The concept of intuitionistic fuzzy sets (IFSs) is an expected explanation for finding the appropriate information. It originated from concept of fuzzy set (FS) theory, which extends the classical conception of a fuzzy set. This paper examines a number of widely employed similarity measures then proposes an IFSs modulus similarity measure and a weight similarity measure. Initially, the authors have discussed numerous existing similarity measures, some of which are unable to justify the axioms of being a similarity measure. Furthermore, some numerical examples are presented to compare the existing similarity measures with the proposed similarity measure. The proposed similarity measure is a practical and effective method for determining the qualitative similarity between IFSs, which do not have any paradoxical nature. In addition, the proposed similarity measure has been demonstrated practically in pattern recognition and medical diagnosis problem. Suggestions for future research comprise the conclusions of the paper.
Information theory is the study of collecting, storing, and sharing digital information. It is a nexus of disciplines such as statistics, computer science, statistical mechanics, and probability theory. This study pertains to intuitionistic fuzzy sets theory, which is a substantial component of fuzzy set theory. Nonetheless, the motive of the study is to find vague information intuitionistic fuzzy entropy measures. The authors are extend the parametric intuitionistic fuzzy entropy measures by using trigonometric functions and investigate the difference between proposed study & existing entropy measures. Furthermore, discuss the significance analysis and authenticity of the proposed study. It concludes that the proposed measure could be a good perspective for decision-making problems. Using a suitable illustration, the applicability of the proposed study has been demonstrated. Depict the graph of proposed and existing entropy measure together with their average measure. Additionally, these estimations enhance the study of information theory and produce superior information.
Intuitionistic fuzzy set theory is a generalized conception of fuzzy set theory first coined in (1986). This is an exhaustive portion of the fuzzy set theory that was proposed in (1965). In recent years, numerous studies have developed similarity and distance measures between interval-valued fuzzy sets (IVFSs) and intuitionistic fuzzy sets (IFSs). However, several of these measures do not behave equally among IFSs. This paper suggests a new similarity as well as weight similarity measure after reviewing a number of widely employed similarity measures between intuitionistic fuzzy sets (IFSs). In addition, the study demonstrates that the proposed measures satisfy the properties of the axiomatic definition for similarity measure and presents two theorems. Moreover, the numerous examples are provided to compare the proposed intuitionistic fuzzy similarity measure with the various existing similarity measures. Furthermore, with some illustrative examples, the proposed similarity measure has been suggested for use in pattern recognition and medical diagnosis problems. The conclusions of the study could give important stakeholders in numerous fields with vital information.
In this era, it is difficult to make the right decision about a topic based on different criteria and come to the right conclusion. We adopt the multi-attribute decision making (MADM) approach to resolve this problem and make the best choice possible by combining several attributes. In this paper, we shall discuss Jensen-Shannon Divergence (JSD) measure and some existing intuitionistic fuzzy divergence measures. Additionally, we will develop Jensen-trigonometric divergence measures for intuitionistic fuzzy sets (IFSs). Mathematical evidence is provided to demonstrate the proposed divergence measure comparability to existing information measures. It will be used to solve the MADM technique and axiomatically discuss some of its properties. Both of the proposed measures are derived from the context of IFSs theory, and they are entirely novel and distinct from earlier studies as well. This study describes the implementation of intuitionistic fuzzy divergence measures in the choice of the best motorbike company among five motorbike vehicle companies. Finally, the TOPSIS, MOORA, and MADM approaches are mostly used in this present study along with an illustrative example to determine the best decision.
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