a fuzzy-based approach for evaluating existing spatial...

A Fuzzy-Based Approach for Evaluating Existing SpatialLayout Configurations

Ayman Assem1, Sherif Abdelmohsen2, Mohamed Ezzeldin31,3Ain Shams University 2American University in Cairo; Ain Shams University1,3{ayman.assem|mohamed.ezzeldin}@eng.asu.edu.eg [email protected]

This paper proposes a fuzzy-based approach for the automated evaluation ofspatial layout configurations. Our objective is to evaluate soft and interdependentdesign qualities (such as connectedness, enclosure, spaciousness, continuity,adjacency, etc.), to satisfy multiple and mutually inclusive criteria, and to accountfor all potential and logical solutions without discarding preferable, likely oreven less likely possible solutions. Using fuzzyTECH, a fuzzy logic softwaredevelopment tool, we devise all possible spatial relation inputs affecting physicaland non-physical outputs for a given space using descriptive rule blocks. Weimplement this fuzzy logic system on an existing residential space to evaluatedifferent layout alternatives. We define all linguistic input variables, outputvariables, and fuzzy sets, and present space-space relations using membershipfunctions. We use the resulting database of fuzzy agents to evaluate the design ofthe existing residential spaces.

Keywords: Fuzzy logic, Space layout planning, Heuristic methods

INTRODUCTIONSeveral approaches have been proposed for evalu-ating and generating spatial layout configurations,including graph theory, quadratic assignment prob-lems, slicing tree, space filling curves, genetic al-gorithms, and evolutionary approaches (Dunker etal., 2003; El-Baz, 2004; Aiello et al., 2012; Buscheret al., 2012). Heuristic methods to address spacelayout planning problems and allocation of objectswithin spatial configurations have been developedwithin several engineering disciplines and includegreedy algorithms, branch and bound methods,dynamic programming, and single-solution meta-heuristic methods such as tabu search (Ahuja et al.

2000; Xie and Sahinidis, 2008; Abdinnour-Helm &Hadley 2000; Merrell et al., 2011; Yu et al., 2011; Ab-delmohsen et al., 2017).

These approaches mostly involved comput-ing distances between spatial configurations us-ing graph algorithms and genetic algorithms, thehierarchical organization of layout elements, andmulti-level space allocation using hybrid evolution-ary techniques. Qualitative aspects of spatial con-figurations, however, related to ambiguities of spaceuse and occupational behavior, ill-defined layoutdesign and spatial uncertainty remain relatively un-addressed. Fuzzy logic systems have recently beenproposed to address ambiguity in architectural de-

Design - ARTIFICIAL INTELLIGENCE - Volume 2 - eCAADe 37 / SIGraDi 23 | 35

sign approaches and requirements, and specificallyin managing uncertainty and soft qualities in spatiallayout design (Ciftcioglu & Durmisevic, 2001; Çek-mis, 2014; Çekmis, 2016). Most of these proposalsattempted to address spatial layout design from anoccupancy-centered perspective, where possibilitiesof occupancy are identified in ambiguously definedspaces or usage patterns, especially in open plandesigns.

This paper proposes a fuzzy-based approach forthe automated evaluation of spatial layout configu-rations by conducting an analysis of spatial param-eters and identifying the nature of spatial relationsusing fuzzy logic. Our heuristic approach involvesanalyzing spatial characteristics and space-space re-lations to assess soft qualities such as connected-ness, spaciousness, convenience of access, continu-ity, adjacency, etc. for a given layout scheme. Weidentify rulesets for logical configurations based onthese relations. We put forward that the resultingrange of possible configurations satisfy an intuitiveprocess without the need for an exhaustive searchthrough all possible solutions, but simultaneously in-clude partially true assumptions and solutions thatreflect how architects would perceive given spatialconfigurations based on intuitive logic.

