Finding the Robust Multi-Modal Route by Integrating the Fuzzy-AHP with the Quantifier-Guided OWA

The purpose of Multi-modal Multi-criteria Personalized Route Planning (MMPRP) is to provide an optimal route between an origin-destination pair by considering weights of effective criteria, in which this route could be a combination of public and private transportation modes. In recent studies, the weighted linear aggregation rules were developed to calculate the impedance of links that were high tradeoff decision strategies. A decision strategy defines whether a user insists on satisfying all of his/her preferences regarding the selection of one route from a set of routes or he/she would be happy if the most of criteria would be satisfied. In this paper, a fuzzy analytical hierarchy process (fuzzy AHP) and quantifier-guided ordered weighted averaging (Q-OWA) operators were integrated to calculate the impedance of links. Fuzzy analytical hierarchy process (fuzzy AHP) weighting method by Saaty embeds fuzzy theory to basic AHP method. In AHP weighting method, a matrix-liked structure is considered by pairwise comparison between criteria with exact numbers. Despite the general popularity, the AHP method is not capable to consider the users’ ambiguity and the lack of clarity in their preferences. To solve this problem of the AHP method, the fuzzy AHP method was proposed to use fuzzy numbers rather than exact ones in pairwise comparisons. In this research, the triangular fuzzy numbers was used for these pairwise comparisons.
To model a family of parameterized decision strategies, Yager introduced the ordered weighted averaging (OWA) operators. This method calculates the user’s risk taking and risk aversion, as well as enters them for selecting the final option. Quantifier-guided OWA is obtained by integrating the fuzzy linguistic quantifiers with the OWA operators. In this study, a class of relative quantifiers, called “Regular Increasing Monotone (RIM)” was used. The main characteristic of these methods is supporting the different decision strategies in calculating the impedances. In this method, the user determines the relative weights with fuzzy AHP method at first. Then by considering his/her desired decision strategy, impedance of the links were calculated. The proposed model can also propose the robust personalized route under the different decision strategies. By considering the different decision strategies, this model provides different routes. Then, by determining minimum and maximum impedance of each link, the model presents the robust personalized route. In this study, subway, BRT, bus, taxi, and walking transportation modes were considered for traveling between nodes. Moreover, time, length, and user’s bother of each transportation mode were considered as effective criteria. This model was implemented in an area in the center of Tehran. The considered area had 21 km2 and consisted of 2 BRT lines, 28 sweep bus lines, and 4 sweep subway lines, and totally more than 45 km of roads. The proposed method was implemented for one of the most crowed path in our case study, i.e., a path from Baharestan square to Enghelab square. Initially, the devoted configuration wizard for the pairwise compression were presented to 45 users (9 users for any decision strategy) and they were asked to weight the criteria. Then, the relative importance of each criterion was calculated by considering the weights assigned within the pairwise compression matrix. Afterwards, they were asked to determine their desirable decision strategies, including “at least one”, “half”, “many” and “all”. Results showed that on average 80.66% of the users with different decision strategies, selected the model proposed route as the best route