Chemical process industries (CPI) handling hazardous chemicals in bulk can be attractive targets for deliberate adversarial actions by terrorists, criminals and disgruntled employees. It is therefore imperative to have comprehensive security risk management programme including effective security risk assessment techniques. In an earlier work, it has been shown that security risk assessment can be done by conducting threat and vulnerability analysis or by developing Security Risk Factor Table (SRFT). HAZOP type vulnerability assessment sheets can be developed that are scenario based. In SRFT model, important security risk bearing factors such as location, ownership, visibility, inventory, etc., have been used. In this paper, the earlier developed SRFT model has been modified using the concepts of fuzzy logic. In the modified SRFT model, two linguistic fuzzy scales (three-point and four-point) are devised based on trapezoidal fuzzy numbers. Human subjectivity of different experts associated with previous SRFT model is tackled by mapping their scores to the newly devised fuzzy scale. Finally, the fuzzy score thus obtained is defuzzyfied to get the results. A test case of a refinery is used to explain the method and compared with the earlier work.