The Ordered Weighted Average Human Development Index

The main aim is to propose a new method for estimating the Human Development Index using ordered weighted average. To develop this method, ordered weighted geometric average (OWGA), induced OWGA prioritized OWA (POWA) operator are studied. Using Human Development Index formulation in combination to aggregations operators presented above is proposed the prioritized induced ordered weighted geometric average (PIOWGA) operator. A mathematical application is carried out to estimate the Human Development Index and compare it with the traditional method and other existing methods. Finally, it is noted that decision makers have an influence on the order given in the ranking by its attitude and criterion, and method can capture the subjective information prioritized by them.

An Approach to Multi-attribute Group Decision Making with Trapezoidal Interval Type-2 Fuzzy Sets and Application to Teaching Quality Assessment

Trapezoidal interval type-2 fuzzy sets (TIT2FSs) are a special kind of type-2 fuzzy sets. TIT2FSs are useful in dealing with fuzziness inherent in decision data and the decision-making process. For multi-attribute group decision-making problems in which the attribute values and attribute weights are TIT2FSs, a new decision-making approach is proposed. On the basis of the concept of barycenters, a new approach to ranking TIT2FSs is given. Four kinds of geometric aggregation operators for TIT2FSs are developed, including the TIT2FS weighted geometric average operator, TIT2FS ordered weighted geometric average operator, TIT2FS hybrid weighted geometric average operator, and extended TIT2FS hybrid weighted geometric average operator. The individual comprehensive values of alternatives are derived through the extended TIT2FS weighted geometric average operators. Using the TIT2FS hybrid weighted geometric average operator and the expert weights, the individual comprehensive values of alternatives are integrated into the collective ones, which are used to rank the alternatives. The practicability and effectiveness of the developed method are illustrated with a teaching quality assessment example.

Properties of comprehensive incidence degrees

Purpose – The purpose of this paper is to study the properties of comprehensive incidence degrees of closeness incidence degrees and similitude incidence degrees. Design/methodology/approach – Based on the new definitions of the closeness incidence degree and the similitude incidence degree, the properties of comprehensive incidence of closeness incidence and similitude incidence are studied in this paper. It is proved that weighted arithmetic average of two closeness incidence degrees as well as power product (including weighted geometric average) of two closeness incidence degrees is still closeness incidence degree; and arithmetic weighted average of two similitude incidence degrees as well as power product (including weighted geometric average) of two similitude incidence degrees is still similitude incidence degree. Mixed weighted arithmetic average of closeness incidence degree and similitude incidence degree and mixed power product (including weighted geometric average) of closeness incidence degree and similitude incidence degree are closeness incidence degrees. Findings – The result shows that the effect of closeness incidence degree is stronger than similitude incidence degree. As long as the weight of closeness incidence degree is not equal to zero, the comprehensive incidence degree results are closeness incidence degrees. Practical implications – Grey incidence degrees have been widely applied in many fields, such as the test of grey model's forecasting effect, the system analysis and so on. The obtained result in this paper is to illustrate two kinds of incidence degrees are incompatible, namely there does not exist both closeness and similitude incidence degree. Originality/value – The paper succeeds in showing that the attempt to get comprehensive incidence degree by arithmetic or geometric weighted average of closeness incidence degree and similitude incidence degree to reflect both closeness and similarity is in vain. And it is undoubtedly a new development in grey system theory.