International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Integration plays a very important role in the fusion methods. In this paper, we put forward the subtraction and division definite integrals based on the fuzzy measure and the admissible order for aggregating not only discrete but also continuous correlative intuitionistic fuzzy information. These definite integrals are implemented by constructing the integrands and the integral limits respectively, and based on which an approach to multi-criteria decision making with correlative intuitionistic fuzzy information is developed. Finally, an illustrative example involving technology improvement of Midwest American Manufacturing Corp is employed to verify the practicality and effectiveness of our approach.

How to efficiently make decision under uncertain is a hot research topic. In this paper, a new aggregating operator for linguistic decision making based on D numbers is proposed. D numbers is a new mathematic tool to model uncertainty, since it ignores the condition that elements on the frame must be mutually exclusive. Compared with these existing aggregating operators, the new method is clear, concise and less computational complexity. A numerical example is used to demonstrate the effectiveness of the proposed method.

The literature discusses several extensions of fuzzy sets. AIFS, IVFS, HFS, type-2 fuzzy sets are some of them. Interval valued fuzzy sets is one of the extensions where the membership is not a single value but an interval. Atanassov Intuitionistic fuzzy sets, for short AIFS, are defined in terms of two values for each element: membership and non-membership. In this paper we discuss AIFS and their relationship with fuzzy measures. The discussion permits us to define counter AIFS (cIFS) and discretionary AIFS (dIFS). They are extensions of fuzzy sets that are based on fuzzy measures.

Nondeterministic variables of certain distributions are employed to represent uncertain lifetimes and repair times in repairable systems, which are usually treated as stochastic variables and the probability distributions of the stochastic variables have crisp parameters. However, in practice, the parameters may not be precisely represented due to a lack of sufficient data. The main purpose of this paper is to apply the random fuzzy theory to the establishment of repairable coherent system models. Then the expressions of limiting availability and steady state failure frequency of the random fuzzy coherent systems are proposed, respectively. Finally, some numerical examples are given for illustration.

The aim of this article is to investigate the approach for multi-attribute group decision-making, in which the attribute values take the form of multi-granularity multiplicative linguistic information. Firstly, to process multiple sources of decision information assessed in different multiplicative linguistic label sets, a method for transforming multi-granularity multiplicative linguistic information into multiplicative trapezoidal fuzzy numbers is proposed. Then, a formula for ranking multiplicative trapezoidal fuzzy numbers is given based on geometric mean. Furthermore, the concept of similarity degree between two multiplicative trapezoidal fuzzy numbers is defined. The attribute weights are obtained by solving some optimization models. An effective approach for group decision making with multi-granularity multiplicative linguistic information is developed based on the ordered weighted geometric mean operator and proposed formulae. Finally, a practical example is provided to illustrate the practicality and validity of the proposed method.

Capacity plays an important role in many areas. A capacity is usually studied under the assumption that it is concave (or convex). In this paper, we perform a further investigation on the Fubini Theorems for concave (or convex) capacities given by Ghirardato (1997) and Chateauneuf and Lefort (2008). We extend Fubini Theorems for capacities to a larger class of functions, which are both μ₁-Choquet integrable and μ₂-Choquet integrable, not to restrict only on slice-comonotonic functions.

In this paper, we have studied representability of both fuzzy biorders and fuzzy weak orders. It has also been shown that union of a finite family of fuzzy weak orders with respect to a t-norm T is a fuzzy quasi-transitive relation with respect to T. In the last theorem, we have obtained a characterization for a T_L-representable fuzzy weak order.

One difficulty faced in knowledge engineering for Bayesian Network (BN) is the quantification step where the Conditional Probability Tables (CPTs) are determined. The number of parameters included in CPTs increases exponentially with the number of parent variables. The most common solution is the application of the so-called canonical gates. The Noisy-OR (NOR) gate, which takes advantage of the independence of causal interactions, provides a logarithmic reduction of the number of parameters required to specify a CPT. In this paper, an extension of NOR model based on the theory of belief functions, named Belief Noisy-OR (BNOR), is proposed. BNOR is capable of dealing with both aleatory and epistemic uncertainty of the network. Compared with NOR, more rich information which is of great value for making decisions can be got when the available knowledge is uncertain. Specially, when there is no epistemic uncertainty, BNOR degrades into NOR. Additionally, different structures of BNOR are presented in this paper in order to meet various needs of engineers. The application of BNOR model on the reliability evaluation problem of networked systems demonstrates its effectiveness.

Aggregation of data has many important applications in various fields, especially in economics, planning, optimization, decision-making and ranking of alternatives. There are many approaches to aggregation reflecting the fact that aggregation is application-depend and there are some considerations which are hard to quantify. The simple formula, FA, which is described in the following is easy to apply and lends itself to standardization and generalization. It is convenient to describe the formula in terms of a model in which the data relate to the grades g₁, …, g_n which a student, call him Robert, received for the collection of courses c₁, …, c_n . Assume that the data are of the form (c₁, g₁), (c₂, g₂), …, (c_n, g_n). The grades are on a scale from 0 to 100. Upon normalization they become numbers in the unit interval which may be interpreted as grades of membership or degrees. We propose two approaches.