The fuzzy weighted average within a generalized means function

The fuzzy weighted average is widely used to solve hierarchical evaluation problems, including fuzzy consideration for the operations of scoring, weighting and aggregating. Previous works considered the fuzziness of score and weight, and used the additive function to aggregate these weighted scores. This study considers the aggregation operator also as a fuzzy variable, and uses a generalized means function to fuzzify the aggregation operator within a fuzzy weighted average. In practice, the proposed model not only considers both the relative important of the criteria and its achieved performance, but also conveys the influence of the DM’s (Decision Maker’s) evaluation attitude. Thus the proposed model can flexibly reflect any DM’s evaluation attitude, such as open, neutral or rigorous. Thereby, the proposed model can make an objective evaluation that approaches a real decision making situation, and thus has the potential to be a useful management tool for improved resolution of fuzzy hierarchical evaluation problems.     

Modeling uncertain variables of the weighted average operation by fuzzy vectors

The paper deals with the fuzzy extension of the weighted average operation. First, we study the convenient ways how uncertain weights and weighted values can be modeled by fuzzy vectors. We show that, in comparison to a tuple of fuzzy numbers that have been used for modeling uncertain values of particular weights and weighted values up to now, fuzzy vectors extend the possibilities of utilizing the vague expert information concerning the weights and weighted values. Next, we focus on computation of a fuzzy weighted average of a fuzzy vector of weighted values with a fuzzy vector of weights. We derive a general formula and we study its special forms. The advantage of the approach presented in the paper is that the resulting fuzzy weighted average is not overly imprecise since every available information about its variables is involved in computation. This fact is illustrated by several examples. Finally, we briefly discuss the problem of defuzzification of the resulting fuzzy weighted average.     

Use of ANP weighted crisp and fuzzy QFD for product development

Quality Function Deployment (QFD) is a popular planning method often used to transform customer demands/requirements into the technical characteristics of a new or improved product or service. In order to better capture (and represent) the multifarious relationships between customer requirements and technical characteristics, and the relative weights among customer requirements, in this study a hybrid analytic network process (ANP)-weighted fuzzy methodology is proposed. The goal is to synthesize renowned capabilities of ANP and fuzzy logic to better rank technical characteristics of a product (or a service) while implementing QFD. To demonstrate the viability of the proposed methodology a real-world scenario, where a new equipment to squeeze the polyethylene pipes to stop the gas flow without damaging the pipes, is developed. The ranking of technical characteristics of the product is calculated using both crisp and fuzzy weights for illustration and comparison purposes.