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Master Thesis


İstanbul Technical University

Institute of Science and Technology

Thesis (M.Sc.)
Defense Date: 20 July 2020

Thesis Advisor: Dr. Michael S. BITTERMANN

Defense Jury: Prof.Dr. Meryam Birgül ÇolakoğluProf.Dr. Arzu Gönenç Sorguç 


National Congress by Oscar Niemayer, 1962, Brazil (photographed by Marcel Gautherot)

Understanding Shape Preferences in Architectural Design

Through Evolutionary Computation


Architecture arouses our feelings. Anything, colors, lights, scales, and shapes we perceive by our senses, causes a cognitive process and results in a feeling. One of our senses, the vision is a major source of information in our comprehension of the built environment. Visual perception involves excessive series of actions between our eyes and brain. Despite little is known about what visual perception exactly is, this complex physical process plays a big role while producing aesthetic experience of a design. This experience doesn’t involve reasoning; it arises only from the act of visually perceiving the object. As a designer’s task, providing such perception qualities, aesthetic experience is a subject in design fields. The general goal in design applications is to choose the shape and material for the object in such a way that the product is desirable by its perceivers/users. Here, we can distinguish two kinds of desirable properties of a product. One kind is the fulfillment of a utilitarian purpose. Another kind is the aesthetical pleasure, which arises solely from the act of visually perceiving the object. Commonly, designers are having difficulty expressing the rationale behind this pleasure because defining the visual pleasantness of a shape is a linguistic concept with associated imprecision and uncertainty. It is a form of qualitative evaluation. The study aims to devise a computational method to get to know the rationale that underlies certain shape preferences.

The method consists of four steps: abstracting the physical attributes of the shape (1); aggregating several attributes to characterize the shape in more general terms (2); tuning the representation of the shape character based on the preference data; and a identification of preferences (4). The suitability of this method is verified by applying it to a shell shape.

The first step of the model is the abstraction. In the context of shape analysis, it refers to extracting relevant information of a shape. Abstractions of a shape can be classified as marginal abstractions and essential abstractions. Marginal abstractions specify detailed qualities of the shape, they define its geometric properties directly relevant for its physical realization such as its width, depth, and height. And essential abstractions specify the general qualities of the shape, such as its symmetry, asymmetry, verticality. In the study, a shell type of shape is treated, which has got three support locations and is formed only with three curves. The reason behind this selection is to have simplicity in the explanation and to trace the relationships among them easier. Architectural shapes are generally defined by means of two planes, the vertical plane and horizontal plane. As a first step, the physical attributes of the exemplary shape are analyzed with respect to these planes.


The basic shape elements are the boundary curves, which give the salient character to the overall shape. The base for the shape is a triangle, the vertices of which A, B and CA and B points have constant coordinates and point C is the only variable determining the triangularity of the plan character. Contour of the shape is formed by three curves and three-line segments between support points. The curves are controlled with control points P1P2, and P3. The locations of the control points determine the symmetry and the rotation angles of them- the verticality and the heights of the curves, the height relations.

When the physical attribute of a shape is exactly matching to the prototypical, then the linguistic label certainly applies to the shape. For instance, a triangle with all angles of exactly 60 degree, is an equilateral triangle. When one of the angles deviates slightly from 60 degree then the linguistic label does not vanish abruptly, but gradually. For example, the triangle in the figure has still an equilateral character to some extent. This is a common experience in shape description and it applies in the interpretation of diverse shape attributes in linguistic terms. In this study, the shape descriptions are represented by fuzzy sets. A fuzzy membership function expresses the association strength of a linguistic label. It associates a number between zero and unity which is referred to as a membership degree of the object.

Screen Shot 2021-02-20 at 22.46.12.png

In the study, in total 17 fuzzy membership functions are used for the representation of the physical attributes of the shape. Each membership function shape is determined in two steps. First step, based on a general notion about the property, shape of the function is selected. Then, the function parameters are optimized with the data obtained by the survey. Although the fuzziness of the concepts, results of the judgments are highly consistent with each other.


This data is used to identify the shape parameters of the membership functions through curve fitting. In this way, an ontology of the basic shape features is established. Every object has a fuzzy membership degree in each of the fuzzy membership functions. Now we can examine membership degrees of the exemplary shape in detail. Degree of the membership depends on the detailed qualities of the object. You can notice that there is an aggregated condition having similar height relation which depends on the three differences between the curves. Each difference should close to be zero at the same time. And similar condition is having an equilateral floor plan which depends on not only one angle but three angles, with the condition that all three are nearly 60 degree. Now let's see how such aggregated conditions are represented in the study.

The second step of the model is the aggregation. To define the overall character of the shape, the physical attributes described previously are aggregated. Four conditions of symmetry are distinguished: all symmetry, two symmetry, two asymmetry, all asymmetry. Six verticality conditions are distinguished: all overhang, all vertical, all recessed, two overhangs, two vertical, two recessed. Three height relation conditions are distinguished: all the three curves have similar heights, their heights are gradually changing, they have heights that are different in a diverse manner. Four triangularity conditions of floor plan are distinguished: an equilateral, an isosceles triangle with one pointed corner, a right-angled, a skewed obtuse.

