Orthopairian Entropy and its Application in Preparation and Evaluation of Carrot and Apple Blended Jam with Multicriteria Decision Making

Yager recognized the broadly generalized q-Rung Orthopair Fuzzy Sets (q-ROFSs) in 2017. This high-class model evaluates uncertainty and vagueness more accurately than Intuitionistic Fuzzy Sets (IFSs) represented by Atanassov in 1986 and Pythagorean Fuzzy Sets (PFSs) developed by Yager in 2014 respectively. We can continually change the value of ‘q’ for determining the facts, so q-ROFSs are reliable and more desirable for the uncertain environment. This theory was clearly formulated to show the ambiguity and uncertain situations mathematically and developed some tools to tackle imprecise information in real-world applications. It has various applications in different fields including fuzzy systems, control system, image processing, data mining and clustering, classification and pattern recognition, control systems, bioinformatics and decision making due to its ability to quantify the uncertainty in a system. The notion of entropy and sigma entropy is commonly used in the field of information theory to quantify the amount of uncertainty or randomness present in a given system. Here, we suggest a novel entropy measure on q-Rung Orthopair Fuzzy Set (q-ROFS) and then extend it to introduce the concept of sigma entropy to measure the fuzziness present in a system under consideration. Also, the suggested entropy measure is axiomatically defined on q-ROFS. We give the proof of every axiom in detail. Furthermore, we put forward some numerical examples with comparisons and analysis to determine the suitability, reliability and consistency of the suggested method. Finally, we develop O-COPRAS (Orthopairian Complex Proportional Assessment) based on proposed entropy measure. To show the practical capability, we apply proposed O-COPRAS for preparing and evaluating blended Jams and ranking for the most economically affected countries in the world by COVID-19 pandemic respectively. Mathematics Subjects Classification 03E72 · 94D05 · 94A17 · 68T10 · 62H30