Sujit Das

Review Article: Applications of neuro fuzzy systems: A brief review and future outline

This paper surveys neuro fuzzy systems (NFS) development using classification and literature review of articles for the last decade (2002-2012) to explore how various NFS methodologies have been developed during this period. Based on the selected journals of different NFS applications and different online database of NFS, this article surveys and classifies NFS applications into ten different categories such as student modeling system, medical system, economic system, electrical and electronics system, traffic control, image processing and feature extraction, manufacturing and system modeling, forecasting and predictions, NFS enhancements and social sciences. For each of these categories, this paper mentions a brief future outline. This review study indicates mainly three types of future development directions for NFS methodologies, domains and article types: (1) NFS methodologies are tending to be developed toward expertise orientation. (2) It is suggested that different social science methodologies could be implemented using NFS as another kind of expert methodology. (3) The ability to continually change and learning capability is the driving power of NFS methodologies and will be the key for future intelligent applications.

Group decision making in medical system

Group decision making for medical diagnosis.Intuitionistic fuzzy soft set and fuzzy soft matrix.Hamming distance and Euclidean approach.Cardinal of intuitionistic fuzzy soft set to compute the weight.Viral fever related diagnosis. In medical system, there may be many critical diseases, where experts do not have sufficient knowledge to handle those problems. For these cases, experts may provide their opinion only about certain aspects of the disease and remain silent for those unknown features. Feeling the need of prioritizing different experts based on their given information, this article uses a novel concept for assigning confident weights to different experts which are mainly based on their provided information. Experts provide their opinions about various symptoms using intuitionistic fuzzy soft matrix (IFSM). In this article, we propose an algorithmic approach based on intuitionistic fuzzy soft set (IFSS) which explores a particular disease reflecting the agreement of all experts. This approach is guided by the group decision making (GDM) model and uses cardinals of IFSS as novel concept. We have used choice matrix (CM) as an important parameter which is based on choice parameters of individual expert. This article has also validated the proposed approach using distance measurements and consents of the majority of experts. The effectiveness of the proposed approach is demonstrated using a suitable case study.

Hypertension diagnosis: A comparative study using fuzzy expert system and neuro fuzzy system

Hypertension is called the silent killer because it has no symptoms and can cause serious trouble if left untreated for a long time. It has a major role for stroke, heart attacks, heart failure, aneurysms of the arteries, peripheral arterial diseases, chronic kidney disease etc. An intelligent and accurate diagnostic system is mandatory for better diagnosis and treatment of hypertension patients. This study develops a fuzzy expert system to diagnose the hypertension risk for different patients based on a set of symptoms and rules. Next we design a neuro fuzzy system for the same set of symptoms and rules using three different types of learning algorithms which are Levenberg-Marquardt (LM), Gradient Descent (GD) and Bayesian Resolution (BR) based learning functions. Then this paper presents a comparative study between fuzzy expert system (FES) and feed forward back propagation based neuro fuzzy system (NFS) for hypertension diagnosis. This paper also presents a comparison among the learning functions (LM, GD and BR) where Levenberg-Marquardt based learning function shows its efficiency over the others. Comparison between FES and NFS shows the effectiveness of using NFS over FES. Here, the input data set has been collected from 10 patients whose ages are between 20 and 40 years, both for male and female. The input parameters taken are age, body mass index (BMI), blood pressure (BP), and heart rate. The diagnosis process, linguistic variables and their values were modeled based on experts knowledge and from existing database.

Group multi-criteria decision making using intuitionistic multi-fuzzy sets

In this paper we propose an efficient approach for group multi-criteria decision making (MCDM) based on intuitionistic multi-fuzzy set (IMFS). First we construct intuitionistic multi-fuzzy matrices for decision makers with respect to the criteria (attributes) of the alternatives. Based on intuitionistic multi-fuzzy matrices, we construct the aggregated intuitionistic multi-fuzzy matrix using the proposed intuitionistic multi-fuzzy weighted averaging (IMFWA) operator. Then we use Hamming distance and Euclidean distance measurements in the context of IMFS between the aggregated matrix and the specified sample matrix to reach the optimal decision. This paper also presents score function and accuracy function of IMFS with an application to MCDM. Finally, a real-life case study related to heart disease diagnosis problem is provided to illustrate the advantage of the proposed approach.

