This paper considers computational methods for obtaining Stackelberg solutions to random fuzzy twolevel linear programming problems. Assuming that the decision makers concerns about the probabilities that their own objective function values are smaller than or equal to certain target values, fuzzy goals of the decision makers for the probabilities are introduced. Using the possibility-based pro...

This article deals with an implementation of probist reliability problems in evidential networks to propagate imprecise probabilities expressed as fuzzy numbers. First, the problem of imprecise knowledge in reliability problems is described concerning system and data reprsentation. Then, the basics of the evidence theory and its use in a directed acyclic graph approach are given. The imprecise ...

In this paper, we formulate the fuzzy perceptive model for discounted Markov decision processes in which the perception for transition probabilities is described by fuzzy sets. The optimal expected reward, called a fuzzy perceptive value, is characterized and calculated by a new fuzzy relation. As a numerical example, a machine maintenance problem is considered.

We use the interpretation of fuzzy sets in terms of coherent conditional probabilities for handling probabilistic fuzzy IF-THEN rules. We show by some examples how this interpretation can help when fuzzy and statistical information need to be combined and the available probabilistic information on the fuzzy events is possibly imprecise or incomplete.

In this paper, two kinds of portfolio selection models are proposed based on fuzzy probabilities and possibility distributions, respectively, rather than conventional probability distributions in Markowitz’s model. Since fuzzy probabilities and possibility distributions are obtained depending on possibility grades of security data o ered by experts, investment experts’ knowledge can be re ected...

The prediction of the behavior and reliability of engineering structures and systems is often plagued by uncertainty and imprecision caused by sparse data, poor measurements and linguistic information. Accounting for such limitations complicates the mathematical modeling required to obtain realistic results in engineering analyses. The framework of imprecise probabilities provides a mathematica...

This article introduces a general framework of multi-granulation fuzzy probabilistic roughsets (MG-FPRSs) models in multi-granulation fuzzy probabilistic approximation space over twouniverses. Four types of MG-FPRSs are established, by the four different conditional probabilitiesof fuzzy event. For different constraints on parameters, we obtain four kinds of each type MG-FPRSs...

Markov chains are well-established probabilistic models of a wide variety of real systems that evolve along the time. Countless examples of applications of Markov chains that successfully capture the probabilistic nature of real problems include areas as diverse as biology, medicine, social science, and engineering. One interesting feature of a kind of Markov chains is their stationary distribu...

A simple probabilistic grounding of the ”fuzzy set membership degree” is presented, and used to provide definitions of the absolute and conditional probabilities of fuzzy sets. Among other possible applications, this allows fuzzy membership values to be coherently incorporated into probabilistic reasoning processes.