The third step of the model is tuning the representation of the shape character based on the preference data. The representation is accomplished by fuzzy neural tree  (FNT) which is a neural computing method introduced by Bittermann and Çiftçioğlu in their article "A fuzzy neural tree based on likelihood". This tuning step of the model includes the representation of shape character by FNT and shape properties as FNT neurons, the two criteria in the representation of understanding and the use of evolutionary multi-objective optimization, and finally an exemplary FNT model identification of preference. In the context of modeling shape preferences by FNT, general qualities of the shape represented in fuzzy sets and they are the inputs of the tree. The membership degrees of them are used in the ensuing logic computations to obtain the essential shape properties. The detailed properties of shape are symmetry, verticality and height relations in vertical sense and triangularity in horizontal sense.  


There are four types of symmetry conditions, depending on the control point locations (X3X4,  X5) and six types of verticality conditions, depending on the control point verticality degrees (X5X6,  X7) of the shape. All symmetry condition is computed by using FNT AND operation of all the three curves’ symmetry membership degrees. Two symmetry condition is also computed by using AND operation of the two curves’ symmetry membership degrees. Because only when the two curves which have similar edge lengths, are symmetric, then axiality arises Otherwise plan character dominates the overall character of the shape, and symmetry cannot be observed. These computations are exactly the same for asymmetry and verticality conditions. There are three types of height relation conditions, depending on the curve heights (h1h2,  h3) All the conditions are computed using AND operation as all three curves’ height have an affect on the type of the relationship among the curves. There are four types of triangular character conditions, depending on the interior angles of the triangle. Equilateral is computed by calculating the distance of each interior angle to the 60 degree. Isosceles&pointy is computed by calculating two things, one is the difference between two base angles and other is the magnitude of the vertex angle. The computation of the right angled does not require a logic operation, since it is directly given by the membership degree of that angle among the three angles of the triangle that is closest to 90 degree. Clearly, the values of the other two angles are dependent on the former so that their evaluations are superfluous in this context of right angled-ness. This computation is exactly the same for being obtuse-skewed. The representation of shape character is achieved by 17 property conditions in total and any shell shape, generated with the defined parameters, satisfies each of the conditions by some degree.

FNT draft@2x (3).png

Fourth step of the model is the identification of preferences. Till here, we've established the basic shape descriptors that different designers can agree with. However, different designers can have different aesthetic preferences depending on particular characteristics of a shape. Commonly designers are having difficulty pinpointing the rationale behind these preferences. Because aesthetical inclinations are loosely related to rationality. And the manifestation instances of the individual are required. (In this study, the individual is me selected 10 samples among 50 randomly generated samples.) As shape character involves multiple basic shape properties, the simultaneous presence of a specific set of properties is more desirable than another one. Understanding the shape preference of an individual is finding the pattern of properties that best corresponds to the preference.

An FNT model represents a possible explanation for the specific set of properties. The number of possible explanations for a preference is large, because there are multiple conditions in the properties. And, most importantly, the relative importance among four properties is not to assume for an individual. Each gets a weight between 0 and 1. To find the particular FNT model that best represents the preferences, evolutionary algorithm is used. The algorithm searches in the space of possible FNT models.

In machine learning, in general, the aim is to model data by minimizing the model error. However, in representing understanding, there is a second aim playing a role next to this. The second aim is that the description is of utmost meaningful. In the context of shape preference, meaningful-ness is having the set of four shape properties as completely as possible in the description namely symmetry, verticality, height relations, and triangularity. The two modeling criteria, minimizing the model error, namely maximizing accuracy of the model and maximizing the expressiveness of the representation of the shape character are conflicting. That’s why an evolutionary multi-objective optimization algorithm is used to identify the model representing in the best way the preferences of an individual. In this modeling context, the attribute ‘best’ refers to the model being accurate as well as expressive.


Representation of

shape character



The algorithm is run multiple times until as many as possible among the preferred designs are represented. Multiple runs are necessary because different patterns of preferences have been applied by the architect so that a single FNT model does not represent all of the preferred solutions. With different possible combinations of property conditions and with a different possible degree of memberships, a variety of shape characters appeared. The identification process reveals that there are four patterns of preferences applied by the architect. Thus, there are four different resulting FNT models explaining the preferences. Among four different trees, the first tree can be considered as the most important one as it represents four of the ten preferred samples. It seems that the architect likes the shapes which have the character of two asymmetry, two overhang, similar height relation, and isosceles&pointy floor plan. This tree can be considered as the model of the aesthetic preference of the architect. And finally, it can be used to understand the preference for any shape. When we put any shape to this model, the magnitude at the FNT output predicts the likelihood that the architect will prefer the shape.


The benefit of attaining the understanding of preferences by computation is that then the preferences become subject to satisfaction in extreme form by a systematic search. A second benefit is that aesthetics related objectives become compatible with non-aesthetic related ones so that the best compromise is found taking the aesthetic preference duly into account.

Outcomes of the study can be listed as follows: 


  1. Understanding preferences has been a persistent problematic issue due to the precise description of soft objectives, in architectural design research.

  2. The shape preferences are subject to transparent computational representation. The study goes beyond merely representing the preference by using computation as a mere mathematical tool; but yielding insight into the ‘understanding’ of cognitive process of aesthetic preference.

  3. The method is fuzzy neural tree combined with multi-objective evolutionary algorithm.  Due to the nature of the method, soft design knowledge is elicited without sacrificing interpretability. (In contrast to pattern recognition which is done by black box style machine learning, such as artificial neural network, we emulate understanding which is by definition in an explicit and linguistic form.)

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