International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

This short paper is devoted to study the law (μ → σ) · λ ≤ μ → σ·λ, with fuzzy sets μ, σ, and λ, in the case the conditional → is functionally expressible by a numerical function J, and the intersection · is functionally expressible by a continuous t-norm T. That is, it deals with the functional inequality T(J(a,b),c) ≤ J(a,T(b,c)) in the unknowns T and J.

The aim of this work is to develop a new compatibility for the uncertain multiplicative linguistic preference relations and determine the optimal weights of decision makers (DMs), which are very suitable to deal with group decision making (GDM) problems involving uncertain multiplicative linguistic preference relations. First, the concepts of compatibility degree and compatibility index for the two uncertain multiplicative linguistic preference relations are proposed. Then we prove the property that the synthetic uncertain linguistic preference relation is of acceptable compatibility under the condition that uncertain multiplicative linguistic preference relations given by DMs are all of acceptable compatibility with a specific linguistic preference relation, which is the scientific basis of using the uncertain multiplicative linguistic preference relations in the GDM. Next, in order to determine the weights of decision makers, we construct an optimal model based on the criterion of minimizing the compatibility index. Finally, we develop an application of the optimal weights approach compared with the equal weights approach where we analyze a GDM regarding the selection of investment.

Data envelopment analysis (DEA) is a non-parametric method for measuring the efficiency of peer operating units that employ multiple inputs to produce multiple outputs. Several DEA methods have been proposed for clustering operating units. However, to the best of our knowledge, the existing methods in the literature do not simultaneously consider the priority between the clusters (classes) and the priority between the operating units in each cluster. Moreover, while crisp input and output data are indispensable in traditional DEA, real-world production processes may involve imprecise or ambiguous input and output data. Fuzzy set theory has been widely used to formalize and represent the impreciseness and ambiguity inherent in human decision-making. In this paper, we propose a new fuzzy DEA method for clustering operating units in a fuzzy environment by considering the priority between the clusters and the priority between the operating units in each cluster simultaneously. A numerical example and a case study for the Jet Ski purchasing decision by the Florida Border Patrol are presented to illustrate the efficacy and the applicability of the proposed method.

Induced quasi-arithmetic aggregation operators are considered to aggregate uncertain linguistic information by using order inducing variables. We introduce the induced correlative uncertain linguistic aggregation operator with Choquet integral and we also present the induced uncertain linguistic aggregation operator by using the Dempster-Shafer theory of evidence. The special cases of the new proposed operators are investigated. Many existing linguistic aggregation operators are special cases of our new operators and more new uncertain linguistic aggregation operators can be derived from them. Decision making methods based on the new aggregation operators are proposed and architecture material supplier selection problems are presented to illustrate the feasibility and efficiency of the new methods.

In this paper, a descriptive decision-making model under uncertainty is proposed which incorporates two types of decision attitudes for uncertainty; one is an attitude about ignorance (optimism/pessimism) and the other one is about risk (risk-seeking and risk-aversion). At first, Evidential Decision Making Problem (EDMP) has been defined where Dempster-Shafer Theory (DST) has been used to represent uncertainty. Then probability approximation approach of solving EDMP is shown. For deciding the decision weights in different attitudes of decision maker, Ordered Weighted Averaging (OWA) operator has been used. Later on, Prospect Theory has been applied to accomplish a descriptive decision-making model. To show the effectiveness of our approach, a real life decision problem of travelers' route choice from a set of alternatives has also been provided.

This paper proposes an Enhanced Particle Swarm Optimization (EPSO) for extracting optimal rule set and tuning membership function for fuzzy logic based classifier model. The standard PSO is more sensitive to premature convergence due to lack of diversity in the swarm and can easily get trapped into local minima when it is used for data classification. To overcome this issue, BLX-α crossover and Non-uniform mutation from Genetic Algorithm (GA) are incorporated in addition to standard velocity and position updating of PSO. The performance of the proposed approach is evaluated using ten publicly available bench mark data sets. From the simulation study, it is found that the proposed approach enhances the convergence and generates a comprehensible fuzzy classifier system with high classification accuracy for all the data sets. Statistical analysis of the test result shows the suitability of the proposed method over other approaches reported in the literature.

In practical applications of graph theory, non-deterministic factors are frequently encountered. This paper employs uncertainty theory to deal with non-deterministic factors in problems of graph connectivity. The concepts of uncertain graph and connectedness index of uncertain graph are proposed in this paper. It presents two algorithms to calculate connectedness index of an uncertain graph.

Many researchers have put forward lots of entropy and distance measures for intuitionistic fuzzy sets (IFSs). This paper firstly reviews some basic concepts for IFSs and several widely used distance measures between IFSs. And then a series of distance measures are presented on the basis of above widely used distance measures. Based on such distance measures and intuitionistic index, a set of entropies for IFSs are proposed and proved to meet the axiomatic requirements given by Szmidt and Kacprzyk in 2001. Besides, two numerical examples are demonstrated to verify the efficiency of the proposed entropies for IFSs. Finally, the paper concludes with suggestions for future research.