# Introduction
o assure a comfortable sitting posture, some seat functions, such as the forward tilt of the seatback or seat swing function (Fig. 1), are included in public seats in railway vehicles and passenger airplanes [1] to [3]. However, it is unclear how these functions contribute to a comfortable sitting posture. Currently designers select seat functions based on their experience or sensory evaluation experiments [4]. Moreover, the conventional design assumes standard conditions in which all passengers have average physiques and standard sitting positions. Consequently, conventional design solutions are often poorly evaluated for non-standard conditions, including those with nonaverage physiques and varied postures (diverse conditions) [5] and [6].
The objectives of this study are to determine which seat functions assure a comfortable sitting posture and then optimize these seat functions for diverse conditions. To determine the relative importance of the seat functions, we conducted a sensory experiment using evaluation factors to elucidate factors for a comfortable sitting posture. We then analyzed the results of the sensory evaluation experiment via an analytic hierarchy process (AHP) and a fuzzy analytic hierarchy process (Fuzzy AHP) [7] and [8]. Second, we constructed a human-seat model for selected seats and performed simulations to optimize seat functions using the model. In this study, the signal-to-noise (SN) ratio from the Taguchi method [9] and [10] was used to consider variations in user physiques and the diversity of sitting postures. Finally, we conducted a sensory experiment to evaluate the optimized design solution. ? Examinees: To incorporate passengers with various physiques, we evaluated passengers using combinations of three different heights and weights.
Of the nine possible combinations, two are statistically rare, and consequently eliminated (Table 1). The height and weight levels are defined using their mean values µ h and µ w and standard deviations ? h and ? w ? Sitting posture: Each examinee adjusted the seat to assume the most comfortable sitting posture.
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? Evaluated seat functions: A sample seat was prepared with five different seat functions: adjustable head rest height, forward tilt, seat swing, seat cushion slide, and footrest. Figure 2 shows the seat functions of the experimental seat. The specifications of the sample seat are identical to an actual public transportation seat found in the Hatsukari express train in Japan. ii.
# Evaluation method
Based on the results of a previous study [11], we chose two factors to evaluate seat functions: the fitness of the sitting posture and the amount of freedom for various sitting postures with a relative weighting of 7 to 3. The examinees evaluated each factor by answering the following questions using the semantic differential (SD) method on a five-point scale. "Is it possible to achieve a comfortable sitting posture?" and "Is it possible to achieve a variety of sitting postures?" b) Analysis of important seat functions for a comfortable sitting posture i. Application of AHP and Fuzzy AHP To analyze the importance of seat functions in assuring a comfortable sitting posture, the results of the evaluation were analyzed using AHP and Fuzzy AHP.
AHP is a decision-making method that considers subjective human criteria. In AHP, a hierarchal model is initially created. The model consists of three components: the design object, evaluation factors, and alternatives. The factors in the decision-making problems are divided based on the hierarchy model. Then the degree of importance for each evaluation factor is determined using an evaluation matrix based on paired comparisons. Finally, the degree of importance of the alternatives based on the hierarchy model is numerically simulated using the degree of importance of the evaluation factors and the results of SD method.
The degree of importance for AHP is an additive measure because the sum is equal to one. However, an additive measure cannot evaluate substitutability and complementarity of a sensory evaluation. Substitutability states that even if there is only one excellent evaluation among a number of evaluations, the overall evaluation is Figure 2 : Specification of the sample seat good evaluation. In contrast, complementarity means that one inferior evaluation lowers the overall evaluation. Because AHP emphasizes overall balance, herein we employ Fuzzy AHP uses non-additive measures (possibility and necessity measures), which are described below.
First, we expressed the additive measure generally used in AHP, the degree of importance y of the alternatives as a weighted sum of the degrees of importance w i (0 ? w i ? 1) of the evaluation factors x i , and the evaluation value f j (x i ) of j th alternative of x i . Then y can be expressed as
= + + = ? = n n i i j i j w w x f w y (1)
evaluation factors. Fuzzy AHP normalizes the degrees of importance w i (0 ? w i ? 1) for cases where w i = 1 for more than one i. For example, wi can be normalized by their maximum value. The classes A l of the number of n is established using w i ' (r 1