The Hesitant Fuzzy Soft Set and Its Application in Decision-Making

This article introduces the concept of hesitant fuzzy soft set (HFSS) by combining Torra’s (2010) hesitant fuzzy set and Molodtsov’s (1999) soft set theory. In order to handle uncertain and imprecise situation especially in medical diagnosis hesitant fuzzy soft sets are found to be more useful. This article investigates a couple of distance measurements procedures and aggregation operators applicable for HFSS. An algorithmic approach is proposed to solve multiple attribute decision-making (MADM) problems using HFSS with the help of aggregation operators and hesitant fuzzy soft matrix (HFSM). Finally, an illustrative example is presented to analyze the proposed approach.

Multiple attribute group decision making using interval-valued intuitionistic fuzzy soft matrix

A noticeable progress has been found in decision making problems since the introduction of soft set theory by Molodtsov in 1999. It is found that classical soft sets are not suitable to deal with imprecise parameters whereas fuzzy soft sets (FSS) are proved to be useful. Use of intuitionistic fuzzy soft sets (IFSS) is more effective in environment, where arguments are presented using membership and non-membership values. In this paper we propose an algorithmic approach for multiple attribute group decision making problems using interval-valued intuitionistic fuzzy soft matrix (IVIFSM). IVIFSM is the matrix representation of interval-valued intuitionistic fuzzy soft set (IVIFSS), where IVIFSS is a natural combination of interval-valued intuitionistic fuzzy set and soft set theory. Firstly, we propose the concept of IVIFSM. Then an algorithm is developed to find out the desired alternative(s) based on product interval-valued intuitionistic fuzzy soft matrix, combined choice matrix, and score values of the set of alternatives. Finally, a practical example has been demonstrated to show the effectiveness of the proposed algorithm.

Intuitionistic Multi Fuzzy Soft Set and its Application in Decision Making

Soft set theory initiated by Molodtsov in 1999 has been emerging as a generic mathematical tool for dealing with uncertainty. A noticeable progress is found concerning the practical use of soft set in decision making problems. This paper introduces the concept of intuitionistic multi fuzzy soft set (IMFSS) by combining the intuitionistic multi fuzzy set (IMFS) and soft set models. Then an algorithmic approach is presented by using induced fuzzy soft set and level soft set for dealing with decision making problem based on IMFSS. Finally the proposed algorithm has also been illustrated through a numerical example.

Triangular fuzzy soft set and its application in MADM

The purpose of this paper is to extend the classical soft set to triangular fuzzy soft set (TFSS) based on triangular fuzzy numbers (TFNs). In uncertain environment, TFNs have an important role for converting linguistic information into numerical values. This study firstly converts the multi-fuzzy soft set (MFSS) into fuzzy soft set (FSS) using the attribute weight information. We use TFN to convert the FSS into TFSS. This study defines some useful operations and properties of TFSSs. We also propose an algorithmic approach for multiple attribute decision making (MADM) problem based on MFSS and TFSS. Finally, a numerical example has been demonstrated to validate the proposed approach.

Correlation measure of hesitant fuzzy soft sets and their application in decision making

Hesitant fuzzy soft set (HFSS) allows each element to have different number of parameters and the values of those parameters are represented by multiple possible membership values. HFSS is considered as a powerful tool to represent uncertain information in group decision-making process. In this study, we introduce the concept of correlation coefficient for HFSS and some of its properties. Using correlation coefficient of HFSS, we develop correlation efficiency which shows the significance of the HFSS. We also propose an algorithm to apply correlation coefficient in decision-making problem, where information is presented in hesitant fuzzy environment. In order to extend the application of HFSS, we propose correlation coefficient in the framework of interval-valued hesitant fuzzy soft set (IVHFSS). We also introduce correlation efficiency in the context of IVHFSS. Then the proposed algorithm is extended using IVHFSS for solving decision-making problems. Finally, two examples that are semantically meaningful in real life are illustrated to show the effectiveness of the proposed algorithms.

Parameter Reduction of Intuitionistic Fuzzy Soft Sets and Its Related Algorithms

Contribution of intuitionistic fuzzy soft set (IFSS) in uncertain real-life applications is inevitable. Computation with IFSS may be complicated by the use of less important parameters. However, there has been a little focus on parameter reduction of IFSSs. In this paper, we introduce two different parameter reduction algorithms in IFSSs to satisfy the different needs of decision makers. The first algorithm is based on selection of a set of parameters whose combined contribution is less important in the decision-making process. The second approach selects parameter(s) which has less deviation in comparison to the other parameters. Finally, the proposed algorithms have been demonstrated using illustrative numerical examples. This study also preserves the decision abilities while reducing the redundant parameters.