Possibility Theory

Training systems based on virtual reality are used in several areas of human activities. In some kinds of training is important to know the trainee's skills. It can be done in those systems but requires high-end computers to achieve good performance. Recently, the use of embedded systems connected to the training system was proposed for training assessment, with the goal of decreasing requirements of the main system. However, some questions are still open and a deep study of this proposal was not performed. This paper provides answers for some of those questions.

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“…Let X be a variable which assumes values ω ∈ Ω. The conditional possibility and necessity measures are given by [16]:…”

Section: Possibility and Necessity Measures (Pmn) Methodsmentioning

confidence: 99%

Performance Profile of Online Training Assessment Based on Virtual Reality:

Segundo

Soares

Machado

et al. 2013

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

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“…A fuzzy variable is an appropriate tool to characterize the vague linguistic description. In two-stage model (10) and (11), the uncertain returns are characterized as two fuzzy variables with the known possibility distributions.…”

Section: The First-stagementioning

confidence: 99%

“…Consequently, the portfolio selection problems are depicted as fuzzy optimization problems. On the basis of fuzzy theory [8][9][10][11][12], some researchers applied various fuzzy optimization methods to portfolio selection problem. Inuiguchi and Tanino [13] dealt with a portfolio selection problem with independently estimated possibilistic return rates and obtained a distributive investment.…”

Section: Introductionmentioning

confidence: 99%

Two-Stage Fuzzy Portfolio Selection Problem with Transaction Costs

Chen

Wang

2015

Mathematical Problems in Engineering

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This paper studies a two-period portfolio selection problem. The problem is formulated as a two-stage fuzzy portfolio selection model with transaction costs, in which the future returns of risky security are characterized by possibility distributions. The objective of the proposed model is to achieve the maximum utility in terms of the expected value and variance of the final wealth. Given the first-stage decision vector and a realization of fuzzy return, the optimal value expression of the second-stage programming problem is derived. As a result, the proposed two-stage model is equivalent to a single-stage model, and the analytical optimal solution of the two-stage model is obtained, which helps us to discuss the properties of the optimal solution. Finally, some numerical experiments are performed to demonstrate the new modeling idea and the effectiveness. The computational results provided by the proposed model show that the more risk-averse investor will invest more wealth in the risk-free security. They also show that the optimal invested amount in risky security increases as the risk-free return decreases and the optimal utility increases as the risk-free return increases, whereas the optimal utility increases as the transaction costs decrease. In most instances the utilities provided by the proposed two-stage model are larger than those provided by the single-stage model.

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“…To define a fuzzy measure on  , we need to define a real number for all the 2 2 n − nontrivial subsets of  , which is a difficult task in many applications of fuzzy measure. In many applications, some particular measures have been used, like decomposable measures [9], λ -measures [2,10], possibility measures [11,12], k -additive measure [13,14], etc.…”

Section: Fuzzy Measures and Choquet Integralmentioning

confidence: 99%

“…In practical situations, if we use some particular measures, like decomposable measures [9], λ -measures [2,10], possibility measures [11,12], k -additive measure [13,14], etc. the number of variables and inequalities will be further reduced, which makes inverse problem easier.…”

Section: Inverse Problemmentioning

confidence: 99%

On inverse problem of Choquet integral

Xu¹

2014

Ind Eng Manage

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Citation: Zhang Z, Xu ZS (2014) On inverse problem of Choquet integral. Ind Eng Manage 3: 125. AbstractThe Choquet integral is a popular tool for dealing with multiple criteria decision making. In practice, if we have a fuzzy measure on the set of criteria, we can use Choquet integral to rank alternatives. In this paper, we consider the inverse problem of Choquet integral: Given a ranking of alternatives, does there exist a fuzzy measure by which we can get the ranking through Choquet integral.

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Possibility Theory

Abstract: The sections in this article are Fundamentals of Possibility Theory Possibility Theory Versus other Uncertainty Frameworks Approximate Reasoning Concluding Remarks

Cited by 110 publications

References 31 publications

Performance Profile of Online Training Assessment Based on Virtual Reality:

Performance Profile of Online Training Assessment Based on Virtual Reality:

Two-Stage Fuzzy Portfolio Selection Problem with Transaction Costs

On inverse problem of Choquet integral

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