Paired structures in knowledge representation

Bipolar disorder diagnosis with cubic bipolar fuzzy information using TOPSIS and ELECTRE-I

Bipolar disorder ([Formula: see text] ) is a neurodegenerative disease that consists of two main manifestations: mania and depression. In the clinical diagnosis of [Formula: see text], there are two primary components. First and foremost is itself [Formula: see text] which is often wrongly diagnosed as unipolar depression in clinical finding. This is so because in clinical diagnosis the first factor is often neglected due to its approach towards positivity. As a result, the element of bipolarity dies down, and the condition worsens. The second disadvantage is that [Formula: see text] is frequently misdiagnosed due to comparable indications and symptoms. To overcome these diagnosis issues, a cubic bipolar fuzzy set (CBFS) which comprises both bipolar fuzzy set (BFS) and interval-valued bipolar fuzzy set (IVBFS) is very helpful for clinical diagnosis of [Formula: see text] . A CBFS has the ability to handle bipolarity with suitable closed intervals to express positive and negative grades to build a solid numerical demonstrating interaction to analyze this disorder effectively. For these objectives, the algorithms of technique for the order of preference by similarity to positive ideal solution (TOPSIS) and elimination and choice translating reality (ELECTRE-I) for multi-criteria decision-making (MCDM) based on CBF information are developed. The application of proposed algorithms is presented for clinical diagnosis of [Formula: see text] . In order to discuss efficiency and validity of the proposed MCDM approaches, we apply the authenticity test for ranking of feasible alternatives and optimal decision by TOPSIS and ELECTRE-I. The comparison analysis of proposed MCDM approaches with existing techniques is also given.

Evaluation of the quality and relevance of a fuzzy partition

This paper proposes a couple of criteria for evaluating the quality and relevance of a fuzzy partition. These criteria are established from a fuzzy classification system and its recursive De Morgan triplet. We propose a comparison process between the classes of a fuzzy partition, based on a translation invariant similarity relation. Therefore a classification process is carried out with the equivalence relations determined by the similarity relation. Such a relation is built on the commutative group structure formed by the elements of the fuzzy classification system. Our approach is illustrated through an example on image analysis by the fuzzy c-means algorithm.

Bipolar fuzzy soft mappings with application to bipolar disorders

Bipolar disorder is a neurological disorder that consists of two main factors, i.e. mania and depression. There are two main drawbacks in clinical diagnosis of the bipolar disorder. First, bipolar disorder is mostly wrongly diagnosed as unipolar depression in clinical diagnosis. This is, because in clinical diagnosis, the first factor is often neglected due to its approach toward positivity. Consequently, the element of bipolarity vanishes and the disease becomes worse. Second, the types of bipolar disorder are mostly misdiagnosed due to similar symptoms. To overcome these problems, the bipolar fuzzy soft set (BFS-set) and bipolar fuzzy soft mappings (BFS-mappings) are useful to tackle bipolarity and to construct a strong mathematical modeling process to diagnose this disease correctly. This technique is extensive but simple as compared to existing medical diagnosis methods. A chart (relation between different types and symptoms of bipolar disorder) is provided which contains different ranges over the interval [Formula: see text]. A process of BFS-mappings is also provided to obtain correct diagnosis and to suggest the best treatment. Lastly, a generalized BFS-mapping is introduced which is helpful to keep patient’s improvement record. The case study indicates the reliability, efficiency and capability of the achieved theoretical results. Further, it reveals that the connection of soft set with bipolar fuzzy set is fruitful to construct a connection between symptoms which minimize the complexity of the case study.

A YinYang bipolar fuzzy cognitive TOPSIS method to bipolar disorder diagnosis

BACKGROUND AND OBJECTIVE

Bipolar disorder is often mis-diagnosed as unipolar depression in the clinical diagnosis. The main reason is that, different from other diseases, bipolarity is the norm rather than exception in bipolar disorder diagnosis. YinYang bipolar fuzzy set captures bipolarity and has been successfully used to construct a unified inference mathematical modeling method to bipolar disorder clinical diagnosis. Nevertheless, symptoms and their interrelationships are not considered in the existing method, circumventing its ability to describe complexity of bipolar disorder. Thus, in this paper, a YinYang bipolar fuzzy multi-criteria group decision making method to bipolar disorder clinical diagnosis is developed.

METHODS

Comparing with the existing method, the new one is more comprehensive. The merits of the new method are listed as follows: First of all, multi-criteria group decision making method is introduced into bipolar disorder diagnosis for considering different symptoms and multiple doctors' opinions. Secondly, the discreet diagnosis principle is adopted by the revised TOPSIS method. Last but not the least, YinYang bipolar fuzzy cognitive map is provided for the understanding of interrelations among symptoms.

RESULTS

The illustrated case demonstrates the feasibility, validity, and necessity of the theoretical results obtained. Moreover, the comparison analysis demonstrates that the diagnosis result is more accurate, when interrelations about symptoms are considered in the proposed method.

CONCLUSIONS

In a conclusion, the main contribution of this paper is to provide a comprehensive mathematical approach to improve the accuracy of bipolar disorder clinical diagnosis, in which both bipolarity and complexity are considered.