There are many alternative gas-fired combi boilers that can be used to heat residential homes. Evaluation and selection of gas-fired combi boilers for buildings is an intricate multi-criteria decision-making (MCDM) problem involving perhaps contradictory quantifiable and qualitative criteria. In this research, as the MCDM approach, hesitant fuzzy linguistic analytic hierarchy process (HF-AHP) and hesitant fuzzy linguistic “multiple objective optimization based on ratio analysis plus full multiplicative form (MULTIMOORA)” (HF-MULTIMOORA) are integrated to assess and rank combi boiler alternatives for buildings. First, with HF-AHP, fuzzy criteria weights are determined and then with HF-MULTIMOORA, boiler alternatives are ranked from best to worst. In this integrated HF-AHP-MULTIMOORA method, evaluations of decision-makers are combined with fuzzy envelope approach and then triangular fuzzy numbers are utilized. For comparison analysis, HF-AHP-TOPSIS method is also applied to the same problem. A case study in Turkey is presented where ten combi boiler alternatives are assessed based on fifteen criteria by five decision-makers. We have used various selection criteria for boilers ranging from maximum temperature, heating capacity up to environmental effects and decided on the best combi boiler for heating residential buildings in Turkey.