### A Diagnostic Decision Model Based on Vague Sets

#### Affiliations

• C. C. S. University, Department of Mathematics, Meerut, 250004, India

#### Abstract

Medical diagnosis involves various kinds of uncertainties in the process. This makes the diagnostic decision analysis an important platform for the applicability of fuzzy sets. Some researchers have given a fuzzy decision making model for medical diagnosis based on fuzzy num- bers and compositional rule. Fuzzy set theoretic analysis is usually centered on the choice of proper membership grades for the elements of fuzzy sets. A single value for the membership grade based on the combined effect of favourable and unfavourable evidence, does not speak much about the appropriateness. Vague set theory takes into account the favourable and unfavourable evidence separately and provides a closed interval in which the membership grade may lie. This paper defines triangular vague numbers to extend the concept of triangular fuzzy numbers and general- izes the model of Yao and Yao using vague set theory. Application of this method to their example covers up the vagueness in the symptom disease relationship and the lack of specificity in patient-symptom observations in a more realistic manner and increases the credibility of the diagnostic decision.

#### Keywords

Vague Set, Lower and Upper Membership Functions, Vague Point, Triangular Vague Number.

#### Subject Discipline

Mathematical Sciences

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