Abstract:  The object of study involves fuzzy logical multi-criterion methods and algorithms within the support systems for the decision making. The immediate object of study involves support systems for decision making in the sphere of dependability of technical equipment systems in the situation of fuzzy information input. The purpose of the study is to provide methodological basis for the development of applied fuzzy systems for the traditional priority studies for the multiple objects in the multi-dimensional set of quantity and quality markers based upon the linguistic statements by the experts. The article provides for the methodology of development for the support system for the decision-making  in the conditions of non-precise information with the use of fuzzy theory of sets and fuzzy methods for the hierarchy analysis. The author provides detailed analysis for several aspects of the topic in question, such as application of decision-making methods for multi-criteria alternative analysis, such as the fuzzy inference and the hierarchy analysis method for fuzzy proximities. The author offers the method for ranging alternatives based upon the multi-dimensional sets of facts and criteria in the situation of fuzzy data input. The methodology of studies is based upon the formation of a model for the decision-making support system, method formalization for processing fuzzy data, algorithm development and providing for the simulation experiment for various values of managing parameters within a model. The provided methodology was implemented based upon an example of the support system for the decision-making  for the expert procedure for the evaluation of general dependability of chemical technological systems.  Implementation of fuzzy logic procedures when managing a complex of dependability markers is based upon the results of expert evaluation of four separate industrial objects within a single complicated technical system of oil and gas chemical production based upon five dependability criteria. Taking an example of the hierarchical structure for dependability of oil and gas equipment, the author offers a model and an algorithm for the evaluation for deriving weights with the use of a fuzzy pairwise comparison matrix based upon the judgment matrix. The experimental calculation results show that the fuzzy pairwise comparison method  is efficient with greater degrees of priority fuzziness 50 to 75 percent. Efficiency of the judgment matrix depends upon the evaluation closeness or incoming linguistic values, however, it is completely dependent upon the correct formalization of data input via formation of the membership functions as well as on the formation of fuzzy rule bases. Fuzzy logical algorithms for decision making support in the sphere of managing the complex of dependability markers for the oil and gas equipment form a non-formalized part of the complex management and support systems for ensuring industrial equipment dependability. Such sub-systems allow for the preliminary evaluation of the general situation in the sphere of equipment dependability based upon the expert information.