A possibility measure can encode a family of probability measures. This fact is the basis for a transformation of a probability distribution into a possibility distribution that generalises the notion of best interval substitute to a probability distribution with prescribed confidence. This paper describes new properties of this transformation, by relating it with the well-known probability ine...

A fuzzy variable is a function from a possibility space to the set of real numbers, while a bifuzzy variable is a function from a possibility space to the set of fuzzy variables. In this paper, a concept of chance distribution is originally presented for bifuzzy variable, and the linearity of expected value operator of bifuzzy variable is proved. Furthermore, bifuzzy simulations are suggested a...

A central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. In this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. The main stages of the modeling process are represented as fuzz...

The purpose of this paper is to provide a review of the current state of fuzzy logic theory in epidemiology, which is a recent area of research. We present four applications of fuzzy logic theory in epidemic problems, using linguistic fuzzy models, possibility measure, probability of fuzzy events and fuzzy decision making techniques. The results demonstrate that the applications of fuzzy sets i...

Fuzzy data given by expert knowledge can be regarded as a possibility distribution by which possibilistic linear systems are defined. Recently, it has become important to deal with fuzzy data in connection with expert knowledge. Three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data. Since our formulations can be reduced to linear programming pr...

The production possibility set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. In data envelopment analysis (DEA), identification of the strong defining hyperplanes of the empirical production possibility set (PPS) is important, because they can be used for determining rates of change of outputs with change in inputs. Also, efficient hyperp...

Stochastic groundwater modeling involves the propagation of probabilistic uncertainty from model input parameters to model estimates, usually via a Monte Carlo method. With the increasing reliance upon expert knowledge to define model inputs, and both fuzzy set and possibility theories to characterize this expert knowledge, alternative means of executing model equations are needed. While the fu...

This chapter introduces the underlying theory of Fuzzy Probability and Statistics related to the differences and similarities between discrete probability and possibility spaces. Fuzzy Probability Theory for Discrete Case starts with the fundamental tools to implement an immigration of crisp probability theory into fuzzy probability theory. Fuzzy random variables are the initial steps to develo...

This paper proposes a fuzzy multi-objective integer linear programming approach to model a material requirement planning (MRP) problem with fuzzy lead times. We incorporate to the crisp MRP model the possibility of occurrence of each one of the possible lead times. Then, an objective function that maximizes the possibility of occurrence of the lead times is considered. By combining this objecti...

Face being the most natural method of identification for humans is one of the most significant biometric modalities and various methods to achieve efficient face recognition have been proposed. However the changes in face owing to different expressions, pose, makeup, illumination, age bring about marked variations in the facial image. These changes will inevitably occur and they can be controll...