SPATIAL RELATIONS AND FUZZY LOGICTraditional scenarios of space layout planning in-volve defining preset holistic notions of relations be-tween spaces that dictate their adjacency and con-figuration logic. For example, a “strong” or “weak” re-lationship between two spaces is roughly defined inconventional spatial relation matrix diagrams basedon universal understandings of connectivity, adja-cency, proximity and visibility. These relationshipsare typically defined generically and may discard (a)a wide spectrum of parameters and variables that af-fect spatial relations, (b) detailed relations betweeninput spatial parameters and spatial relation outputs,and (c) the inclusionof partially true solutions for spa-tial configurations.

In this context, our approach deals with soft

computing methodologies (Ciftcioglu & Durmisevic,2001; Bittermann, 2009). Rather than well defineddesign issues, our approach is more concerned with(a) the understanding and evaluation of soft andhighly interdependent aspects of design, (b) the sat-isfaction of multiple and mutually inclusive criteriasimultaneously including functional, aesthetic, envi-ronmental, and spatial issues, and (c) the considera-tion of both technical and non-technical aspects ofdesign, such as visibility, intimacy, adjacency, con-nectedness, enclosure, spaciousness and accessibil-ity, (d) accounting for all potential and logical designsolutions and alternatives that encompass a wide va-riety of parameters, without discarding preferable,likely or even less likely possible solutions.

Fuzzy logic approaches are based, as opposed toclassical two-valued logic that assumes only true orfalse propositions, on propositions that may be bothpartially true and partially false (Figure 1).

Figure 1Difference betweenclassical and fuzzyspatial relationinput variables(Top: Classical set,Bottom: Spatialrelation inputvariables usingfuzzy curves)

36 | eCAADe 37 / SIGraDi 23 - Design - ARTIFICIAL INTELLIGENCE - Volume 2

The classical set demonstrates one and only truthvalue for a finite number of logical variables. In fuzzylogic however, input variables are passed into thefuzzy logic system as a fuzzy variable, presented asa vector of membership degrees, as they stem origi-nally fromaqualitativeor linguistic source. TheX-axisrepresents alternatives of the factor under study; forexample, proximity, while the Y-axis represents thefuzzy degree which lies between 0 and 1. For exam-ple, point a in the figure represents the highest de-sired value of the fuzzy curve, while (0,0) and (10,0)represent the lowest. All other points represent val-ues that are desired and not desired at the same timewith varying degrees (e.g. point b in the figure lieson the curvewhere the value is 50%desired and 50%undesired simultaneously).

APPROACHWe propose a fuzzy logic approach whereby spatialinputs (e.g. space area, spaceproportion, viewing an-gles, sum of openings per space, etc.) that affect spe-cific outputs (e.g. adjacency, spaciousness, connect-edness, etc.) are identified for a given space. Basedon the fuzzy curves for each of the input variables,we devise a rule block which comprises the controlstrategy of the fuzzy logic system and linguisticallydefines the relation between inputs and outputs asif-then equations. These equations describe the sit-uation for which the rules are designed and the re-sponse of the fuzzy system for that specific situation,as shown in Figure 2. Consequently, a finite yet ex-tensive set of specific relations can be identified foreach of the descriptive outputs that contribute to theevaluation of physical and non-physical attributes ofa given space. Using fuzzyTECH, a software develop-ment tool for fuzzy logic and neural-fuzzy solutions,we devise all possible spatial relation inputs affectingphysical and non-physical outputs for a given spaceusing descriptive rule blocks, describing the fuzzifi-cation and defuzzification processes. As a case study,we implement this fuzzy logic system on an existingresidential space to evaluate spatial layout configura-tion alternatives. We define some space-space rela-

tions and present these relations using fuzzy curves.We define all linguistic input variables, output vari-ables, and fuzzy sets (e.g. high, medium, low).

Figure 2Example of usingfuzzy rules incontrolling therelation betweenspatial inputs andoutput By specifying the influence of input variables on the

output variable (Figure 3), the rule blockwizard in thesoftware uses this data to determine the necessaryrulesets in (If-Then) equation format. We use the re-sulting database of fuzzy agents to evaluate the de-sign of the existing residential building.

