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Abstract. In the last few years there has been a growing interest in route building oriented mobile applications with the following features of navigation and sending timely notifications about arrival. Despite the large body of existing knowledge on navigational services, there has been an important issue relative to positioning accuracy. The paper discusses a possible solution to comparison problem, which is linked to the determination of the closeness to destination metro station through finding a difference between user's current coordinates and fixed-point coordinates. With this end in view, fuzzy logic approach is used to develop Routes Recommender System (RRS) that utilizes linguistic variables to express the vague and uncertain term 'closeness to…'. The paper provides detailed explanation of each variable considered in the fuzzy inference system (FIS), set of fuzzy rules in line with graphical representation of system's output. Based on Mamdani model, we propose a set of test cases to check maintainability of the model and provide a description about received results. At a later time, an Android-based mobile application aimed at public transport route building will be developed whose notification system will be based on our model`s implementation presented. It should be emphasized that the paper examines potentials of the modeling approach based on interval type-2 fuzzy sets (IT2FS) that attract much attention these days in various research studies and conventional Mamdani fuzzy inference system (MFIS) as applied to real and rather topical problem. The significance of developing such models may be of a high demand for appropriate representation of factors that are inherently vague and uncertain. Hence, this study may also contribute to future research on similar topics.

E-commerce is a runaway activity growing at an unprecedented rate all over the world and drawing millions of people from different spots on the globe. At the same time, e-commerce affords ground for malicious behavior that becomes a subject of principal concern. One way to minimize this threat is to use reputation systems for trust management across users of the network. Most of existing reputation systems are feedbackbased, and they work with feedback expressed in the form of numbers (i.e. from 0 to 5 as per integer scale). In general, notions of trust and reputation exemplify uncertain (imprecise) pieces of information (data) that are typical for the field of e-commerce. We suggest using fuzzy logic approach to take into account the inherent vagueness of user's feedback expressing the degree of satisfaction after completion of a regular transaction. Brief comparative analysis of well-known reputation systems, such as EigenTrust, HonestPeer, Absolute Trust, PowerTrust and PeerTrust systems is presented. Based on marked out criteria like convergence speed, robustness, the presence of hyper parameters, the most robust and scalable algorithm is chosen on the basis of carried out sets of computer experiments. The examples of chosen algorithm's (PeerTrust) fuzzy versions (both Type-1 and Interval Type-2 cases) are implemented and analysed.

The Analytic Hierarchy Process (AHP) enables decision-makers to prioritize alternatives. However, when an expert expresses judgments using natural language statements (e.g. words or phrases) inherent vagueness of language constructs can cause the interpretation to be imprecise. The fuzzy Analytic Hierarchy Process (FAHP) can be viewed in the context of the classical AHP expansion. While performing pairwise comparisons domain experts are accustomed to operating with verbal terms in their judgments. Most existing FAHP approaches do not consider a human’s confidence in the estimates provided. This paper presents a model that gives weight to the constraints on domains of expert assessments as they are almost always supplied with certain degrees of confidence. Interval type-2 membership functions (IT2MF) along with the probability-theoretical procedure for comparison of intervals can be applied here as suitable modeling options. Empirical comparison of FAHP that makes use of triangular fuzzy numbers and IT2MF-based FAHP is also presented.