An Optimized Intuitionistic Fuzzy Associative Memories (OIFAM) to Identify the Complications of Type 2 Diabetes Mellitus (T2DM)

An Optimized Intuitionistic Fuzzy Associative Memories (OIFAM) to Identify the Complications of Type 2 Diabetes Mellitus (T2DM)

Felix A. (Department of Mathematics, School of Advanced Sciences, VIT Chennai, India) and Dhivya A. D. (Department of Mathematics, Norbuling Rigter College, Paro, Bhutan)
Copyright: © 2020 |Pages: 20
DOI: 10.4018/IJFSA.2020070102

Abstract

Fuzzy associative memories (FAM) is a recurrent neural network, consisting of two layers. Since points of the fuzzy set are defined in a cube, it maps between cubes. That is, it maps from input fuzzy set into an output fuzzy set. While the input layer is deliberated as the cause infusing agent the output layer influences the requisite effect. It is a powerful technique to analyze the cause and effect of any problem. Determining the most influential factors in the cause and effect group of any problem is a challenging task. To quench such a task, this present study constructs an optimized intuitionistic fuzzy associative memory using an intuitionistic fuzzy set and a variance of fitness formula. To check the validity of the proposed model, Type 2 diabetes mellitus is taken for diagnosing the early complications of T2DM patients from the risk factors.
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1. Introduction

Bart Kosko proposed many models such as Fuzzy Cognitive Maps (FCM) (1986), Bidirectional Associative Memories (BAM) (1988), Fuzzy Associative Memories (FAM) (1997), etc., using the concepts of neural networks and fuzzy logic. Fuzzy Associative Memories (FAM) is an associative model originated in the early 1990's with the advent of Kosko's FAM (1997, 1992). In FAM, Fuzzy set defines a point in a cube and a fuzzy system defines a mapping between cubes. This fuzzy system map from the balls of fuzzy sets in the domain space to the balls of fuzzy sets in range space. This continuous systems and neural systems estimate function which behave like as associative memories also map close inputs to close outputs. Like many other associative memory models, Kosko's FAM consists of a single-layer Feed Forward FNN that stores the fuzzy rule “If x is Xk then y is Yk” using a fuzzy Hebbian learning rule in terms of max-min or max-product compositions for the synthesis of its weight matrix W. It is a powerful method to analyze the relationship between causes and effects of any problem. It has been applied successfully to problems such as backing up a truck and trailer (Kosko, 1992), target tracking (Kosko, 1997), pesticides on agricultural labourers (Balasangu et al., 2011), Impacts of climate change (Devadoss and Ajay, 2013), music-emotion recognition (Devadoss and Aseervatham, 2014), Oral cancer (Felix et al., 2018), Youth violence and aggressiveness (Devadoss and Felix, 2012), etc.

Since fuzzy modeling captures vagueness and it resembles with human way of thinking, fuzzy logic attracted many research fraternity in the field of medical diagnosis problems. Fuzzy set assigns only membership value between zero and one. By considering the non-membership of the fuzzy set and hesitation part, Atanassov K T extended intuitionistic fuzzy set (IFS) (Atanassov, 1986) from the fuzzy set by adding an additional non-membership degree, which may express more flexible information when it is compared with the fuzzy set. Intuitionistic fuzzy set is the generalization of the fuzzy sets. When there may arise some hesitations, IFS theory is more suitable to deal with incomplete information exist in real world problem. Recently, Fuzzy Associative Memories is enhanced using intuitionistic fuzzy sets. IFAM was designed based on Goumldel fuzzy implication operator and its dual fuzzy co-implication operator, a learning rule for multiple intuitionistic fuzzy pattern pairs (Li et al., 2013). Euclidean Distance based Intuitionistic Fuzzy Valued Associative Memories was constructed to study the behavioral changes of road user was analyzed (Devadoss et al., 2012). Emerging decision-making tool intuitionistic fuzzy soft matrices is proposed in dealing medical diagnosis problem (Sarala, 2014). Interval-valued fuzzy soft sets in stochastic multi-criteria decision-making system and Pythagorean Fuzzy Choquet Integral Based MABAC Method for Multiple Attribute Group Decision Making was designed (Peng and Yang, 2017; Peng and Yang, 2016).

Moreover, researchers have also successfully coped up with uncertainty in medical diagnosis problems such as Headache (Ahn et al., 2011), medical hypothetical case (Muthukumar and Krishnan, 2014), homeopathic drug selection (Das et al., 2015), web-based medical diagnostic support system (Das et al., 2016) with aid of IFS theory. Type 2 diabetes mellitus (T2DM) represents not only a medical problem but also a social problem (Mendis et al., 2011) as it was the eighth leading cause of death among both sexes and the fifth leading cause of death in women in 2012 (WHO, 2016). It is also one of the most alarming diseases in both developed and developing countries. Since there are no awareness of what symptoms or risk factors promote T2DM. For instance, risk factors such as sedentary life style, physical inactivity, and impaired glucose tolerance are contributing to induce different complications. Also the problem varies between each and every person, it cannot be decided that all the person have the same symptoms or factors to diagnose. Undiagnosed T2DM lead the complications such as eyesight, kidney and heart. Therefore, a new attempt is made in this present study to construct Optimized Intuitionistic Fuzzy Associative memories using variance of fitness formula to identify the complications of T2DM patients.

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