Evaluation and ranking of urban sustainability based on sustainability assessment by fuzzy evaluation model

Abstract

Urban sustainability can be considered as a part of sustainable development, which emphasizes the balance between three dimensions of environmental, economic, and social sustainability to improve human well-being and the quality of life. In this study, it was attempted to assess urban sustainability in the most critical, populous, and expanded district of Tehran (district 4) using sustainability assessment by fuzzy evaluation. For this purpose, 52 primary indices which were divided into 8 secondary components were employed. Among them, 18 indices for environmental issues were grouped into three secondary indices as E₁, to E₃, and 34 indices for economic–social and cultural issues were classified into five secondary indices as H₁ to H₅. The results revealed that 56% of the study area was potentially unsustainable and 44% of it had a medium sustainability in terms of environmental aspects. Furthermore, 65% of the study area had a medium human well-being sustainability and 35% of it was potentially unsustainable in terms of economic–social and cultural aspects. Finally, 45% of the study area was found unsuitable in terms of overall urban sustainability. The functional sample proposed in the present study can provide the directors and planners with the required information about the condition of sustainability in the most important district of Tehran.

Appendices

Appendix 1

Triangular membership function

$${\text{Triangular}}\left( {x;a,b,c} \right) \, = \left\{ {\begin{array}{*{20}l} 0 \hfill & {x < a} \hfill \\ {x - a} \hfill & {} \hfill \\ {-\!\!-} \hfill & {a \le x \le b} \hfill \\ {b - a} \hfill & {} \hfill \\ {c - x} \hfill & {} \hfill \\ {-\!\!-} \hfill & {b \le x \le c} \hfill \\ {c - b} \hfill & {} \hfill \\ 0 \hfill & {c \le x} \hfill \\ \end{array} } \right.$$

where a, b, and c represent the x coordinate for capital triangle; and x represents the real value (Crisp Value) from the private variable fuzzy universe of discourse. Function outputs ranging from 0 to 1 represent the value of the degree of membership of x. b with a value of 1 membership degree increases membership degree of the elements located between a and b closer to b element of, while the elements located between b and c have a considerably less membership degree closer to c element.

Appendix 2

Examples of the codes which used in the study:

The following figure shows that 49 rules were used to calculate OSUS.

Appendix 3

Examples of the rules:

• R₁ if ES is FL and HS is VL then OSUS is L

  $$\left( {0.33 \, \times \, 0 \, = \, 0} \right)$$

• R₂ if ES is L and HS is S then OSUS is FL

  $$\left( {0.16 \times \, 0.5 = 0.08} \right)$$

• R₃ if ES is S and HS is S then OSUS is I

  $$\left( {0.5 \times 0.5 = 0.25} \right)$$

• R₄ if ES is FL and HS is FH then OSUS is I

  $$\left( {0.33 \times 0.66 = 0.21} \right)$$

Considering the defuzzification formula:

$$\begin{aligned} {\text{OSUS}} & = 0.25 \times 0 + 0.375 \times 0.08 + 0.5 \\ & \quad \times \left( {0.25 + 0.21} \right) /0 + 0.08 + 0.46 = 0.481 \\ \end{aligned}$$