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The problem of a justified use of Fuzzy MCDA (FMCDA) models, which are fuzzy extensions of a classical MCDA method, is explored for Fuzzy MAVT models as an example. The use of such models under conditions of distinctions in ranking of alternatives and violation of the basic FMCDA axiom forms a problem that the authors call as a presumption of model adequacy.

Measurements are basic for all quantitative science and for many human activities. Usually numbers are considered to be basic for the description of measurement results of one-dimensional continuous quantities. By the limited accuracy of every measurement equipment the result of one measurement of a continuous quantity is not a number but a more or less vague result. This unavoidable uncertainty has to be analyzed in order to obtain realistic results. Using the concept of so-called fuzzy numbers, which are special fuzzy subsets of the set of real numbers, helps to give a more realistic description of the uncertainty of individual measurement results. Consequences of this description for the analysis of measurement data are described in this contribution.

Under the circumstance that opinions of experts of group decision making are assumed as L – R fuzzy numbers, the membership functions are moved toward the left according to the sizes of their expectations. The similarity degree of two experts' opinions is calculated for an alternative where their expectations equal zero and the mean distance of two members' opinions is represented as their opinion differences. Using simple additive weighting (SAW) method, a new aggregation for fuzzy opinions under group decision making is proposed in this paper. For each expert, the degree of similarity between his and the others is averaged. The weight of specific expert's opinion in aggregation is proportional to the degree of average agreement of that expert.

In this paper, the α-level stability for a fuzzy control system and the compatibility between the rule base and control arithmetic are introduced. The existence of finite fuzzy state total set with α-level is obtained. Furthermore, the paper points out that the Mamdani control method is compatible in α-level with its control rule base. So the control dynamic features can be estimated by means of the rule base. The analysis shows that for a plantP controlled by the Mamdani controller is α-level stable as long as the plant is α-level stably controlled by the rule base.

The supply chain network design involves the choice of plants and distribution centers to be opened and the distribution network design to satisfy the customer demand with minimum cost. This paper designs supply chain network in uncertain environment, in which the demands of customers are assumed to be stochastic variables, and the operation costs are considered as fuzzy numbers. We formulate model by fuzzy programming and develop monkey-king algorithm to solve the proposed model. Moreover, a numerical example is presented to illustrate the effectiveness of model and solution algorithm.

The use of fuzzy numbers (FNs) for uncertainty treatment within Multi-Criteria Decision Analysis (MCDA) is a claiming approach for examination of multicriteria problems in fuzzy environment. For proper use of a fuzzy extension for the MCDA method (FMCDA), the fulfilment of corresponding axioms/requirements, associated with this method, should be analyzed. For empirical MCDA methods (e.g., TOPSIS, AHP, PROMETHEE) the basic axiom concerns the properties of generalized criterion for this method. The goal of this contribution is exploring violation of basic axioms for FMCDA methods for Fuzzy TOPSIS (FTOPSIS) as an example. The ways of adjustment of fuzzy MCDA methods to correct use is briefly discussed.