The Sound of Architecture

Acoustic atmospheres can be fleeting, elusive, or short-lived. Sometimes they are constant, but more often they change from one moment to the next, forming distinct impressions each time we visit certain places. Stable or dynamic, acoustic atmospheres have a powerful effect on our spatial experience, sometimes even more so than architecture itself. This book explores the acoustic atmospheres of diverse architectural environments, in terms of scale, function, location, or historic period—providing an overview of how acoustic atmospheres are created, perceived, experienced, and visualized. Contributors explore how sound and its atmospheres transform architecture and space. Their essays demonstrate that sound is a tangible element in the design and staging of atmospheres and that it should become a central part of the spatial explorations of architects, designers, and urban planners. The Sound of Architecture will be of interest to architectural historians, theorists, students, and practicing architects, who will discover how acoustic atmospheres can be created without complex and specialized engineering. It will also be of value to scholars working in the field of history of emotions, as it offers evocative descriptions of acoustic atmospheres from diverse cultures and time periods.

Do We See Scale?

In my final post I consider whether all our visual cues to scale function at the level of cognition rather than vision, and the kind of theory that ‘vision without scale’ would imply.

Fermatean fuzzy linguistic weighted averaging/geometric operators based on modified operational laws and their application in multiple attribute group decision-making

Fermatean fuzzy linguistic (FFL) set theory provides an efficient tool for modeling a higher level of uncertain and imprecise information, which cannot be represented using intuitionistic fuzzy linguistic (IFL)/Pythagorean fuzzy linguistic (PFL) sets. On the other hand, the linguistic scale function is the better way to consider the semantics of the linguistic terms during the evaluation process. In the present paper, we first define some new modified operational laws for Fermatean fuzzy linguistic numbers (FFLNs) based on linguistic scale function (LSF) to overcome the shortcomings of the existing operational laws and prove some important mathematical properties of them. Based on it, the work defines several new aggregation operators (AOs), namely, the FFL-weighted averaging (FFLWA) operator, the FFL-weighted geometric (FFLWG) operator, the FFL-ordered weighted averaging (FFLOWA) operator, the FFL-ordered weighted geometric (FFLOWG) operator, the FFL-hybrid averaging (FFLHA) operator and the FFL-hybrid geometric (FFLHG) operator under FFL environment. Several properties of these AOs are investigated in detail. Further, based on these operators, a multiple attribute group decision-making (MAGDM) approach with FFL information is developed. Finally, to illustrate the effectiveness of the present approach, a real-life supplier selection problem is presented where the evaluation information of the alternatives is given in terms of FFLNs.

A Certain Class of Relatively Equi-Statistical Fuzzy Approximation Theorems

The aim of this paper is to introduce the notions of relatively deferred Nörlund uniform statistical convergence as well as relatively deferred Norlund point-wise statistical convergence through the dierence operator of fractional order of fuzzy-number-valued sequence of functions, and a type of convergence which lies between aforesaid notions, namely, relatively deferred Nörlund equi-statistical convergence. Also, we investigate the inclusion relations among these aforesaidnotions. As an application point of view, we establish a fuzzy approximation (Korovkin-type) theorem by using our new notion of relatively deferred Norlund equi-statistical convergence and intimate that this result is a non-trivial generalization of several well-established fuzzy Korovkin-type theorems which were presented in earlier works. Moreover, we estimate the fuzzy rate of the relatively deferred Nörlund equi-statistical convergence involving a non-zero scale function by using the fuzzy modulus of continuity.

The reference ideal TOPSIS method for linguistic q-rung orthopair fuzzy decision making based on linguistic scale function

The linguistic q-rung orthopair fuzzy set is a powerful tool in representing linguistic assessments. Considering that the traditional decision making methods cannot deal with the situation that the best choice may not be the minimum or the maximum but between them, we propose an innovative TOPSIS method with linguistic q-rung orthopair fuzzy numbers based on the reference ideal theory. Firstly, the new operations of linguistic q-rung orthopair fuzzy sets are introduced based on the linguistic scale function. In addition, we propose the Minkowski distance measure of linguistic q-rung orthopair fuzzy numbers to make up for the defects of the existing distance measures based on the linguistic scale function. By using the new operations of linguistic q-rung orthopair fuzzy numbers, we propose the linguistic q-rung orthopair fuzzy weighted averaging operator and the linguistic q-rung orthopair fuzzy weighted geometric operator to aggregate linguistic decision information. Furthermore, we develop a reference ideal TOPSIS method to the linguistic q-rung orthopair fuzzy decision making problems. Finally, an example concerning the postgraduate entrance qualification assessment is given to illustrate the feasibility of the proposed method. Some comparative analysis is also given to show the efficiency of the method, in addition, the sensitivity analysis and stability analysis of the proposed method are also given.

Oxidation and electrical properties of chromium–iron alloys in a corrosive molten electrolyte environment

Chromium–iron (CrFe) binary alloys have recently been proposed to serve as the “inert” anode for molten oxide electrolysis (MOE). Herein, the effects of anodic polarization on physical and functional properties of CrFe anodes in the corrosive environment of MOE are studied via empirical observations and theoretical calculations. The findings indicate that the alloys form an inner chromia–alumina solid-solution covered by an MgCr2O4 spinel layer. A survey into the electrical properties of the detected oxides suggests that the layered oxide scale function as an efficient conductor of electricity at elevated temperature. The formation mechanism of the oxides is also investigated.