Figure 3The influence of aspatial relationinput variable on anoutput variable

In the sections below, we introduce operational def-initions and notations for space entities, and a de-tailed account of the proposed spatial relation inputsand outputs, and the fuzzy logic inference flow frominput variables to output variables using rule blockscontaining the linguistic control rules.

Definition of Space EntitiesIn order to introduce the spatial relation inputs andoutputs, we present first some basic definitions andnotations for spatial entities and their variableswhichare seen to informspace-space relations in the fuzzifi-cation and defuzzification process. For a given space(Sn), we identified the following sets of entities andtheir notations, as shown in Figure 4:

Set 1: SpaceDimensions andBoundaries: This in-cludes basic “SpaceDimensions” (X_Sn, Y_Sn), “SpaceArea” (A_Sn), “Center of Space” (C_Sn), “Corner Pointof Space” (CRn_Sn), “SpaceWall” (Wn_Sn), “FreeWall”(or external wall) (FWn_Sn), and “Viewing Angle fromCenter of Space” towards the exterior (CAn_Sn).


Figure 4Definition of spaceentities

Set 2: Door Openings and Relations: This includes“Door Opening of Space” (SnDn), “Door OpeningPoints” (Pn_SnDn) denoting the start and end pointsfor agivendooropening, “DoorOpeningCenter” (C_-SnDn), “Door Wall Part” (WPn_SnDn) which denotesthe remainingwall segment in a doorwall, and “Door

Visible Area” (VA_SnDn) which denotes the area inspace visible through a given door opening.

Set 3: Window Openings and Relations: Thisincludes “Window Opening of Space” (SnOn), “Win-dow Opening Points” (Pn_SnOn) denoting the startand end points for a given window opening, “Win-dow Opening Center” (C_SnOn), “Window Wall Part”(WPn_SnOn) which denotes the remaining wall seg-ment in a window wall, and “Window Visible Area”(VA_SnOn) which denotes the area in space visiblethrough a given window opening.

Spatial InputsBased on the space entity definitions above, we de-veloped 16 linguistic variables for spatial inputs andtheir fuzzy sets and membership functions to initi-ate the fuzzification process. Different combinationsof these inputs formulate rule blocks for defining avariety of spatial outputs for any given spatial lay-out configuration. Table 1 illustrates the codes devel-oped for these inputs, their basic definition, calcula-tion method, unit, and fuzzy sets or descriptors.

The spatial inputs IN01_Area_Sn, IN02_Propor-tion, and IN03_Number_FWn compute the area, pro-portion of space dimensions, and number of freewalls per space respectively. Inputs IN04_Length_-SnDn and IN05_Ratio_SnDn compute the length of agiven door opening and its percentage in relation towall lengths per space. Inputs IN06_Sum_SnOn andIN07_Ratio_SnOn compute the total window open-ing lengths and their percentage in relation to to-tal wall lengths per space. Inputs IN08_Ratio_VA_-SnDn and IN09_Ratio_VA_SnOn compute the ratio ofdoor and window visible area per space respectively,whereas IN10_Sum_CAn_Sn computes the total an-gle of viewing from the center of a given space.

Inputs IN11_Length_CenterToDoorVector andIN12_Angle_CenterToDoorVector compute the dis-tances and angles of the internal space vectorsfrom center of space to door, while inputs IN13_-Length_SpaceToSpaceVector and IN14_Angle_Space-ToSpaceVector compute the distances and anglesof the external vectors from space door to space


Table 1Variables of spatialinputs

door. Inputs IN15_Length_SRN and IN16_Length_-SRF compute averages of the distances between thetwo nearest and farthest vectors between spaces,calculated from space corner points.

