Neutrosophic classifier: An extension of fuzzy classifer
Graphical abstract
Block diagram for a neutrosophic classification system using fuzzy logic toolbox of Matlab.
Highlights
► Introduces an extension to fuzzy classifier: a neutrosophic classifier. ► Proposed neutrosophic classifier employs neutrosophic logic for its working, that is an extension of fuzzy logic. ► Neutrosophic classier is compared with the commonly used fuzzy classifiers on the following parameters: nature of membership functions, number of rule and indeterminacy in the results generated. ► It is proved in the paper that extended fuzzy classifier: neutrosophic classifier; optimizes the said parameters in comparison to the fuzzy counterpart.
Introduction
Classification is the process of arranging data into homogeneous classes on the basis of the common features present in the data [1].
Various machine learning based techniques are used for input data classifications that provide a rational answer for all possible inputs [2]. Fuzzy matching of input and subsequent fuzzy processing is an active research area that has been successfully applied to varied domains from control theory to artificial intelligence [3], [4].
This paper is written with the aim of focusing on the classification performed on the data which is uncertain, imprecise, incomplete and ambiguous. In this paper authors propose a new classification technique based on neutrosophic logic which is an extension of fuzzy logic.
Section snippets
Present work
Fuzzy logic was given by Prof. L.A. Zadeh in his seminal paper during second half of last century [5]. Though with weak acceptance initially, slowly it has emerged as one of the important soft computing techniques to model uncertainty [6]. Real world information is full of uncertainties, gaps and inconsistent information. This uncertainty can be encountered in varied forms like uncertainty in outcome of tossing a coin; whether it will be a head or tail is an example of classical bivalence where
Neutrosophic logic
Quite recently, neutrosophic logic was proposed by Florentine Smarandache which is based on the non-standard analysis that was given by Abraham Robinson in 1960s [13]. Neutrosophic logic was developed to represent mathematical model of uncertainty, vagueness, ambiguity, imprecision, incompleteness, inconsistency, redundancy and contradiction [14]. Neutrosophic logic is a logic in which each proposition is estimated to have the percentage of truth in a subset T, the percentage of indeterminacy
How neutrosophic logic is different from fuzzy logic
Neutrosophic logic proposes that between an idea 〈A〉 and its opposite 〈Anti-A〉, there exists a gamut of continuous power spectrum of neutralities which can be represented by 〈Neut-A〉 [14].
If 〈α〉 be an attribute, for a proposition 〈P〉 and a referential system {R}, applying Neutrosophic logic yields (T, I, F)]−0,1+[[3]. Then:
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〈P〉 is T% 〈α〉, I% indeterminate or 〈Neut-α〉, and F% 〈Anti-α〉.
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It can be shown that 〈α〉 is at some degree 〈Anti-α〉, while 〈Anti-α〉 is at some degree 〈α〉.
This important concept
Neutrosophic classifier: an extension of fuzzy classifier
A classifier is an algorithm that predicts the class label on the basis of the object descriptor. Commonly used classifier in the soft computing domain is fuzzy classifier. Fuzzy classifier uses fuzzy sets or fuzzy logic in the course of its training or operation. This paper proposes extension of fuzzy classifier that is neutrosophic classifier that will use neutrosophic logic which is a superset of fuzzy logic. Definition 4 Neutrosophic classifier: a classifier that would use neutrosophic logic principles
Fuzzy classifier—Matlab implementation of FIS-iris classification
Simple Mamdani type fuzzy classifier is designed using MATLAB for iris data set.
As overlapping is inherent of fuzzy logic so appropriate overlapping membership functions have been designed for all the Iris dataset attributes and output classes. Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8 gives the membership function designed for Iris sepal length, sepal width, petal length, petal width and Iris output classes designed for Mamdani type fuzzy classifier.
It can be generalized that the outputs
Proposing neutrosophic classifier on the lines of fuzzy classifier
Neutrosophic systems similar to their fuzzy counterparts would be capable of utilizing knowledge obtained from human operators. In majority of the real world classifiers it is difficult to devise a precise mathematical model that would simulate system behavior; also it is unlikely that the data acquired by the system would be 100% complete and determinate [11]. Incompleteness and indeterminacy in the data can arise from inherent non-linearity, time-varying nature of the process to be
Experimental results
Table 1 shows the details of training and testing sample using FIS. 30 instances from each class have been used for training (for making rule set) and 20 from each class have been used for testing.
Table 2 discusses the results of testing done using FIS. When FIS is used for classification, two overlapping zones are recorded for output classes (Fig. 8a).
- Overlapping zone 1
Iris setosa and versicolor (no FIS result was recorded in this overlapping zone)
- Overlapping zone 2
Iris versicolor and virginica
- case i
FIS output < 0.65, indicates higher
Evaluation of results
Fig. 12 gives the analysis of the results of testing done using neutrosophic classifier in comparison to the results generated by fuzzy classifier. It particularly gives the result analysis of the values lying in ambiguous zone (values given by indeterminacy and falsity in neutrosophic logic and results lying in overlapping regions for fuzzy logic).
Results generated by FIS and NIS are labeled as follows:
- a.
Non-ambiguous: FIS results that lie in single output membership function indicate clear
Conclusions
As the proposed neutrosophic approach partitions the pattern space into non-overlapping decision regions for pattern classification so both the complexity and computational load of the classifier are reduced and thus the training time and classification time are extremely short. Although the decision regions are partitioned into non-overlapping subspaces, we can achieve good classification performance since the decision regions can be correctly determined via our proposed neutrosophic approach.
Future directions
Results shown in the paper are encouraging so in future proposed extension of fuzzy classifier that is neutrosophic classifier can be extended by exploring more complicated domains in which indeterminacy and falsity is tightly integrated in the data captured. If after detailed investigation strong correlation is found between human reasoning and neutrosophic classifier results then definitely a real time application exploiting neutrosophic logic can be developed; possibly replacing existing
A.Q. Ansari is working as a professor and HOD of the department of electrical engineering at Jamia Millia Islamia, New Delhi. His area of research and specialization are computer networking and data communication, image processing, networks on chip and soft computing.
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A.Q. Ansari is working as a professor and HOD of the department of electrical engineering at Jamia Millia Islamia, New Delhi. His area of research and specialization are computer networking and data communication, image processing, networks on chip and soft computing.
Ranjit Biswas is working as a professor in Department of Computer Science at Jamia Hamdard University, New Delhi. His areas of research and specialization are rough set technology & applications, fuzzy logic & applications, soft sets & systems, AI and graph theory.
Swati Aggarwal is a pursuing PhD at Jamia Millia Islamia, New Delhi. She has done BTech (computer science) in 2001 and MTech (IT) in 2005. Currently she is working as assistant professor in computer science department at ITM University, Gurgaon. Her interests include neutrosophic logic, fuzzy sets, artificial intelligence, neural network and soft computing.