Efficient Methods for solving some decision making problems under fuzzy environment and its extensions

Abstract

In daily life problems, a process is followed by an individual or group of persons to finalize a decision. This process is called DM and the problems are called DMPrs. DMPrs can be mainly classified into the two following categories: Single/multi-attribute DMPrs: This category contains those DMPrs in which a finite number of alternatives are known and the aim is to rank these alternatives e.g., To rank 50 students of a class on the basis of the marks, secured in Mathematics, is a single attribute DMPr. To rank 50 students of a class on the basis of marks, secured in Mathematics, Physics and Chemistry, is a MADMPr. Single/multi-objective DMPrs: This category contains those DMPrs in which the aim is to find a way which will maximize/minimize one or more functions subject to various restrictions e.g., To find the quantity of the product that should be supplied from various sources to various destinations in such a manner that the total TrC is minimum is a single objective DMPr. To find the quantity of the product that should be supplied from various sources to various destinations in such a manner that the total TrC as well as the total transportation risk is minimum is a multi-objective DMPr. One of the important steps of DM is to collect the information/data regarding the problem. It is pertinent to mention that it is not always possible to represent the collected data/information as a RN e.g., The cost to hire a cab between two fixed places cannot be represented by a RN as it varies from time to time depending on the traffic/weather-conditions/route etc. The rating of a movie review cannot be presented by a RN instead it can be expressed in linguistic terms such as poor, average, good, excellent etc. In the literature, different ways have been introduced to handle these types of data. One of the way, used by several researchers, to handle the same is to express the data as FS and its extensions . In the last few years, several researchers have proposed various methods for solving DMPrs under fuzzy environment and its extensions. These methods can be classified into different categories. Some of these categories are as follows: Methods for solving DMPrs under IF environment: This category contains all those methods for solving DMPrs in which some or all the collected information/data is expressed as IFS. Methods for solving DMPrs under IVIF environment: This category contains all those methods for solving DMPrs in which some or all the collected information/data is expressed as IVIFS . Methods for solving DMPrs under DHF soft environment: This category contains all those methods for solving DMPrs in which some or all the collected information/data is expressed as DHFSS. Methods for solving DMPrs under IVIF soft environment: This category contains all those methods for solving DMPrs in which some or all the collected information/data is expressed as IVIFSS. Methods for solving DMPrs under neutrosophic environment: This category contains all those methods for solving DMPrs in which some or all the collected information/data is expressed as SVNS. Methods for solving DMPrs under interval-valued neutrosophic environment: This category contains all those methods for solving DMPrs in which some or all those collected information/data is expressed as IVNS . Methods for solving DMPrs under IVPF environment: This category contains all those methods for solving DMPrs in which some or all those collected information/data is expressed as IVPFS. In the last few years, various approaches have been proposed for solving MADMPrs under various extensions of fuzzy environment. After a deep study, some limitations and/or shortcomings have been observed in the existing methods for solving DMPrs under various extensions of fuzzy environment. Keeping the same in mind, the aim of this thesis is To point out as well as to overcome the limitations of some existing methods.