Contributions to the study on approximations of fuzzy numbers

Abstract

This thesis entitled Contributions to the Study on Approximations of newlineFuzzy Numbers which consists of six chapters is basically necessary to newlinethe study on approximations of triangular and trapezoidal fuzzy numbers newlineand its applications. This thesis extensively examines the concepts of newlineapproximations of fuzzy numbers and their different types and properties. newlinexxiii newlineAs the work is on approximation of fuzzy numbers, it deals with the newlinesituations where the concepts of fuzzy numbers are applied. It reveals three newlinetypes of fuzzy applications namely, on duality linear programming problem newlinewith close interval approximations of fuzzy numbers, on problems having newlinetouch with transportation problem with value-ambiguity interval newlineapproximation of fuzzy numbers, on aggregation opinions using triangular newlineapproximation of fuzzy numbers and also comparison of different newlineapproximations of fuzzy numbers in fuzzy game environment. newlineChapter 1 is introductory in nature which unfolds the fundamental newlinetheoretical background of this thesis. It also records the chronological newlinedetails of literature survey on the topic of this thesis. It also contains the newlinemotivation and scope of this thesis study which provides not only the newlinesummary of the thesis but also the scope and application of the results of newlinethis theory. newlineChapter 2 deals with the study on aggregation opinions using triangular newlineapproximation of fuzzy numbers. The trapezoidal approximation of fuzzy newlinenumbers has also been discussed. Chapter 3 analyses the study of interval newlineapproximation of fuzzy numbers and duality linear programming problem newlinein close interval approximations trapezoidal fuzzy numbers. newlineChapter 4 advances the notions of transportation problems with the aid of newlinevalue ambiguity interval approximation of trapezoidal fuzzy numbers. We newlinehave proposed a new method to find the solution to the transportation newlineproblem in value ambiguity interval approximations of trapezoidal fuzzy newlinexxiv newlinenumbers. Also we have proposed a method for ranking of fuzzy numbers newlineusing the value.