Please use this identifier to cite or link to this item: http://prr.hec.gov.pk/jspui/handle/123456789/15770
Title: Some different types of picture fuzzy aggregation operators and their application in multi attribute decision making problems
Authors: Khan, Saifullah
Keywords: Physical Sciences
Mathematics
Issue Date: 2020
Publisher: Abdul Wali Khan University, Mardan
Abstract: The study of multi-attribute decision making (in short MCDM) is that to identify and indicates the best result from all possible options. The decision makers (in short DM) are usually invited to arrange their assessment data against the set of alternatives on the multi-attributes and hence obtained the best result by means of MADM techniques. Since in 1965, Zadeh was first developed the fruitful idea of the fuzzy set (in short FS) to express the inaccurate and unreliable decision information. In this concept, Zadeh only discussed the membership grade of the function. Hence FS is an extension of the charateristic function whose membership grade of the function is oscillate in between 0 and 1. The idea of the FS theory has been studied by different researchers in various fields of the real life. In the process of having access to deal with different problems, people may lack the sufficient level of knowledge to identify the domain of the problem, "due to the complexity of socio-economic environment". As a result, they find themselves uncertain in deciding their preferences over different problems. Thus it becomes difficult to find out the sense of affirmation or negation. For instance, In voting system, a voter is unable to take any bold decision. His mind is confused between two contrasting situations, whether to support or reject any side. This shows the hesitation and ambiguity, on the part of voter, regarding the voting system. Therefore, In 1986 the Atanassov's worked on such kind of problems and develop the core idea of intuitionistic fuzzy set (in short IFS). The IFS is an extension of the FS. In this concept, Atanassov's discussed a membership, non-membership and hesitancy grade of the function. Hence, the sum of their membership and non-membership grade of the function is oscillate in between 0 and 1. Since the idea of the IFS has been rapidly developed and applied in many field to the real life, because they clearly describe the ambiguity and hesitation of the objects more delicately and comprehensively. But in real life, there are some problems which could not be symbolized in IFS. As a result, they find themselves uncertain in deciding their preferences over different problems. For instance, in voting system, a voter is unable to take any bold decision including many answers of such type: yes, no, abstain, refusal. Since a IFS can’t be used to completely express all the information in such problems. Therefore, Cuong worked on such kind of problems and introduced the core idea of the picture fuzzy set (in short PFS), the PF set notion is the extension of the IF set. In the concept of the PFS, Cuong basically added the neutral term along with the positive membership and negative membership grade of the function, and their sum are always oscillated in between 0 and 1. After ix the introduction of the PFS, many researchers have attempt to contribute the important role in PFS. Like Wei, in 2017, and Jana et al., in 2019, developed the idea of PF aggregation operations and PF Dombi aggregation operations respectively, to solve the MADM problems. This thesis contains five chapter, In chapter first, we discuss the some definition like as, FS, IFS, PFS, score and accuracy function and also some related aggregation operational laws and operators, respectively. In chapter two, we developed the basic concept of picture fuzzy Einstein aggregation information and also their properties. Furthermore, a group decision making (DM) problem is illustrated through an example. Also a comparative study of the developed and existing method is performed to prove the validity of the proposed method. In chapter three, we developed the basic concept of PF Einstein hybrid aggregation operation to aggregate the PF information and also their application in detail. In chapter four, we presented the concept of logarithmic aggregation information of PFNs for MADM problem. In this chapter, we also developed an algorithm to express the MADM problem using PF information. To prove the effectiveness and reliability of the developed method, we applied this operators to a circulation center evaluation problem. In chapter five, we develop the core idea of logarithmic picture fuzzy Dombi aggregation operation by using Dombi t-norm and t-conorm to aggregate the PF information and its properties in detail. Key Words: Picture fuzzy Einstein operational laws, Einstein aggregation operators, logarithmic operational laws, logarithmic picture fuzzy aggregation operators, logarithmic picture fuzzy Dombi aggregation operators, decision making problems
Gov't Doc #: 20918
URI: http://prr.hec.gov.pk/jspui/handle/123456789/15770
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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