Unbiased Fuzzy Estimators in Fuzzy Hypothesis Testing

In this paper, we develop fuzzy, possibilistic hypothesis tests for testing crisp hypotheses for a distribution parameter from crisp data. In these tests, fuzzy statistics are used, which are produced by the possibility distribution of the estimated parameter, constructed by the known from crisp statistics confidence intervals. The results of these tests are in much better agreement with crisp statistics than the ones produced by the respective tests of a popular book on fuzzy statistics, which uses fuzzy critical values. We also present an error that we found in the implementation of the unbiased fuzzy estimator of the variance in this book, due to a poor interpretation of its mathematical content, which leads to disagreement of some fuzzy hypotheses tests with their respective crisp ones. Implementing correctly this estimator, we produce test statistics that achieve results in hypotheses tests that are in much better agreement with the results of the respective crisp ones.

Modeling pricing decision problem based on interval type-2 fuzzy theory

In practical decision-making problems, decision makers are often affected by uncertain parameters because the exact distributions of uncertain parameters are usually difficult to determine. In order to deal with this issue, the major contribution in this paper is to propose a new type of type-2 fuzzy variable called level interval type-2 fuzzy variable from the perspective of level-sets, which is a useful tool in modeling distribution uncertainty. With our level interval type-2 fuzzy variable, we give a method for constructing a parametric level interval (PLI) type-2 fuzzy variable from a nominal possibility distribution by introducing the horizontal perturbation parameters. The proposed horizontal perturbation around the nominal distribution is different from the vertical perturbation discussed in the literature. In order to facilitate the modeling in practical decision-making problems, for a level interval type-2 fuzzy variable, we define its selection variable whose distribution can be determined via its level-sets. The numerical characteristics like expected value and second order moments are important indices in practical optimization and decision-making problems. With this consideration, we establish the analytical expressions about the expected values and second order moments of the selection variables of PLI type-2 trapezoidal, normal and log-normal fuzzy variables. Furthermore, in order to derive the analytical expressions about the numerical characteristics of the selection variable for the sums of the common PLI type-2 fuzzy variables, we discuss the arithmetic about the sums of common PLI type-2 fuzzy variables. Finally, we apply the proposed optimization method to a pricing decision problem to demonstrate the efficiency of our new method. The computational results show that even a small perturbation of the nominal possibility distribution can affect the quality of solutions.

Possibilistic Uncertainty Quantification in 1-D Consolidation Problems

In this study, we use possibility distribution as a basis for parameter uncertainty quantification in one-dimensional consolidation problems. A Possibility distribution is the one-point coverage function of a random set and viewed as containing both partial ignorance and uncertainty. Vagueness and scarcity of information needed for characterizing the coefficient of consolidation in clay can be handled using possibility distributions. Possibility distributions can be constructed from existing data, or based on transformation of probability distributions. An attempt is made to set a systematic approach for estimating uncertainty propagation during the consolidation process. The measure of uncertainty is based on Klir's definition (1995). We make comparisons with results obtained from other approaches (probabilistic…) and discuss the importance of using possibility distributions in this type of problems.

A MAGDM Method Based on Possibility Distribution Hesitant Fuzzy Linguistic Term Set and Its Application

The sustainable third-party reverse logistics provider (3PRLP) selection, as the core of sustainable supply chain management, has become paramount in research nowadays. In the actual evaluation process, the decision makers may hesitate in a few linguistic terms and have different partiality towards each term, hence the possibility distribution based hesitant fuzzy linguistic term sets (PDHFLTSs), as expressed by a consecutive or non-consecutive linguistic term set, is suitable for such an evaluation. The purpose of this paper is to solve sustainable 3PRLP selection problems with linguistic information by developing an effective and robust method. We firstly redefine the covariance-based correlation coefficient that can simplify the computation to calculate the consensus degree, and then introduce the hesitant degree in context of possibility distribution information, in order to enrich measures of PDHFLTSs. On this basis, the weights of experts are computed for expression aggregation. Secondly, to overcome attributes’ weights staying constant, the combination of group utility function and variable weight approach is introduced to give the weights of attributes. Most importantly, a decision method, called MULTIMOORA, is optimized by improving the ranking position method, and then, through the combination with PDHFLTS, we proposed a possibility distribution based hesitant fuzzy linguistic MULTIMOORA method with great robustness. At last, the presented method is applied to the field of sustainable third-party reverse logistics provider selection in the e-commerce express industry and the effectiveness is verified by several comparative analyses.