For each of the linguistic variables, we identifieda set of descriptors or fuzzy sets (for example: low,medium, and high descriptors for space area; narrow,regular, andwide descriptors for door lengths; squar-ish, rectangular, and linear configuration descriptorsfor space proportion, etc.). Each of these descrip-tors describes the spatial input more or less well de-pending on the computed measurement or dimen-sion. Each descriptor is defined by a membershipfunction which highlights the associated degree ofmembershipof the linguistic term for anyvalueof thespatial input variable. The membership functions ofall descriptors for one linguistic variable are typicallyshown in one collective graph. The graph in Figure5 plots the membership functions of the descriptorsfor the variable IN02_Proportion, and Table 2 displaysthe definition points for each of the descriptors.

Figure 5Membershipfunction graph forspatial input“IN02_Proportion”

Table 2Definition points ofmembershipfunction for spatialinput“IN02_Proportion”

Spatial OutputsWe identified 10 linguistic variables for spatial out-puts and their fuzzy sets and membership functionsfor the defuzzification process. Table 3 illustrates thecodes developed for these outputs, their basic defi-nition, unit, and fuzzy sets or descriptors. The 10 lin-guistic variables target primarily two sets of outputs:1) outputs that describe individual space character-istics, including spaciousness, openness, intimacy,continuity, directionality, and enclosure, and 2) out-puts that describe space-space relations, includingadjacency, visibility, convenience of access, and con-nectedness.


Table 3Variables for spatialoutputs

Regarding the first set of outputs which describeindividual space characteristics, OUT01_Spacious de-notes the degree of abundance and sufficiency ofroom per space; how spacious it is. OUT02_Opennessdenotes the degree of exposure of space to externalviewing and the outdoor environment. OUT03_In-timacy denotes the degree of privacy and intimatescale of space. OUT04_Continuity denotes the de-gree of free and unobstructed flow within a givenspace, both physically and visually. OUT05_Direction-ality denotes the basic orientation and configurationof space in terms of prevailing circulation and pro-portionality. OUT06_Enclosure denotes the degreeof physical or virtual boundedness and sense of en-closure of space. As for the second set of outputswhich describe space-space relations, OUT07_Adja-cency indicates the degree of proximity and immedi-acy of space connection toother neighboring spaces.OUT08_Visibility indicates the degree of visual accessand viewing from one space to another. OUT09_-AccessConv indicates the degree and level of conve-nience and comfort of physical accessibility fromonespace to another. OUT10_Connectedness indicatesthe degree of physical connectivity and linkage ofone space to multiple spaces.

For each of the linguistic variables of these spa-tial outputs, we identified a set of descriptors or fuzzysets (e.g. low, medium, high for spaciousness; mini-mal, partial, maximum for enclosure; poor, average,

strong for connectedness; weak, regular, strong forvisibility and adjacency, etc.). Each descriptor is de-finedby amembership functionwhich highlights theassociated degree of membership of the linguisticterm for any value of the spatial output variable. Thegraph in Figure 6 plots the membership functions ofthe descriptors for the variable IN02_Proportion, andTable 4 displays the definition points for each of thedescriptors.

Figure 6Membershipfunction graph forspatial output“OUT06_Enclosure”

Table 4Definition points ofmembershipfunction for spatialoutput“OUT06_Enclosure”Rule Blocks

We identified 10 rule blocks for the proposed fuzzylogic system, whereby different combinations of spa-tial inputs contribute to the degree of satisfactionof a given spatial output. For example, for RuleBlock 09 (RB09_AccessConv), as shown in Figure 7,if the descriptor for the input ”IN13_Length_Space-


ToSpaceVector“, which describes the length of thevector between the door centers for any two givenspaces, is ”Near“, and the descriptor for the input”IN14_Angle_SpaceToSpaceVector“, which describesthe angle of that vector, is ”Direct“, then the descrip-tor for the output ”OUT09_AccessConv“, which de-scribes the degree of physical accessibility betweenthose two spaces, is ”High“. By contrast, if the descrip-tor for the input ”IN13_Length_SpaceToSpaceVector“is ”Far“, and that of the input ”IN14_Angle_Space-ToSpaceVector“ is ”Indirect“, then the descriptor forthe output ”OUT09_AccessConv“ is ”Low”.

