International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In many systems, randomness and uncertainty are present simultaneously. Uncertain random variables provide a tool to deal with these inexact phenomena. This paper proposes a concept of risk index to quantify the risk of an uncertain random system. In addition, a risk index theorem is proved in order to calculate the risk index, and is applied to series systems, parallel systems and standby systems. Finally, a concept of expected loss is suggested for an uncertain random system.

Intuitionistic fuzzy preference relation has turned out to be a powerful structure in representing the decision makers' preference information especially when the decision makers are not able to express their preferences accurately due to the unquantifiable information, incomplete information, unobtainable information, partial ignorance, and so forth. The aim of this paper is to develop some techniques for group decision making with intuitionistic fuzzy preference information. Based on the multiplicative consistency of intuitionistic fuzzy preference relation, three algorithms are proposed for intuitionistic fuzzy group decision making. In the case that the decision makers act as separate individuals, the priority vector of each decision maker can be derived directly from the individual intuitionistic fuzzy preference relation, after which an overall priority vector is obtained by synthesizing those individual priorities together. As for the scenario that the decision makers act as one individual, two different algorithms based on the multiplicative consistency are proposed to deal with this case. The main idea of the former procedure is firstly constructing a social intuitionistic fuzzy preference relation, while that of the later is building a fractional programming model. Some practical examples are given to demonstrate the developed algorithms.

Decision making by considering multiple information sources could provide interesting results. For that reason, fusion formalisms were a major concern in the belief function community. In this context, the Belief function theory allows information fusion thanks to its combinations tools that it integrates. Nevertheless, belief function theory highlights a limit in the merging of contradictory (conflictual) sources. Many authors tackled this problem offering contributions in this field. Unfortunately, no proposed operator has distinguished by its adequacy regardless the type of handled sources. In this paper, we demonstrate the limits of some referenced works and we diagnostic the issues origin. We propose a conflict management approach based on an extra-information that guides the treatment. We also integrate a generic associative base borrowed from the data mining domain in order to apply the adequate conflict management.

Multi-criteria decision making with hesitant fuzzy information is a new research topic since the hesitant fuzzy set was firstly proposed. This paper investigates a multi-criteria decision making problem where the weight information is partially known. We firstly propose the hesitant fuzzy positive ideal solution and the hesitant fuzzy negative ideal solution. Motivated by the TOPSIS (Technique for Order Preference by Similarity to an ideal Solution) method, we definite the satisfaction degree of an alternative, based on which several optimization models are derived to determinate the weights. Subsequently, in order to make a more reasonable decision, we introduce an interactive method based on some optimization models for multi-criteria decision making problems with hesitant fuzzy information. Finally, a practical example on evaluating the service quality of airlines is provided to illustrate our models and method.

In modeling Multi-Criteria Decision Making (MCDM) problem, we usually assume that the decision maker is able to elicitate his preferences with precision and without difficulty. However, in many situations, the expert is unable to provide his assessment with certainty or he is unwilling to quantify his preferences. To deal with such situations, a new MCDM model under uncertainty is introduced. In fact, we focus here on the problem of modeling expert opinions despite the presence of incompleteness and uncertainty in their preference assessments. Besides, our proposed solution suggests to model these preferences qualitatively rather than exact numbers. Therefore, we propose to incorporate belief preference relations into a MCDM method. The expert assessments are then formulated as a belief function problem since this theory is considered as a useful tool to model expert judgments.

Uninorms, as binary operations on the unit interval, have been widely applied in fuzzy set theory. In this paper, we study uninorms with nilpotent underlying t-norm and t-conorm. We prove that such a uninorm belongs to or . Moreover, some construction methods of uninorms from given t-norm and t-conorm are discussed.

In the framework of interval transferable-utility (TU) games, we propose an equivalence theorem to characterize the family of all interval solutions that admit a potential. Further, we also provide several axiomatizations of the interval Shapley value based on this equivalence theorem.

The connection between probability and possibility has been studied for decades. Several studies have intended to provide a unified interpretation for these concepts; other studies attempt to discover their transformation relationship. This paper addresses these problems using a unified perspective. By extending the viewpoint of interpreting the grade of membership as a conditional probability, we introduce the conditional probability mass function and likelihood mass function to describe randomness and fuzziness, respectively. We draw the conclusion that conditional probability is undetermined itself and can be used for describing either randomness or fuzziness, depending on how it is interpreted. A fuzzy Bayesian theorem is presented based on the fuzziness interpretation of conditional probability. Additionally, a probability-possibility conversion is derived by assigning different interpretations for conditional probability of the Bayesian theorem, which is notably similar to Klir's normalized transformation. An example of target recognition demonstrates that the fuzzy Bayesian classifier outperforms the usual Bayesian classifier.

For uncertain variable sequences, conditions of convergences such as Cauchy convergence in measure, convergence almost surely and convergence uniformly almost surely are given. Consequently, the relationships among convergences of uncertain variable sequences are shown. These results have not been proposed in literature so far.