m-Polar Fuzzy Elimination and Choice Translating Reality Methods

Abstract

Real situations are very often ambiguous and unclear in a number of ways. Due to lack of data, the future state of the system may not be fully known. This form of uncertainty has long been properly handled by fuzzy set theory and bipolar fuzzy set theory. The idea of an m−polar fuzzy set provides a convenient starting point for the creation of a theoretical system-work which is similar, in many respects, to the framework used in the case of bipolar fuzzy sets, but is more general than the latter and may theoretically prove to have a much wider scope of application, especially in the fields of decision-making and information processing. m−polar fuzzy set theory is very efficient for conflicting resolution of multiple criteria by providing flexible and hence better evaluation of options. It is a powerful tool for depicting fuzziness and uncertainty under multi-polar information. In this dissertation, new mathematical models based on m−polar fuzzy sets have been constructed to overcome the limi tations entailed in single-valued and two-valued uncertainty. The notions of rough m−polar fuzzy sets and m−polar fuzzy soft sets, as new hybrid models for soft com puting, are introduced and some of their fundamental properties are investigated. New similarity measures for these hybrid models based on the distances are proposed. An m−polar fuzzy ELECTRE-I approach is introduced as a brand-new extension of the xix ELECTRE-I approach, for multi-criteria decision-making problems based on m−polar fuzzy sets. Proposed technique is more flexible and practical for real-world problems, specially when data comes from multi-polar information. In proposed approach, the ratings of the alternatives under subjective criteria and its normalized weights are as sessed by the decision maker. Comparison of our proposed approach with previously existing approaches is also given. The new m−polar fuzzy ELECTRE-I approach through the outranking system is good enough to cope with uncertainty than canon ical strategies. Certain aggregation operators, namely, m−polar fuzzy Hamacher weighted average operator, m−polar fuzzy Hamacher ordered weighted average op erator, m−polar fuzzy Hamacher hybrid average operator, m−polar fuzzy Hamacher weighted geometric operator, m−polar fuzzy Hamacher weighted ordered geometric operator and m−polar fuzzy Hamacher hybrid geometric operator are introduced. The strengths and characteristics of these operators are illustrated by comparison analysis. The ELECTRE-II approach is explored in an m−polar fuzzy environment and introduced a new method named m−polar fuzzy ELECTRE-II. In order to thor oughly investigate the basic information and determine the outranking of alternatives, three levels of concordance and discordance are defined, which are finally more con vincingly devoted to the ranking of alternatives. The viability, relevance, and efficacy of our proposed models is demonstrated by real-world decision-making problems in pattern recognition, medical diagnosis and selection process. Efficient algorithms to solve the decision-making problems are developed. The principle focus of this research is to provide a complete mathematical method to enhance the accuracy of canonical techniques.