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In this paper we study some fuzzy order in fuzzy sets based on t-norm fuzzy arithmetic. The definition of the order comes from the extension principle for interval order: a > b iff a − b > 0 and from measurement sciences. In measurement sciences the order is given by a comparator whose operation is based on empirical determination of the difference of two input signals. Fuzzy comparison based on fuzzy sets subtraction is considered as an extension of substraction operation, namely a fuzzy set B is greater than a fuzzy set A if B − A is greater than zero in fuzzy arithmetic. In the paper we show that this fuzzy order is irreflexive, transitive, asymmetric and compact, subhomothetic, Archimedean and semi-Ferrers. Our idea refers to the work of M. K. Urbański (Modeling the measurement in algebraic fuzzy structures, Warsaw 2003, in polish) and to the fundamental problems in the measurement theory. [ABSTRACT FROM AUTHOR]

This article has been retracted: please see Elsevier Policy on Article Withdrawal (https://www.elsevier.com/about/policies/article-withdrawal). This article has been retracted at the request of the Editors-in-Chief after receiving a complaint about citation issues. The editors solicited further independent reviews which indicated that the statements in this paper substantially overlap with the PhD thesis of Z. Furdzik [O własnościach pewnych rozkładów przestrzeni topologicznych na iloczyny kartezjańskie, 1968 (unpublished, in Polish), Institute of Mathematics of the Polish Academy of Sciences, Warsaw], without proper citation. [ABSTRACT FROM AUTHOR]

This article has been retracted: please see Elsevier Policy on Article Withdrawal (https://www.elsevier.com/about/policies/article-withdrawal). This article has been retracted at the request of the Editors-in-Chief after receiving a complaint about citation issues. The editors solicited further independent reviews which indicated that the statements in this paper substantially overlap with the PhD thesis of Z. Furdzik [O własnościach pewnych rozkładów przestrzeni topologicznych na iloczyny kartezjańskie, 1968 (unpublished, in Polish), Institute of Mathematics of the Polish Academy of Sciences, Warsaw], without proper citation. [ABSTRACT FROM AUTHOR]

• Comparison of the Polish and Ukrainian models of metropolis management • Delimitation of the Warsaw metropolis • Problems of the development of the Warsaw metropolis • Historical difficulties in the development of the Lviv metropolis [ABSTRACT FROM AUTHOR]

• The user experience varies according the urban context of the station. • The users felt more comfortable while using less centrally located stations. • Liveable environment around the station increased users' safety. • Legible layout of the concourse level should be a priority in architectural design. Underground spaces have emerged as a promising solution for enhancing the overall quality of life in cities by allowing for better land use, reducing noise, and improving air quality. However, the subterranean placement of non-infrastructure facilities gives rise to numerous apprehensions, predominantly concerning the experience of their users. The underground environment may evoke fears and anxieties, disrupt cognitive and physiological responses, and affect personal safety. This paper examines the extent to which the specific spatial characteristics of underground non-transfer metro stations influence the passenger experience measured by the subjective indicators of comfort and safety. The research combines survey data collected from 1400 users with spatial data obtained from space syntax analyses and field investigations of 28 underground metro stations in Warsaw, Poland. Based on the results of multiple regression analysis, a set of spatial features that affect user comfort and safety was identified. The results show that passengers' experience is shaped by several architectural characteristics of metro 'stations, as well as their accessibility and position in the city and neighbourhood. Among the most influential architectural features is the configuration of the concourse level followed by the geometry of the platform hall and the use of art elements. Based on the findings presented in the study, potential design strategies that could improve the user experience are proposed and discussed. The recommended approaches offer valuable insights for designers aiming to improve the existing metro stations and facilitate more effective designs for new underground facilities. [ABSTRACT FROM AUTHOR]