Informatica

Nowadays, it is agreed that fuzzy sets are suitable for capturing and representing the concept of vagueness and uncertainty, and various fuzzy reasoning systems are being developed based on them. Researchers have proposed fuzzy set extensions to improve the performance and accuracy of these systems. The research questions arise regarding how fuzzy sets have evolved and what the main trends in their evolution are. To address these questions, our research presents a chronological and bibliometric analysis of fuzzy sets based on papers extracted from the Web of Science database. The main findings and contributions have been identified, systematized and visualized in a fuzzy set keyword map of 65 fuzzy set extensions. These extensions are primarily used for decision-making, reasoning, and prediction, particularly in the context of digital transformation, by integrating digital technologies into all areas of business, transforming operations and enhancing value delivery to customers. As organisations increasingly adopt digital technologies, the need for robust frameworks to manage uncertainty becomes critical. The main trends indicating the directions of fuzzy sets development, an overview of the variety and popularity of fuzzy sets over the years, and the impact of countries engaged in fuzzy set research are also identified and reported. The results support researchers and practitioners working on fuzzy sets and their applications by providing valuable insights into the fuzzy set topic, its existing extensions, and, more generally, to any field of investigation where fuzzy sets are relevant, particularly in the realm of digital transformation.

Fuzzy sets can be used in many old-fashioned aspects of our lives in order to reach better performance and make fairer judgments. Evaluation through examination is typically conducted by educational centers, and multiple choice question (MCQ) exams are widely applied to score the examinees. Since scoring is potentially a difficult process to judge, we propose to evaluate examinees by fuzzy evaluation method. This method can overcome the main shortcoming of the classical MCQs, i.e. the random selection of the choices. The evaluation of the proposed fuzzy MCQ is more accurate and its ranking of examinees is fairer than classical MCQ.

The paper presents the process of the selection of a potential supplier, which have to be the most appropriate to stakeholders. The selection is based on a set of criteria: Delivery Price, Financial Position, Production Specifications, Standards and Relevant Certificates, Commercial Strength, and the Performance of supplier, etc. The criteria for evaluation and their importance are selected by taking into consideration the interests and goals of the stakeholders. The solution of problem was made by applying a new Additive Ratio ASsessment (ARAS) method with the grey criteria scores – ARAS-G method. The proposed technique could be applied to substantiate the selection of effective alternative of sustainable development, impact on environment, structures, technologies, investments, etc.

The objective of this paper is the description, justification, and web-based implementation of polynomial time algorithms for equilibrium search of Quadratic Bimatrix Games (QBG). An algorithm is proposed combining exact and heuristic parts. The exact part has the Irelevant Fraud (IF) component for cases when an equilibrium exists with no pure strategies. The Direct Search (DS) component finds a solution if an equilibrium exists in pure strategies. The heuristic Quadratic Strategy Elimination (QSE) part applies IF and DS to reduced matrices obtained by sequential elimination of strategies that lead to non-positive IF solutions. Finally, penalties needed to prevent unauthorized deals are calculated based on Nash axioms of two-person bargaining theory. In the numeric experiments QSE provided correct solution in all examples. The novel results include necessary and sufficient conditions when the QBG problem is solved by IF algorithm, the development of software and the experimental testing of large scale QBG problems up to n=800. The web-site http://pilis.if.ktu.lt/~jmockus includes this and accompanying optimization models.

Multi-criteria decision making is used in many areas of human activities. Each alternative in multi-criteria decision making problem can be described by a set of criteria. Criteria can be qualitative and quantitative. They usually have different units of measurement and different optimization direction. The normalization aims at obtaining comparable scales of criteria values. The normalization of criteria values is not always needed, but it may be essential. In the new program LEVI 3.1 the following normalization methods are possible: vector, linear scale, non-linear and new logarithmic techniques. Logarithmic normalization has never been used before. The present research is focused on introducing a new logarithmic method for decision making matrix normalization.