A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators

An It2fs Model for Sharia Credit Scoring: Analysis & Design

Credit scoring system is a classic problem which is still interesting to study. There are many studies on credit scoring. But, most of them only discuss feasibility analysis. In fact, credit scoring system should accommodate all processes from feasibility analysis until the end of contract. This study is aimed to analyze and design scoring of default status and fines computation processes in Islamic bank. BPMN 2.0 was used to model their processes. Beside that, this study proposed new mechanisms and algorithms using Interval Type-2 Fuzzy Sets for maintaining Sharia rules and fairness guarantee. The results showed that the new methods offer more fair and comply to sharia than existing methods

Measuring agreement on linguistic expressions in medical treatment scenarios

Quality of life assessment represents a key process of deciding treatment success and viability. As such, patients’ perceptions of their functional status and well-being are important inputs for impairment assessment. Given that patient completed questionnaires are often used to assess patient status and determine future treatment options, it is important to know the level of agreement of the words used by patients and different groups of medical professionals. In this paper, we propose a measure called the Agreement Ratio which provides a ratio of overall agreement when modelling words through Fuzzy Sets (FSs). The measure has been specifically designed for assessing this agreement in fuzzy sets which are generated from data such as patient responses. The measure relies on using the Jaccard Similarity Measure for comparing the different levels of agreement in the FSs generated. Synthetic examples are provided in order to show how to calculate the measure for given Fuzzy Sets. An application to real-world data is provided as well as a discussion about the results and the potential of the proposed measure

Employing an Enhanced Interval Approach to encode words into Linear General Type-2 fuzzy sets for Computing With Words applications

In 1996, Zadeh coined Computing With Words (CWWs) to be a methodology in which words are used instead of numbers for computing and reasoning. One of the main challenges which faced the CWWs paradigm has been modelling words adequately. Mendel has pointed out that the CWWs paradigm should employ type-2 fuzzy logic to model words. This paper proposes employing an Enhanced Interval Approach (EIA) to create Linear General Type-2 (LGT2) fuzzy sets from Interval Type-2 (IT2) fuzzy sets to encode words for CWWs applications. We have performed experiments on 18 words belonging to 3 different linguistic variables (having 6 linguistic terms each). Interval data has been collected from 17 subjects and 18 linguistic terms have been modeled with IT2 fuzzy sets using EIA. The proposed conversion approach uses several key points within the parameters of IT2 fuzzy sets to redesign the linguistic variable using LGT2 fuzzy sets. Both IT2 and LGT2 fuzzy sets have been evaluated within a CWWs Framework, which aims to mimic the ability of humans to communicate and manipulate perceptions via words. The comparison results show that LGT2 fuzzy sets can be better than IT2 fuzzy sets in mimicking human reasoning as well as learning and adaptation since the progressive Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE) values for LGT2 based CWWs Framework converge faster and are lower than those for IT2 based CWWs Framework