International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Intuitionistic fuzzy sets can describe the uncertainty and complexity of the world flexibly, so it has been widely used in multi-attribute decision making. Traditional intuitionistic fuzzy aggregation operators are usually based on the probability measure, namely, they consider that the attributes of objects are independent. But in actual situations, it is difficult to ensure the independence of attributes, so these operators are unsuitable in such situations. Fuzzy measure is able to depict the relationships among the attributes more comprehensively, so it can complement the traditional probability measure in dealing with the multi-attribute decision making problems. In this paper, we first analyze the existing intuitionistic fuzzy operators based on fuzzy measure, then introduce two novel additive intuitionistic fuzzy aggregation operators based on the Shapley value and the Choquet integral, respectively, and show their advantages over other ones.

This paper uses the priority labels to express the detailed prioritized relationship between criteria and develops some scaled prioritized geometric aggregation operators, including the scaled prioritized geometric score (SPGS) operator and the scaled prioritized geometric averaging (SPGA) operator. We also present the uncertain scaled prioritized geometric scoring (USPGS) operator and the uncertain scaled prioritized geometric averaging (USPGA) operator. We investigate the properties of these operators and build the models to derive the weights by maximizing square deviations from a possible range to distinguish the candidate alternatives. The principal advantage of these scaled prioritized geometric aggregation operators is that they are very stable and satisfy monotonicity. Furthermore, we investigate approaches to multi-attribute decision making based on the proposed operators or models and examples are illustrated to show the feasibility and validity of the new approaches. Finally, some further discussions are given.

This paper propose a Berwald type inequality and a Favard type inequality for Sugeno integrals. That is, we first show that

This paper proposes the use of binary trees for representing and managing the potentials involved in Influence Diagrams. This kind of tree allows representing context-specific independencies that are finer-grained compared to those encoded using other representations. This enhanced capability can be used to improve the efficiency of the inference algorithms used for Influence Diagrams. Moreover, binary trees allow computing approximate solutions when exact inference is not feasible. In this work we describe how binary trees can be used to perform this approximate evaluation and we compare them with other structures present in the literature.

This paper considers the identification of problems which generate anomalies at firms through the observed symptoms on the basis of fuzzy relations and Zadeh's compositional rule of inference. A procedure for determining the fuzzy cause vector of an economic and financial diagnosis problem is proposed, which consists of the design of fuzzy relational matrix and the resolution of a system of fuzzy relational equations. An efficient algorithm for solving fuzzy relational equations in terms of the associated set covering problem is introduced. It utilizes a back-tracking method to generate each minimal covering, where no duplicate or non-minimal coverings exist. A numerical example of firms' insolvency causes diagnosis is also included.

Response Surface Methodology (RSM) is a group of mathematical and statistical methods used for exploring the optimum operating conditions through statistical design of experiments. Obtaining the suitable analytical model between input variables and one or more responses is the main stage in RSM studies. When the response has replications, these replicated values may cause error. The proper modeling approach should be preferred according to the source of error, which is randomness or measurement error. In this study, Bayesian approach and fuzzy approach are used to estimate the model parameters in which the error becomes randomness and measurement error, respectively. The novelty of this study is analysis of response surface model parameters, which are obtained by using Bayesian approach and fuzzy approach, through interval analysis. The interpretation of model parameters and the comparison of modeling approaches are evaluated by interval arithmetic metrics. The suggested approaches are applied on replicated response measured two data sets and the results are discussed.

A new method for reinforcement fuzzy controllers is presented by this article. The method uses Artificial Bee Colony algorithm based on Q-Value to control reinforcement fuzzy system; the algorithm is called Artificial Bee Colony-Fuzzy Q learning (ABC-FQ). In fuzzy inference system, precondition part of rules is generated by prior knowledge, but ABC-FQ algorithm is responsible to achieve the best combination of actions for the consequence part of the rules. In ABC-FQ algorithm, each combination of actions is considered a food source for consequence part of the rules and the fitness level of this food source is determined by Q-Value. ABC-FQ Algorithm selects the best food resource, which is the best combination of actions for fuzzy system, using Q criterion. This algorithm tries to generate the best reinforcement fuzzy system to control the agent. ABC-FQ algorithm is used to solve the problem of Truck Backer-Upper Control, a reinforcement fuzzy control. The results have indicated that this method arrives to a result with higher speed and fewer trials in comparison to previous methods.

An observer based adaptive fuzzy controller for nonlinear system is proposed. Parameters in the proposed adaptive fuzzy controller are tuned on-line by the genetic algorithm (GA). For on-line tuning, a parsimonious parameterization scheme for fuzzy controller called orthogonal modulated membership functions (mmf)³⁵ is utilized. A simplified GA called micro GA that greatly improves the learning efficiency is applied. The valid range of mmf parameters will be proved in this paper. With the valid range of mmf parameters, the search by MGA for the optimal parameterization of the adaptive fuzzy controller is more focused resulting in fast convergence to the optimal solutions. A Lyapunov theorem based supervisory control is added to the fuzzy controller assuring that close loop stability is always maintained for the adaptive fuzzy controller during the learning process.