In this section, we discuss two multi-attribute decision-making problems under PF environment using Yager aggregation operators.
5.1. Selection of Top Rank Country in Health Care System
Basically, health care is the recovery and maintenance of human body through prevention, diagnosis and treatment of diseases and other physical or mental deteriorations. For best health care, health system should be well-ordered and maintained. There are a lot of things which are counted in health care system such as psychology, nursing, medicine, physical therapy and many other things. Every human body needs a good health to spend a happy life. Due to lack of good health care system, people face different difficulties. A good health system is influenced by economic and social factors and a best health care system demands solid funding mechanism, a perfectly competent workforce, well-maintained facilities, etc. The countries which are financially stable with a good accessible health care system. To determine level of health care quality in every country, there are different factors such as care process (preventive care measures, coordinated care, and engagement and patient preferences), access (unavoidability and timeliness), administrative performance, equity, and health care outcomes (population health and disease-specific health outcomes).
The purpose of this application is to rank the top country among different countries in health care system according to “World Health Organization” (WHO) by applying PFYWAA and PFYWGA operators. Let be a set of alternatives (countries), where
Let be a set of three attributes, where
and
be the weight vector of the attributes given by the decision-maker such that
. The Pythagorean fuzzy values
of the alternatives according to different attributes are given in
Table 1, where
is the positive membership degree for which alternative satisfies the given attribute, given by the decision-maker and
is the membership degree for which alternative does not satisfy the given attribute, where
and
.
Applying the PFYWAA operator given in Equation
3, to find the aggregate value
of each country corresponding to given attributes and take
.
Now we find the score values of
which are given as,
As Hence, . Thus, Netherlands is on the top rank country in health care system among other two countries.
Now, applying the PFYWGA operator given in Equation
6 to find the aggregate value
of each country corresponding to given attributes
Now we find the score values of
which are given as,
As Hence, . Thus, Netherlands is the top rank country in health care system among other two countries.
We conclude from
Table 2 that by applying both operators, Netherlands is on the top of rank. Therefore, we can use any operator between these two operators.
The whole method which we have adopted in this application is given in
Figure 1.
5.2. Selection of Top Rank University in Education Sector
Ranking is the mean of selecting the high position of anything or person in any field. Basically, ranking is a relationship between a set of different sources, in which it can be judged which is superior than others. All other fields, raking in education sector is too much important. Rankings are the significantly help maintain and build institutional position and reputation. The high rank of institute promotes the chances of falling into a prospective student shortlisting process. There are a lot of ways to help students in identifying the best colleges and universities for them. By visiting different institutes in particular settings will help to evaluate what feels right. Rankings can help the students to sort out which institutes are considered the most selective and important. National and international partnerships and collaborations are also affected by the university rankings. For the university with high rank, it will increase the chances of willingness of others to partner with them or support their membership in helping the academic or professional issues. There is an increasing impact of university rankings on the higher education associations and their environment, influencing, the decisions of the future students in their elect of schools, the government policy of financing higher education institutions along with the way of managing the universities. It is exacting for the ranking organizations to give the objective picture of the position of different universities in relation to one another.
The objective of this application is to select the top rank university among different universities by applying PFYWAA and PFYWGA operators. Let be a set of alternatives (universities), where
Let be a set of three attributes for the selection of universities, where
and
be the weight vector of the attributes given by the decision-maker such that
. The PF values
of the alternatives according to different attributes are given in
Table 3, where
is the positive membership degree for which alternative satisfies the given attribute and
is the membership degree for which alternative does not satisfy the given attribute, where
and
.
Applying the PFYWAA operator given in Equation
3, to find the aggregate value
of each university corresponding to given attributes and take
.
The score values of
are,
As Hence, . Thus, University of Punjab Lahore is the top rank university in education sector among other two universities.
Now, applying the PFYWGA operator given in Equation
6 to find the aggregate value
of each country corresponding to given attributes
Now we find the score values of
which are given as,
As Hence, . Thus, University of Punjab Lahore is the top rank university in education sector among other two universities.
We conclude from
Table 4 that by applying both operators, University of Punjab Lahore is on the top of rank. Therefore, we can use any operator between these two operators.
The whole method which we have adopted in this application is given in
Figure 2.