Bidirectional Approximate Reasoning Research Articles

A spherical fuzzy correlation coefficient based on statistical viewpoint with its applications in classification and bidirectional approximate reasoning

Spherical fuzzy sets are more powerful in modelling the uncertain situations than picture fuzzy sets, fermatean fuzzy sets, Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. In this paper, we first define the variance and covariance of spherical fuzzy sets. Then, using variance and covariance, we define the unique spherical fuzzy set correlation metric in line with the statistical coefficient of correlation. Two spherical fuzzy sets are correlated in both direction and strength using the provided measure of correlation. We discussed its many characteristics. We compared the measure of correlation with the current ones through linguistic variables. We established its validity by showing its application in bidirectional approximate reasoning. We also resolve a pattern identification issue in the spherical fuzzy environment using the provided correlation function, and we compare the results with several current measurements.

An Innovative Fermatean Fuzzy Distance Metric With its Application in Classification and Bidirectional Approximate Reasoning

An Innovative Fermatean Fuzzy Distance Metric With its Application in Classification and Bidirectional Approximate Reasoning

Enhancing multiple attribute group decision making flexibility based on information fusion technique and hesitant Pythagorean fuzzy sets

Abstract The aim of this paper is to develop some novel hesitant Pythagorean fuzzy sets (HPFSs) based methods in enhancing fuzzy related problems flexibility. In view of the effectiveness of hesitant fuzzy sets (HFSs) for expressing the hesitant situation, and the powerfulness of Pythagorean fuzzy sets (PFSs) in handling vagueness and uncertainty, we combine the best aspects of HFSs and PFSs and consider a new concept called the HPFSs. Firstly, some existing basic properties and operators are extended and improved in detail. For the sake of application, considering the deficiencies of pessimistic-optimistic normalization principles in dealing with hesitant fuzzy related sets, on the basis of lowest common multiple principle in number theory, an improved normalization algorithm is proposed to reserve the fidelity of original information. Then, a flexible and multipurpose generalized distance measure for HPFSs is presented. Further, under the HPFSs environment, a multiple attribute group decision making method based on the extended hesitant Pythagorean fuzzy VIKOR is presented. Three numerical examples, one from the bidirectional approximate reasoning system and other from the medical diagnosis and selection model of health management center, are presented to elaborate on the performance of our approach and compared their results with the several existing approaches results.

Dual hesitant fuzzy matrix games: based on new similarity measure

The dual hesitant fuzzy set is an effective mathematical approach to deal with the data which are imprecise, uncertain or incomplete information. Dual hesitant fuzzy set is an extension of hesitant fuzzy set which encloses fuzzy set, intuitionistic fuzzy set and hesitant fuzzy set as a special one. In this paper, the axiomatic definition of similarity measure between the dual hesitant fuzzy set is presented. A new similarity measure by considering membership and non-membership functions of dual hesitant fuzzy set is introduced. It is shown that the corresponding distance measure can be obtained from the proposed similarity measure. To check the utility, the proposed similarity measure is applied in a bidirectional approximate reasoning system into matrix game. Matrix game with precise data is hardly applicable in real-life decision-making problem. In view of more realistic sense, we choose the elements as dual hesitant fuzzy into the payoff of the matrix game, which is treated as dual hesitant fuzzy matrix game. Mathematical formulation of dual hesitant fuzzy matrix game with on restriction (DHFMGR) is described. Four algorithms are emerged on the proposed similarity measure, which are provoked to find the optimal value of the DHFMGR. A numerical example is incorporated to illustrate the applicability and feasibility of the proposed measure in dual hesitant fuzzy matrix game. The paper ends with the conclusions including an outlook for future study in this direction.

Correlation coefficients for picture fuzzy sets

Picture fuzzy sets are extension of Atanassov's intuitionistic fuzzy sets. Picture fuzzy set based models may be adequate in situations when we face human opinions involving more answers of types: yes, abstain, no, refusal. It can be considered as a powerful tool represent an uncertain information in the process of cluster analysis. In this paper, we present a geometrical interpretation of picture fuzzy sets. We propose correlation coefficients for picture fuzzy sets which considers the degree of positive membership, degree of neutral membership, degree of negative membership and the degree of refusal membership. Effectiveness of the proposed correlation coefficient has been established in a bidirectional approximate reasoning systems. We apply the correlation coefficient to clustering analysis under picture fuzzy environments. Advantages of proposed correlation coefficients and drawbacks of existing correlation coefficients have been discussed.

A new method for solving dual hesitant fuzzy assignment problems with restrictions based on similarity measure

Zhu et al. (2012) proposed dual hesitant fuzzy set as an extension of hesitant fuzzy sets which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as a special case. Dual hesitant fuzzy sets consist of two parts, that is, the membership and nonmembership degrees, which are represented by two sets of possible values. Therefore, in accordance with the practical demand these sets are more flexible, and provides much more information about the situation. In this paper, the axiom definition of a similarity measure between dual hesitant fuzzy sets is introduced. A new similarity measure considering membership and nonmembership degrees of dual hesitant fuzzy sets has been presented and also it is shown that the corresponding distance measures can be obtained from the proposed similarity measures. To check the effectiveness, the proposed similarity measure is applied in a bidirectional approximate reasoning systems. Mathematical formulation of dual hesitant fuzzy assignment problem with restrictions is presented. Two algorithms based on the proposed similarity measure, are developed to finds the optimal solution of dual hesitant fuzzy assignment problem with restrictions. Finally, the proposed method is illustrated by numerical examples.

