Informatica

In this paper we establish equivalence between a theory of fuzzy functional dependences and a fragment of fuzzy logic. We give away to interpret fuzzy functional dependences as formulas in fuzzy logic. This goal is realized in four steps. Truth assignment of attributes is defined in terms of closeness between two tuples in a fuzzy relation. A corresponding fuzzy formula is associated to a fuzzy functional dependence. It is proved that if a relation satisfies a fuzzy functional dependence, then the corresponding fuzzy formula is satisfied and vice verse. Finally, equivalence of a fuzzy formulas and a set fuzzy functional dependence is demonstrated. Thus we are in position to apply the rule of resolution from fuzzy logic, while calculating fuzzy functional dependences.

Linguistic hesitant fuzzy sets (LHFSs) permit the decision maker to apply several linguistic terms with each having several membership degrees to denote his/her preference of one thing. This type of fuzzy sets can well address the qualitative and quantitative cognitions of the decision maker as well as reflect his/her hesitancy, uncertainty and inconsistency. This paper introduces a distance measure between any two LHFSs and then defines a correlation coefficient of LHFSs. Considering the application of LHFSs, the weighted distance measure and the weighted correlation coefficient of LHFSs are defined. To address the interactions between elements in a set, the Shapley weighted distance measure and the Shapley weighted correlation coefficient are presented. It is worth noting that when the elements are independent, they degenerate to the associated weighted distance measure and the weighted correlation coefficient, respectively. After that, their application to pattern recognition is studied. Furthermore, an approach to multi-attribute decision making under linguistic hesitant fuzzy environment is developed. Meanwhile, numerical examples are offered to show the concrete application of the developed procedure.

In order to survive in the present day global competitive environment, it now becomes essential for the manufacturing organizations to take prompt and correct decisions regarding effective use of their scarce resources. Various multi-criteria decision-making (MCDM) methods are now available to help those organizations in choosing the best decisive course of actions. In this paper, the applicability of weighted aggregated sum product assessment (WASPAS) method is explored as an effective MCDM tool while solving eight manufacturing decision making problems, such as selection of cutting fluid, electroplating system, forging condition, arc welding process, industrial robot, milling condition, machinability of materials, and electro-discharge micro-machining process parameters. It is observed that this method has the capability of accurately ranking the alternatives in all the considered selection problems. The effect of the parameter λ on the ranking performance of WASPAS method is also studied.

This paper proposes a new multi-attribute ranking procedure based on distance from decision-maker preferences. This method has two phases. In the first phase, the decision maker is asked to define the preferred performance for each attribute. In the second phase, Weighted Sum method and new distance-based normalization procedure are used to determine the overall performance rating of alternatives.

The new method for the construction of partial order on the set of multicriteria alternatives is presented. This method belongs to the family of Verbal Decision Analysis methods and gives a more efficient means of problem solution. The method is based on psychologically valid operations for information elicitation from a decision maker: comparisons of two distances between the evaluations on the ordinal scales of two criteria. The information received from a decision maker is used for the construction of a binary relation between a pair of alternatives which yields preference, indifference and incomparability relations. The notion of a method decisive power is introduced. The illustrative example is given.