The article introduces a new proposal of a defuzzification method, which can be implemented in fuzzy controllers. The first chapter refers to the origin of fuzzy sets. Next, a modern development based on this theory is presented in the form of ordered fuzzy numbers (OFN). The most important characteristics of ordered fuzzy numbers are also presented. In the following chapter, details about the defuzzification process are given as part of the fuzzy controller model. Then a new method of defuzzification is presented. The method is named center of circles intersection (CCI). The authors compare this method with a similar geometric solution: triangular expanding (TE) and geometric mean (GM). Also, the results are compared with other methods such as center of gravity (COG), first of maxima (FOM) and last of maxima (LOM). The analysis shows that the proposed solution works correctly and provides results for traditional fuzzy numbers as well as directed fuzzy numbers. The last chapter contains a summary, in which more detailed conclusions are provided and further directions of research are indicated.

The problem considered in the paper is motivated by production planning in a foundry equipped with a furnace and a casting line,

which provides a variety of castings in various grades of cast iron/steel for a large number of customers. The goal is to create the order of

the melted metal loads to prevent delays in delivery of goods to customers. This problem is generally considered as a lot-sizing and

scheduling problem. However, contrary to the classic approach, we assumed the fuzzy nature of the demand set for a given day. The paper

describes a genetic algorithm adapted to take into account the fuzzy parameters of simultaneous grouping and scheduling tasks and

presents the results achieved by the algorithm for example test problem.

The new approach to the construction project planning is presented in the article. The classical net model is enriched by the fuzzy decision node. The decision node allows for alternate choices dependent on appearing circumstances. The alternative net model with fuzzy decision node is an acyclic multi-graph, where some, chosen nodes (events) have multiple connections. These connections represent alternative methods of the certain work execution. Every work (activity) (i, j) in the net model with alternative methods of work execution, despite the basic information comprising the execution time, the cost, the number of necessary workers, should comprise additional information e.g. about a complexity of works, a real feasibility. The alternative ways of a given work execution are evaluated in the decision node based on the fuzzy decision model. Each method is evaluated by assigning it the preference level in a form of the value of the membership function – „equal or higher” μ_≥. The most preferable way of the work execution in a given circumstances, will have the highest value of preference level. When the choice is done the net model is solved in the traditional way. Therefore, the paper concentrates on the process of choosing the method of work execution in the fuzzy decision node. The example calculations accompanying the process of decision taking are presented too. The model requires the use of linguistic variables, a fuzzy numbers, as well as fuzzy preference relations together with some calculations applied the probability theory.

The purpose of this article is to develop a multicriteria group decision making (MCGDM) method in dual hesitant fuzzy (DHF) environment by evaluating the weights of the decision makers from the decision matrices using two newly defined prioritized aggregation operators based on score function to remove the inconsistencies in choosing the best alternative. Prioritized weighted averaging operator and prioritized weighted geometric operator based on Einstein operations are described first for aggregating DHF information. Some of their desirable properties are also investigated in details. A method for finding the rank of alternatives in MCGDM problems with DHF information based on priority levels of decision makers is developed. An illustrative example concerning MCGDM problem is considered to establish the application potentiality of the proposed approach. The method is efficient enough to solve different real life MCGDM problems having DHF information.