Exponential Possibility Distributions Research Articles

Japanese Economic Analysis by Possibilistic Regression Model Building Through Possibility Maximization

A possibilistic regression model illustrates the potential possibilities inherent in the target system by including all data in the model. Tanaka and Guo employ exponential possibility distribution to build a model, while Inuiguchi et al. and Tajima are independently working on coinciding between the center of a possibility distribution and the center of a possibilistic regression model. Typically, samples influence and distort the shape of the model if they are far from the center of data. Yabuuchi and Watada have developed a model for describing the system possibility using the center of a possibilistic fuzzy regression model and an approach that mends the distortion of the model. The objective of this paper is to analyze the Japanese economy using our model, and to show the usefulness of our model by analysis results.

Decision analysis based on fused double exponential possibility distributions

In this paper, the possibility grades given by an expert are approximated by double possibility distributions, called upper and lower possibility distributions to characterize uncertainty knowledge from this expert. The upper and lower possibility distributions have some similarities to upper and lower approximations in rough set theory. Multi-source knowledge from multiple experts is represented by a set of exponential possibility distributions. Based on the consistency index defined by the possibility measure of each pair of possibility distributions, a fusion model is proposed to integrate multiple possibility distributions into a new one representing a refined knowledge. As an application, a portfolio selection problem with multiple experts is considered.

Group decision with inconsistent knowledge

In this paper, dual exponential possibility distributions, namely, upper and lower exponential possibility distributions, are identified from the given data to characterize a decision-maker's knowledge. A decision group's knowledge can be represented by a set of such dual possibility distributions. The inherent diversity of knowledge among decision-makers is characterized by a conflict index. A conflict resolution model is proposed based on the conflict index, which integrates multiple possibility distributions identified into a new one to represent compromised knowledge of a decision group. As an application, a portfolio selection problem with multiple decision-makers is considered.

Possibility distributions of fuzzy decision variables obtained from possibilistic linear programming problems

In this paper, several kinds of possibility distributions of fuzzy variables are studied in possibilistic linear programming problems to reflect the inherent fuzziness in fuzzy decision problems. Interval and triangular possibility distributions are used to express the non-interactive cases between the fuzzy decision variables, and exponential possibility distributions are used to represent the interrelated cases. Possibilistic linear programming problems based on exponential possibility distributions become non-linear optimization problems. In order to solve optimization problems easily, algorithms for obtaining center vectors and distribution matrices in sequence are proposed. By the proposed algorithms, the possibility distribution of fuzzy decision variables can be obtained.

Upper and lower possibility distributions of fuzzy decision variables in upper level decision problems

In this paper, a kind of decision problem in upper-level decision-making systems is formalized by a set of fuzzy satisfaction levels offered by decision-makers. These fuzzy satisfaction levels leave some feasible region for decision variables. The exponential possibility distributions of decision variables are studied to obtain an approximate region for decision variables. Upper and lower possibility distributions are obtained to represent solutions with different fuzzy degrees in decision-making procedure.

Exponential possibility regression analysis by identification method of possibilistic coefficients

This paper introduces exponential possibility regression analysis by the proposed identification method. To identify the exponential possibility distribution, first we solve all possible different sets of the input-output linear systems from the given data and obtain the corresponding coefficient vectors. Then, we select minimum number of coefficient vectors which represent all the given data. Using the selected coefficient vectors, we apply the identification method to determine a possibility distribution of coefficients in the fuzzy linear system. As a criterion to select minimum coefficient vectors, we use the inner product. By the proposed approach, the smaller area of possibility distribution can be obtained. This is the main characteristic of our proposed regression, comparing with the other regression analyses.

Portfolio selection based on upper and lower exponential possibility distributions

In this paper, two kinds of possibility distributions, namely, upper and lower possibility distributions are identified to reflect experts' knowledge in portfolio selection problems. Portfolio selection models based on these two kinds of distributions are formulated by quadratic programming problems. It can be said that a portfolio return based on the lower possibility distribution has smaller possibility spread than the one on the upper possibility distribution. In addition, a possibility risk can be defined as an interval given by the spreads of the portfolio returns from the upper and the lower possibility distributions to reflect the uncertainty in real investment problems. A numerical example of a portfolio selection problem is given to illustrate our proposed approaches.

Exponential possibility regression analysis

This paper aims at giving the application of possibility theory based on exponential distributions to regression analysis. A general outline of the possibility theory is illustrated by exponential possibility distributions. It is shown that possibility analysis is well corresponding to statistical analysis. Using exponential possibility analysis, we propose possibility regression analysis which is suitable for rough phenomena arising from social and economic systems. The spread of the given data can be directly transferred into the exponential possibility distribution of coefficients in the regression model by the proposed method.

Evidence theory of exponential possibility distributions

This paper studies a certain form of evidence theory using exponential possibility distributions. Because possibility distributions are obtained from an expert knowledge or can be identified from given data, a possibility distribution is regarded as a representation of evidence in this paper. A rule of combination of evidence is given similar to Dempster's rule. Also, the measures of ignorance and fuzziness of evidence are defined by a normality factor and the area of a possibility distribution, respectively. These definitions are similar to those given by G. Shafer and A. Kaufman et al., respectively. Next, marginal and conditional possibilities are discussed from a joint possibility distribution, and it is shown that these three definitions are well matched to each other. Thus, the posterior possibility is derived from the prior possibility in the same form as Bayes' formula. This fact shows the possibility that an information-decision theory can be reconstructed from the viewpoint of possibility distributions. Furthermore, linear systems whose variables are defined by possibility distributions are discussed. Operations of fuzzy vectors defined by multidimensional possibility distributions are well formulated, using the extension principle of L. A. Zadeh.