International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this paper, a two-dimensional Hardy type inequality for fuzzy integrals is proved. Also, some illustrative examples are presented.

The group decision making problem with inter-dependent or interactive attributes is studied. By using the Choquet integral and the inducing variables, we develop the induced 2-tuple correlated averaging (ITCA) operator, the generalized induced 2-tuple correlated averaging (GITCA) operator and the quasi-arithmetic induced 2-tuple correlated averaging (QITCA) operator. The characteristics of the proposed operators are that the evaluation values of decision makers are in linguistic arguments, the correlations among the elements can be reflected and the ordering of the arguments is based on other associated variables instead of their own values. The properties of these operators are studied and new multiple attribute decision making method based on the new operators is proposed. Finally, architecture material supplier selection problem is provided to illustrate the feasibility and efficiency of the proposed method.

The concept of possibilistic mean value and variance of fuzzy numbers has been applied to investment decisions by using a nonlinear type of fuzzy numbers called adaptive fuzzy numbers. In this paper, by extending the notion of adaptive fuzzy number, we propose a more flexible methodology. Our aim is to allow decision maker more flexibility in dealing with ambiguity and uncertainty. To illustrate the use of our approach and its ability in dealing with ambiguity and imprecision we analyze, as an application, the fuzzy net present value of future cash flows and give some numerical results.

Triangular intuitionistic fuzzy numbers (TIFNs) are a special case of intuitionistic fuzzy sets. The purpose of this paper is to develop a new decision making method based on possibility variance coefficient to solve the multi-attribute decision making (MADM) problems, in which the attribute values are in the form of TIFNs and the weight preference information is incomplete. The possibility mean, variance and standard deviation for a TIFN are introduced as well as the possibility variance coefficient. Hereby, a new method to rank TIFNs is given on the basis of the possibility variance coefficients. The bi-objective mathematical programming, which minimizes the possibility variance coefficients of membership and non-membership functions for alternative's overall attribute values, is constructed. Using the max-min method, two non-linear fractional programming models are transformed into the linear programming models through the Charnes and Cooper transformation. Thus, the Pareto optimal solution to the bi-objective mathematical programming can be derived by solving the single-objective programming model. The ranking order of alternatives is obtained according to the minimum possibility variance coefficients. A personal selection example is given to verify the developed method and to demonstrate its feasibility and effectiveness. The analysis of comparison with other method is also conducted.

In this paper, we present a new intuitionistic fuzzy decision-making technique based on similarity measures and the ordered weighted average (OWA) operator. We develop the intuitionistic fuzzy ordered weighted similarity (IFOWS) measure. The main advantage of the IFOWS measure is that it can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Moreover, it provides a very general formulation that includes a wide range of aggregation similarity measures and aggregates the input arguments taking the form of intuitionistic fuzzy values rather than exact numbers. We further develop the interval-valued intuitionistic fuzzy ordered weighted similarity (IVIFOWS) measure. Then we apply the developed similarity measures for consensus analysis in group decision-making with intuitionistic fuzzy information. Finally, a practical case is used to illustrate the developed procedures.

We define some operations over Atanassov's intuitionistic fuzzy sets (AIFSs), such as Einstein intersection, Einstein product, Einstein scalar multiplication and Einstein exponentiation, etc., and then define new concentration and dilation of AIFSs. These definitions will be useful while dealing with various linguistic hedges like “very”, “more or less”, “highly”, “very very” etc., involved in the problems under intuitionistic fuzzy environment. We also prove some propositions and present some examples in this context.

Cuadras (Constructing copula functions with weighted geometric means, Journal of Statistical Planning and Inference139 (2009) 3766–3772) showed that geometric mean of the Cuadras–Augé copula and the Gumbel–Barnett copula is a copula by means of generalized function. In this paper, we adopt the method proposed by Durante et al. (2-Increasing binary aggregation operators, Information Sciences177 (2007) 111–129) to investigate weighted geometric mean of the Cuadras–Augé copula and the Gumbel–Barnett copula, as well as weighted geometric mean of the Gumbel–Barnett copula and the New copula. We also consider weighted geometric mean of Archimedean copulas.

With the development of uncertainty reasoning and information fusion, there have emerged several theories including fuzzy set theory, Dempster-Shafer evidence theory, probability theory and rough set theory, etc., for representing and dealing with the uncertain information. When the fusion of the uncertain information originated from different sources is needed, how to construct a general framework for different theories of uncertainty or how to establish the connection between different theoretical frameworks has become a crucial problem. Particularly, to combine two kinds of information represented respectively by the BPA and the FMF, this paper proposes two transformations of an FMF into a BPA by solving a constrained maximization or minimization optimization problem. The objective function is the uncertainty degree of the body of evidence (BOE) and the corresponding constraints are established based on the given FMF. In fact the transformation of an FMF into a BPA is the transformation of fuzzy sets into random sets, which is currently accepted as a unified framework for several theories of uncertainty. Our proposed approaches have no predefinition of focal elements and they can be used as the general transformations of fuzzy sets into random sets. Some examples and analyses are provided to illustrate and justify the rationality and effectiveness of the proposed approaches.