Abstract
The paper aims to present an integrated approach to solve the decision-making problem under the probabilistic hesitant fuzzy information (PHFI) features, which is an extension of the hesitant fuzzy set. The considered PHFI not only allows multiple opinions, but also associates occurrence probability to each opinion, which increases the reliability of the information. Motivated by these features of PHFI, an approach is presented to solve the decision problem with partial known information about the attribute and expert weights. In addition, an algorithm for finding some missing values in the preference information is presented and stated their properties. Afterward, the Hamy mean operator has been used to aggregate the different collective information into a single one. Also, we presented a COPRAS method to the PHFI for ranking the given alternatives. The presented algorithm has been demonstrated through a case study of cloud vendor selection and its validity has been revealed by comparing the approach results with the several existing algorithm results.
Highlights
Hesitant fuzzy set (HFS) [1] is a promising extension to the classical fuzzy set that promotes multi-criteria decision-making (MCDM) with effective uncertainty management
The confidence of each element is obtained that acts as potential information for MCDM
Zheng et al [43] rightly pointed out the superiority of COPRAS method as (i) simple and straightforward approach; (ii) considers the nature of criteria for better ranking of alternatives; (iii) offers ranking from different angles based on the calculation of complex proportional factors; and (iv) final ranking of alternatives is influenced by strategy values that associates degree of importance to the types of criteria
Summary
Hesitant fuzzy set (HFS) [1] is a promising extension to the classical fuzzy set that promotes multi-criteria decision-making (MCDM) with effective uncertainty management. Zheng et al [43] rightly pointed out the superiority of COPRAS method as (i) simple and straightforward approach; (ii) considers the nature of criteria for better ranking of alternatives; (iii) offers ranking from different angles based on the calculation of complex proportional factors; and (iv) final ranking of alternatives is influenced by strategy values that associates degree of importance to the types of criteria. Driven by these advantages of COPRAS approach, a step-wise procedure for ranking alternatives with PHFI is given below. A single matrix of order 6 × 7 is obtained with six cloud vendors rated based on seven criteria
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