The characteristic function of a crisp set assigns a value either 1 or 0 to each object in a set and thereby distinguishesthe members and non-members of crisp set under consideration. The function can be generalized such that the values assigned to the
elements of a set fall within a specific range from 0 to 1 and indicate the membership
grade of these elements in the set in question. Larger values denote higher degree of
set membership. Such function is called a membership function, and the set defined
by it is known as fuzzy set. In short, it can be opinedthat the crisp set and logic divide
the world of yes or no, true or false but nothing in between. On the other hand, fuzzy
sets and logic deal with objects that are of degree with all possible grades between
yes or no.Thus, fuzzy set represents the vague or ill-defined (not well-defined)
concept like good, very good, poor, intelligent, large, and medium large etc., and
hence, it can be extensively applied in a wide range of area. Zadeh developed
this novel concept of fuzzy sets that created a new branch of Mathematics which is
used tocharacterize the uncertainty.A lot of significant developments have been made
by the researchers in the last five decades and applied it in a large variety of fields.
It is observed that in fuzzy set theory (FST) the non-membership function is the
complement of the membership function. But in many situations, complement of membership function may not reflect the exact non-membership grades of an element to a set. Later, Atanassov defined both the membership function and nonmembership function which also characterized some hesitation degree between them.
This newly defined set is called Intuitionistic fuzzy set (IFS). As IFS can represents
the incomplete/ ill-defined information in a more specific manner than FST,
therefore, IFS become more popular among the researchers in uncertainty modeling
problems. Furthermore, Atanassov and Gargov introduced the notion of
Interval-valued intuitionistic fuzzy sets (IVIFSs) extending the concept IFS, in
which, the membership and non-membership grades are represented by intervals.
Starting from our many daily life situations up to very complex system; making
decision is undoubtedly one of the most necessary activities of human being. It is a
logical judgment process to identifying and choosing the right alternatives based on
the preferences and values of the decision maker with respect to its criteria. In
mathematical point of view, there should be some methodology and algorithm
through which one can make a logical and proper decision. Recently, decision
making processes have become popular in industries, in different managerial level of
the concerned department of many organizations because of their global
competitiveness, making good planning and to survive successfully in respective
marketplace. Therefore, decision making plays a vital role especially in purchase
department for reducing material costs, minimizing production time as well as
improving the quality of product or service.
