The technology based self service banking (TBSSB) refers to automated banking services that customer avail in self service mode using various electronic banking channels, without any interaction with bank employees. Researchers have used numerous methods to evaluate automated banking service quality. In this paper, a methodology to quantify the overall effect of key TBSSB service quality attributes is discussed. The TBSSB service quality index is calculated by using fuzzy along with graph

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... and matrix methods. Broad attributes affecting TBSSB service quality are identified. The fuzzy numbers are used to convert intangible attributes to crisp scores and then graph theoretic approach has been applied to calculate the single numerical index. This study may help bank management to take various decisions pertaining to TBSSB service quality using TBSSB index. It will also assist academicians in better understanding of TBSSB services. In the past, studies were conducted to evaluate automated banking service quality by using numerous methods. Most of the evaluation methods emphasized on grouping of various attributes affecting automated banking service quality into dimensions (factors) using factor analysis. Some studies also used approaches like Analytical Hierarchy Process (AHP), Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE), Elimination and Choice Expressing Reality (ELECTRE), Fuzzy TOPSIS etc for evaluating automated banking service quality. Joseph et al., [2] investigated the impact of the technology enabled service delivery on perceived service quality in Australian banking. The researchers identified the six dimensions of e-banking service quality as: convenience/accuracy; feedback/complaint management; efficiency; queue management; accessibility and customisation using the items generated from focus groups. Broderick & Vachirapornpuk [3] identified five key elements that are regarded as central influences on perceived service quality. The elements are customer expectations of the service, the image and reputation of the service organization, aspects of the service setting, the actual service encounter, and customer participation. [4] proposed 22-item instrument to capture key characteristics of Banks' Automated Service Quality from the customers' perspective. The instrument was designed to measure five dimensions of service quality which included ATM quality, telephone banking quality, Internet banking quality, customer perception of core service and customer perception of price. Ibrahim et al., [5] explored six key factors of the electronic service quality perceptions of UK banking customers. The factors include the provision of convenient/accurate electronic banking operations; the accessibility and reliability of service provision; good queue management; service personalisation; the provision of friendly and responsive customer service; and the provision of targeted customer service. Rasolinezhad [6] ranked five electronic banking methods comprising ATM banking, Phone banking, Internet banking, Mobile banking and SMS banking in Iran using Analytic Hierarchy Process (AHP). Amiri et al., [7] investigated and explained effective factors for improving e-banking by using Fuzzy TOPSIS in Persian bank. Ganguli and Roy [8] conducted a research on undergraduate students of a University in the Massachusetts state of the USA. They identified four generic service quality dimensions in the technology-based banking servicescustomer service, technology security and information quality, technology convenience, and technology usage easiness and reliability. Kahraman & Kaya [9] proposed an e-banking website quality assessment methodology based on an integrated fuzzy AHP-ELECTRE approach to rank the alternatives. Fuzzy AHP was used to assign weight to criterion and fuzzy ELECTRE was used to assess the quality levels of the websites. Elbadrawy et al., [10] developed a hybrid model evaluation of e-banking services. By using PROMETHEE in conjunction with AHP, they proposed a structured model for evaluating the performance of the three electronic banking services; ATMs, Telephone Banking, and Internet Banking. AHP was used to determine the relative importance of service quality multi-criteria dimensions from bank customers' point of view, and PROMETHEE method was applied for ranking the performance of different electronic banking services. From the literature survey, it is observed that there is hardly any literature on mathematical modelling of automated banking service quality using Fuzzy numbers and Graph Theoretic Approach resulting in single numerical index. Measurement using Fuzzy Numbers As per Kahraman et al., [11] , the opinion from humans is usually vague and subjective. Fuzzy set theory, introduced by Zadeh [12] may be used to manage the vagueness and subjectivity of human thoughts, particularly linguistic variables since it can represent vague expressions such as "usually," "fair" and "satisfied," which are regarded as the