An Analytic Framework for Social Life Cycle Impact Assessment- Part1:Methodology

electronic supplementary material

Societal LCA

An analytic framework for social life cycle impact assessment- part1:methodology

Sheng-Wen Wang1 • Chia-Wei Hsu2,3 • Allen H. Hu1

Received: 6 May 2014 / Accepted: 6 April 2016

Responsible editor: Marzia Traverso

1Institute of Environmental Engineering and Management, National Taipei University of Technology, Taipei, Taiwan

2Department of Travel and Eco-tourism, Tungnan University, New Taipei City, Taiwan

3Department of Business Administration, National Central University, Taoyuan, Taiwan

Chia-Wei Hsu

Allen H. Hu

This study applies the CFPR method to determine the relative weights of thesubcategories and indicators forSLCIA method. Several calculation stepsand concepts are essential, as explained below (Hsu et al. 2012).

(1) Construct pairwise comparison matrices among the attributes (i = 1, 2, , n).

Following this step, the evaluators (k = 1, 2, , m) are asked which of the two adjoining criteria is better for a set of n1 preference values {, , , }, such as

where denotes the preference intensity toward attributes iand jassessed by the kth evaluator, =1indicates the indifference between attributes iand j, = 3, 5, 7,9 shows that attribute iis better than attribute jto the degree of semantics, and = , , , indicates that attribute iis worse than attribute jto the degree of semantics.

The sign “” indicates that the evaluators do not provide any preference information on the remaining, which can be obtained by inverse comparison.

The corresponding reciprocal fuzzy preference relation P=(),∈ [0, 1] associated with Ais defined as follows:

g () ·(1). (1)

The preference matrix is assumed to be additively reciprocal and is given by the following:

1 , j (2)

Furthermore, the additive transitivity property is given by the following:

( ) ( ) ( ), ∀i, j, k, or equivalently,

, ∀i, j, k = 1, . . . , n. (3)

Thus, for consistent fuzzy preference relations P = (), the following statements are equivalent:

, ∀ij, i,j = 1, . . . ,n (4)

i, j = 1, . . . , n. (5)

(2) Preference value is transformed into in the interval scale [0, 1] using (1), (2), and (5); thereafter, the remaining is obtained using the additive reciprocal transitivity property as follows:

If this preference matrix contains any value that is not included in the range of 0 to 1,but in an interval [a, 1 a], then a transformation function is required to preserve thereciprocity and additive transitivity. The transformation function is given by the following:

f() , (6)

wherea indicates the minimum absolute value in this preference matrix.

(3) Evaluator opinions are added to obtain the aggregated importance weights of attributes.Suppose is the transformed fuzzy preference value of evaluator k forassessing attributes i and j. The arithmetic mean method was used to integrate thejudgment values of evaluators.

(). (7)