Abstract
The uncertainty in the data information for decision making is a most challenging and critical fear. In order to reduce the uncertainty in the decision making expert information for decision making problem, the Linear Diophantine fuzzy number is taking more critical part in reducing the uncertainty in information. Therefore the primary aim of this paper is to develop some different types of similarity and distance measures for linear Diophantine fuzzy numbers. With the frequent occurrence of emergency events, emergency decision making (EDM) plays a significant role in the emergency situations. It is essential for decision makers to make reliable and reasonable emergency decisions within a short time period since inappropriate decisions may result in enormous economic losses and chaotic social order. Accordingly, to ensure that EDM problems can be solved effectively and quickly, this paper proposes a new EDM method based on the novel distance and similarity measures under Linear Diophantine fuzzy (LDF) information. The similarity measure is one of the beneficial tools to determine the degree of similarity between objects. It has many crucial applications such as decision making, data mining, medical diagnosis, and pattern recognition. In this study, some novel distances and similarity measures of linear Diophantine fuzzy sets are presented. Then, the Jaccard similarity measure, exponential similarity measure, Cosine and Cotangent function based on similarity measures for LDFSs were proposed. The newly defined similarity measures are applied to medical diagnosis problem for COVID-19 virus and the results are discussed. A comparative study for the new similarity measures is established, and some advantages of the proposed work are discussed.
Highlights
The main motivation of the proposed work is to discuss each extension of fuzzy set (FS); in intuitionistic fuzzy set, the two membership explain the uncertainty of the object but the IFS failed to explain the real life problem, i.e, consider a real life world problem, if the values of membership degree (MD) and non-membership degree (NMD) are greater than 0.5 i.e 0.6 and 0.7, 0.6+0.7>1, in this case the Pythagorean fuzzy set describe the real life world problems
The newly defined similarity measures are applied to medical diagnosis problem for COVID-19 virus and the results are discussed
It should be noted that the Diophantine space increases as we give space to the reference parameters and the boundary limits have a greater space for both degrees which can convey a broader variety of the fuzzy data
Summary
We define different types of similarity measure (SM) of LDFS and we discuss the basic properties of the proposed SMs. We will use the notion of the cosine, exponentail, square root cosine and Jaccard functions to develop the simarity measures between LDFSs. Definition 12: Consider a family of LDFSs LDF(L). A mapping M:LDF(L) × LDF(L) → [0,1] is said to be simiarity measure, if the following conditions hold. 3) M(L1, L2) = M(L2, L1) 4) If L1 ⊆ L2 and L2 ⊆ L3, M(L1, L3) = min{M(L1, L2), M(L2, L3)
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