Normal [formula omitted] functions-based fuzzy information measures with applications in MADM and pattern recognition

Abstract

Fuzzy and non-standard fuzzy information measures act upon vague information entailed in linguistic variables or uncertain numerical data following some goal for which they discover the “best alternative” or “correct pattern”. This paper introduces the concept of normalKN functions instrumental to generate a class of fuzzy knowledge measures. In addition to the axiomatic approach, we investigate various general methods to obtain normalKN functions from the notions of auto-morphisms, restricted equivalence functions, and restricted dissimilarity functions. Further, aggregatingnormal KNfunctions, we propose three knowledge measures of a fuzzy set and exploit their significance in practical applications. This concerns Multiple Attribute Decision Making (MADM) problems, the issue of appropriate weight computation, and the understanding of structured linguistic variables. Additionally, we consider the real case study for the ranking of universities. A novel methodology to transform a given fuzzy knowledge measure into a family of similarity measures of fuzzy sets is also suggested. Furthermore, we discuss an application of the proposed similarity measures in the context of pattern recognition and the MADM problem using artificial and real data sets. The comparative study of the proposed measures shows their advantage over existing ones because of specific theoretical and practical aspects.