These are however not the only two possiblecombinations indicating a comprehensive evalua-tion of the degree of physical accessibility betweenthose two spaces. Other possibilities include com-binations of “Near”, “Regular” and “Far” fuzzy setsor descriptors for the first spatial input and “Direct”and “Indirect” fuzzy sets for the second spatial in-put, which yield varying results for the “AccessConve-nience” output, including “High”, “Medium” or “Low”degrees.

For this specific rule block, 2 spatial inputs(IN13_Length_SpaceToSpaceVector and IN14_Angle_-SpaceToSpaceVector) were identified for 1 spatial out-put (OUT09_AccessConv), with 6 rules describing thedifferent conditions for evaluating the degree of ac-cess convenience. This typically varies for each ruleblock, depending on the number of involved spatialinputs, number and nature of descriptors, and theunderlying rule controlling the relation between thespatial input(s) and spatial output.

The overall structure of the fuzzy logic systemin its entirety is composed of 16 input variables, 10output variables, 10 rule blocks that control the re-lations between spatial input and output variables,2343 rules, and 79 membership functions. Figure 8illustrates the overall structure of the proposed fuzzylogic system, and how the combinations of differentspatial inputs formulate the final 10 spatial outputsusing the developed rule blocks.

Figure 7RB09_AccessConv:Rule block forcontrolling therelation betweeninputs 13 &14 andOutput 09

Figure 8Overall structure ofproposed fuzzylogic system


CASE STUDYWe introduce two cases that involve two residentialspaces in close proximity and are connected througha circulation space, as shown in Figure 9. The twocases vary slightly in terms of their geometric config-uration, area, space proportion, and door-to-door lo-cation. For each of the cases, we identified the basicspace entity definitions (following the definitions de-veloped earlier in Figure 4), including space area, ra-tio, center of space, corners of space, number of freewalls, door opening length, door wall part length,door opening center, door opening points, windowopening length, window wall part length, windowopening center, window opening points, door visi-ble area, space 01 center to space 02 center relations(including 3 vector lengths and angles), viewing an-gles from the centers of both spaces, and the spa-tial network relations between the two spaces com-puted from their corners, including the nearest vec-tors (SRN) and farthest vectors (SRF).

Figure 9Case studyinvolving twospatialconfiguration cases

To initiate the fuzzification process, we computedall 16 spatial input parameters for both cases using

Grasshopper, including space area and proportion,number of free walls, length and ratio of door open-ings, sum and ratio of window openings, ratio ofdoor andwindow visible area, sum of viewing anglesfromcenters of both spaces, internal andexternal dis-tances and angles of space-space vectors, and the av-erage lengths of the nearest and farthest vectors be-tween both spaces, computed from their corners. Ta-ble 5 shows the computedvalues for spatial inputs forboth cases.

Table 5Computed valuesfor spatial inputs forthe two residentialcases (fuzzification)

Using the fuzzyTECH fuzzy logic software, we usedthe developed rule block logic to translate the dif-ferent spatial inputs and their fuzzy sets into the 10spatial outputs, thereby resulting in an automatedevaluation of the degrees of spaciousness, openness,intimacy, continuity, directionality, enclosure, adja-cency, visibility, convenience of access, and connect-edness for both cases, as shown in Table 6.

The results of the automated evaluation of thetwo spatial configuration cases demonstrate inter-esting findings. As shown in the table, subtle varia-tions in the shape geometry of the two spaces canresult in large discrepancies in the output variables.For example, the degree of visibility for case 1 wasrecorded at 93%, as opposed to 7% in case 2. Trac-ing this output back to its spatial input constituents,two main spatial inputs are shown to affect the de-gree of visibility: (1) IN04_Length_DoorOpenings and(2) IN08_Ratio_DoorVisibleArea. While thedooropen-ing length remains the same in both cases (at 1.10m),


the computed value for the door visible areawas 0.84for case 1 and 0.07 for case 2.