Approximate reasoning algorithm of interval-valued fuzzy sets based on least square method

In this paper, we develop a new method for bidirectional approximate reasoning of interval-valued fuzzy sets by employing least squares method and investigate some properties for our proposed approximate reasoning method. Furthermore, we use four numerical examples to illustrate our proposed method reasonable.

A new similarity measure between interval-valued intuitionistic fuzzy sets

Interval-valued intuitionistic fuzzy sets gained attention from researcher for their applications in various field. The main of this paper is to propose a new similarity measure for interval-valued intuitionistic fuzzy sets. Some properties of proposed similarity measure has been presented this paper. Also the proposed and existing similarity measure are compared to show that the proposed similarity measure is more reasonable than some of the existing similarity measures. For practical use, proposed similarity measure is applied to pattern recognition and in a bidirectional approximate reasoning systems.

Adaptive self-organized maps based on bidirectional approximate reasoning and its applications to information filtering

Similarity measuring is one substantial part in self-organizing maps (SOM) for its direct influence on the mapping results. The common used similarity measuring method – Euclidean distance cannot always express the exact similarity. In this paper, a novel adaptive self-organized maps based on bidirectional approximate reasoning (ASOMBAR) is proposed to improve the competitive and cooperative process based on the similarity measuring. Unlike the SOM, the proposed ASOMBAR employs the novel fuzzy similarity distance and fuzzy matching criterion to replace the Euclidean distance and original matching criterion, respectively. The fuzzy similarity distance describes the similarity relation more precisely than the Euclidean distance does. The fuzzy matching criterion pays more attention on the large weighted elements and less emphasis on the small weighted elements. Moreover, the new compatible topological neighborhood is also modified basing on the new fuzzy similarity distance and fuzzy matching criterion. Since the ASOMBAR network is self-organizing, the weights of the networks change adaptively according to the input changes. Compared with the well-known growing neural gas (GNG) and SOM, ASOMBAR (when λ ⩾ 0.5) converges quicker to a smaller distortion error. An information filtering example is used to show the effectiveness of ASOMBAR.

A similarity-based bidirectional approximate reasoning method for decision-making systems

This paper presents a similarity-based bidirectional approximate reasoning method which can express the decision maker's disposition. For this, we shall propose a new type of similarity measure based on the ordered weighted aggregation (OWA) operator. The proposed similarity measure has a structure to involve the disposition of a decision maker by choosing a suitable weighting vector of the OWA operator. From this property, we derive a simple and flexible type of similarity-based bidirectional approximate reasoning method which can support the making of a decision under more complex situations such as industrial inspection systems for example.

Bidirectional approximate reasoning for rule-based systems using interval-valued fuzzy sets

In this paper, we extend the work of Chen et al. [Fuzzy Sets and Systems 91 (1997) 339–353] to present a new method to deal with bidirectional approximate reasoning for rule-based systems based on the direction of matching between interval-valued fuzzy sets. We also use some examples to illustrate the bidirectional approximate reasoning process. Because the proposed method can perform bidirectional approximate reasoning based on the direction of matching between interval-valued fuzzy sets, it is more reasonable and more powerful than the one presented in Chen et al., Fuzzy Sets and Systems 91 (1997) 339–353. The proposed method can provide a useful way to deal with bidirectional approximate reasoning for rule-based systems using interval-valued fuzzy sets.

Bidirectional approximate reasoning based on interval-valued fuzzy sets

This paper proposes a bidirectional approximate reasoning method based on interval-valued fuzzy sets, where fuzzy production rules are used for knowledge representation, and the fuzzy terms appearing in the fuzzy production rules of a rule-based system are represented by interval-valued fuzzy sets. The proposed method is more flexible than the one presented in the paper by Bien and Chun [IEEE Trans. Fuzzy Systems 2 (1994) 177] due to the fact that it allows the fuzzy terms appearing in the fuzzy production rules of a rule-based system to be represented by interval-valued fuzzy sets rather than general fuzzy sets. Furthermore, because the proposed method requires only simple arithmetic operations, and because it allows bidirectional approximate reasoning, it can be executed much faster and more flexible than the single-input-single-output approximate reasoning scheme presented in the paper by Gorzalczany [Fuzzy Sets and Systems 21 (1981) 10].

An inference network for bidirectional approximate reasoning based on an equality measure

An inference network is proposed as a tool for bidirectional approximate reasoning. The inference network can be designed directly from the given fuzzy data (knowledge). If a fuzzy input is given for the inference network, then the network renders a reasonable fuzzy output after performing approximate reasoning based on an equality measure. Conversely, due to the bidirectional structure, the network can yield its corresponding reasonable fuzzy input for a given fuzzy output. This property makes it possible to perform forward and backward reasoning in the knowledge base system. >