to experimental results obtained on a set of lottery gambles with gains and losses. Our predictions, involving no fitting parameters, are in very good agreement with experimental data. The use of quantum decision making in game theory is described. A principal scheme of creating quantum artificial intelligence is suggested.

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Section: General Definition Of Utility Factorsmentioning

confidence: 99%

Section: B Choice Between Two Prospectsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantitative Predictions in Quantum Decision Theory

Yukalov

Sornette

2018

IEEE Trans. Syst. Man Cybern, Syst.

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“…Here, Ã is an imprecise constraint on values of a variable X and B is an imprecise estimation of reliability of Ã. One can refer to Aliev, Huseynov, Aliyev and Alizadeh (2015) for the arithmetic of Z-numbers and to Aliev, Pedrycz, Kreinovich and Huseynov (2016) for the general theory of decisions (GTD) on the basis of a Z-number concept. The GTD uses the idea of combined states argument of BDMCSII and develops a unified decision model which subsumes most of the well-known decision theories as its special cases including BDMCSII.…”

Section: P(smentioning

confidence: 99%

Toward a General Model of Financial Markets

Aliyev

2023

Understanding Complex Systems

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This paper aims to discuss the possibilities of capturing efficient market hypothesis and behavioral finance under a general framework using the literature of decision theories and information sciences. The focus is centered on the broad definition of rationality, the imprecision and reliability of information. The main thesis advanced is that the root of behavioral anomalies comes from the imprecision and reliability of information. Modeling on basis of imprecision and reliability of information within the broad definition of rationality will lead us to a more general model of financial markets.

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“…For example, in reality, uncertainties may exist in the membership function of fuzzy mathematical programming (FMP). As a result, a fuzzy set may be present, resulting in a type-2 fuzzy set (T2FS) [27,28,29,30,31,32,33]. In addition, when facing T2FS problems, uncertainties may exist in the objective function or left-hand constraints.…”

Section: Introductionmentioning

confidence: 99%

An Inexact Optimization Model for Crop Area Under Multiple Uncertainties

Ren

Hong-bo

2019

IJERPH

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This paper developed a type-2 fuzzy interval chance constrained programming model for optimizing a crop area, which integrated chance constrained programming and type-2 fuzzy interval programming. The developed model was then applied to a case study in Wuwei City, Gansu Province, China, and the maximization of economic benefit was selected as the planning objective. Furthermore, different water-saving irrigation modes were considered as the development mode. A series of optimal irrigation water and planting structure schemes were obtained under different violation probabilities in each water-saving scenario. The obtained results could be helpful to make decisions on the planting structure and the optimal use of irrigation water and land resources under multiple uncertainties.

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The general theory of decisions

Cited by 44 publications

References 43 publications

Quantitative Predictions in Quantum Decision Theory

Quantitative Predictions in Quantum Decision Theory

Toward a General Model of Financial Markets

An Inexact Optimization Model for Crop Area Under Multiple Uncertainties

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