Table 6Results ofautomatedevaluation ofspatial outputs(defuzzification)

Other revealing findings are related to the interestingdichotomies that can be deduced from such a resultfor the two cases, for example the degree of open-ness (50% - 16%) versus the degree of enclosure (50%- 50%), the degree of spaciousness (36% - 53%) ver-sus the degree of intimacy (52% - 50%), the degree ofcontinuity (63% -87%)versus thedegreeofdirection-ality (31% - 56%), the degree of spaciousness (36% -53%) versus the degree of openness (50% - 16%). Onthe other hand, some values are in close correlation,such as the degree of convenience of access (88% -37%), the degree of adjacency (82% - 36%), and thedegree of connectedness (88% - 40%). These results,involving both the seemingly contradicting and thecorrelating, only corroborate the assumption of thisresearch, where spatial relations cannot be evaluated

in their totality asmerely “strong” or “weak” relations,but are rather far more nuanced and involve a widerangeof attributes that aremore telling about thena-ture of spatial relations and configuration logic.

DISCUSSION AND FUTUREWORKThis paper introduced a fuzzy logic system for the au-tomated evaluation of soft qualities of spatial con-figurations, including individual space characteristicsand space-space relations. The findings of the paperconfirm the initial assumption related to spatial am-biguity and uncertainty, where conventional spatialrelation matrix diagrams tend to describe those re-lations in a holistic fashion as “strong” or “weak” re-lations, while discarding many of the nuances asso-ciated with soft qualities of space, such as spacious-ness, intimacy, openness, enclosure, connectedness,etc. The paper attempted to evaluate these qualitiesby providing a detailed account of space entity def-initions, calculation methods for spatial inputs, anddevising rule blocks to address spatial outputs thattake into account complex combinations of thesespatial inputs and their fuzzy sets or descriptors.

The findings of this paper only open the door forextensive research in several areas pertaining to theautomated evaluation of spatial configurations. Oneof the limitations of this research pertains to buildingtypology. The discussed cases were relatively simpleand arbitrary residential spaces. Other building ty-pologies and spaces have their complexities and willaffect the nature and understanding of the describedoutputs and rule blocks, and hence the nature of theevaluation process itself. Scale is also a significantfactor and potential. The relations described in thispaper, although demonstrated in the context of twosimple residential rooms, can be applied in principleto different scales, levels of detail, and relations, in-cluding but not limited to furniture layout schemesin different spatial typologies, departmental spacesand zones, vertically stacked spaces in building con-figurations, urban neighborhoods and clusters, etc.This opens the door for studying a larger and morecomplex set of relations than only space-space re-


lations, but also involves space-object and object-object relations, and for evaluating alternative de-sign schemes at different levels of detail, ranging inessence from rooms to cities.

Another significant and influential limitationper-tains to relying solely on two-dimensional spatialconfigurations. Incorporating 3-dimensional andvolumetric data for space layout configurations willdefinitely extend to include a larger dataset and be-come more inclusive and accurate when it comes todescribe soft qualities such as spaciousness, enclo-sure, visibility, and the like. Further work is needsin this area to enhance the fuzzification process forinclusion of such dimensions. The studied geome-tries in this paper were also of average complexity,involving simple and primitive geometrical shapes,and basic orthogonal configurations. Geometricalcomplexity is yet another factor thatwill need furtherresearch, andwill help refine and revisit the space en-tity definitions developed in this paper.

This paper has also focused in principle on phys-ical qualities of space and relatively quantifiable at-tributes that can be tangibly reduced to geometricalentities. More research should focus on non-physicalattributes, or non-physical components in the evalu-ation of soft qualities in space layout configurations,wherenotions suchasperceptionandexperiencebe-come incorporated into the understanding of seem-ingly mere physical qualities such as visibility, open-ness, continuity, intimacy, etc. Other dimensionssuch as light, material, texture, color, and the incor-poration of environmental aspects should contributeto such an area of research.

As a long-term goal, findings from this researchand future studies should eventually address gener-ative aspects of design, where results of evaluatingspatial layouts should inform architects with a moreinclusive design process that includes partially trueassumptions and solutions based on intuitive logic.

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