International Journal of Mathematics Trends and Technology (IJMTT) – Volume 58 Issue 1 – June 2018
Execution of N-Valued interval neutrosophic sets in medical diagnosis A.Edward Samuel#1, R.Narmadhagnanam*2 #
Ramanujan Research Centre, P.G. & Research Department of Mathematics, GAC(A),Kumbakonam,TN,India.
Abstract In this paper, cosecant similarity measure among n-valued interval neutrosophic sets are proposed and some of its properties are discussed herein. Finally, an application of medical diagnosis is presented to find out the disease impacting the patient. Keywords N-valued interval neutrosophic set, cosecant similarity measure, medical diagnosis. I. INTRODUCTION A number of real life problems in engineering, medical sciences, social sciences, economics etc., involve imprecise data and their solution involves the use of mathematical principles based on uncertainty and imprecision. Such uncertainties are being dealt with the help of topics like probability theory, fuzzy set theory [1], rough set theory [2] etc., Healthcare industry has been trying to complement the services offered by conventional clinical decision making systems with the integration of fuzzy logic techniques in them. As it is not an easy task for a clinician to derive a fool proof diagnosis, it is advantageous to automate few initial steps of diagnosis which would not require intervention from an expert doctor. Neutrosophic set which is a generalized set possesses all attributes necessary to encode medical knowledge base and capture medical inputs. As medical diagnosis demands large amount of information processing, large portion of which is quantifiable, also intuitive thought process involve rapid unconscious data processing and combines available information by law of average, the whole process offers low intra and inter personal consistency. So contradictions, inconsistency, indeterminacy and fuzziness should be accepted as unavoidable as they are integrated in the behaviour of biological systems as well as in their characterization. To model an expert doctor it is imperative that it should not disallow uncertainty as it would be then inapt to capture fuzzy or incomplete knowledge that might lead to the danger of fallacies due to misplaced precision. As medical diagnosis contains lots of uncertainties and increased volume of information available to physicians from new medical technologies, the process of classifying different sets of symptoms under a single name of disease becomes difficult. In some practical situations, there is the possibility of each element having different truth membership, indeterminate and false membership functions. The unique feature of n-valued interval neutrosophic set is that it contains multi truth membership, indeterminate and false membership. By taking one time inspection, there may be error in diagnosis. Hence, multi time inspection, by taking the samples of the same patient at different times gives the best diagnosis. So, n-valued interval neutrosophic sets and their applications play a vital role in medical diagnosis. In 1965, Fuzzy set theory was firstly given by Zadeh [1] which is applied in many real applications to handle uncertainty. Sometimes membership function itself is uncertain and hard to be defined by a crisp value. So the concept of interval valued fuzzy sets was proposed to capture the uncertainty of grade of membership. In 1986, Atanassov [3] introduced the intuitionistic fuzzy sets which consider both truth-membership and falsitymembership. De et al [4] presented an application of intuitionistic fuzzy set in medical diagnosis. Jun Ye [5] introduced the concept of cosine similarity measures for intuitionistic fuzzy sets. Tian Maoying [6] presented the cotangent similarity function for intuitionistic fuzzy sets. Later on, intuitionistic fuzzy sets were extended to the interval valued intuitionistic fuzzy sets. Intuitionistic fuzzy sets and interval valued intuitionistic fuzzy set scan only handle incomplete information not the indeterminate information and inconsistent information which exists commonly in belief systems. So, Neutrosophic set (generalization of fuzzy sets, intuitionistic fuzzy sets and so on) defined by Florentin Smarandache [7] has capability to deal with uncertainty, imprecise, incomplete and inconsistent information which exists in real world from philosophical point of view. Wang et al [8] proposed the single valued neutrosophic set. Similarity and entropy between neutrosophic sets were proposed by Mamjumdar and Samanta [9]. Wang et al [10] proposed the set theoretic operations on an instance of neutrosophic set is called interval valued neutrosophic set which is more flexible and practical than neutrosophic
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