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Register a new userA Novel Fuzzy Approximate Reasoning Method Based on Extended Distance Measure in SISO Fuzzy System
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Son-Il Kwak
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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This paper presents an original method of fuzzy approximate reasoning that can open a new direction of research in the uncertainty inference of Artificial Intelligence(AI) and Computational Intelligence(CI). Fuzzy modus ponens (FMP) and fuzzy modus tollens(FMT) are two fundamental and basic models of general fuzzy approximate reasoning in various fuzzy systems. And the reductive property is one of the essential and important properties in the approximate reasoning theory and it is a lot of applications. This paper suggests a kind of extended distance measure (EDM) based approximate reasoning method in the single input single output(SISO) fuzzy system with discrete fuzzy set vectors of different dimensions. The EDM based fuzzy approximate reasoning method is consists of two part, i.e., FMP-EDM and FMT-EDM. The distance measure based fuzzy reasoning method that the dimension of the antecedent discrete fuzzy set is equal to one of the consequent discrete fuzzy set has already solved in other paper. In this paper discrete fuzzy set vectors of different dimensions mean that the dimension of the antecedent discrete fuzzy set differs from one of the consequent discrete fuzzy set in the SISO fuzzy system. That is, this paper is based on EDM. The experimental results highlight that the proposed approximate reasoning method is comparatively clear and effective with respect to the reductive property, and in accordance with human thinking than existing fuzzy reasoning methods.
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This paper shows a novel fuzzy approximate reasoning method based on the least common multiple (LCM). Its fundamental idea is to obtain a new fuzzy reasoning result by the extended distance measure based on LCM between the antecedent fuzzy set and the consequent one in discrete SISO fuzzy system. The proposed method is called LCM one. And then this paper analyzes its some properties, i.e., the reductive property, information loss occurred in reasoning process, and the convergence of fuzzy control. Theoretical and experimental research results highlight that proposed method meaningfully improve the reductive property and information loss and controllability than the previous fuzzy reasoning methods.
The pythagorean fuzzy set (PFS) which is developed based on intuitionistic fuzzy set, is more efficient in elaborating and disposing uncertainties in indeterminate situations, which is a very reason of that PFS is applied in various kinds of fields. How to measure the distance between two pythagorean fuzzy sets is still an open issue. Mnay kinds of methods have been proposed to present the of the question in former reaserches. However, not all of existing methods can accurately manifest differences among pythagorean fuzzy sets and satisfy the property of similarity. And some other kinds of methods neglect the relationship among three variables of pythagorean fuzzy set. To addrees the proplem, a new method of measuring distance is proposed which meets the requirements of axiom of distance measurement and is able to indicate the degree of distinction of PFSs well. Then some numerical examples are offered to to verify that the method of measuring distances can avoid the situation that some counter? intuitive and irrational results are produced and is more effective, reasonable and advanced than other similar methods. Besides, the proposed method of measuring distances between PFSs is applied in a real environment of application which is the medical diagnosis and is compared with other previous methods to demonstrate its superiority and efficiency. And the feasibility of the proposed method in handling uncertainties in practice is also proved at the same time.
Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies $Delta^0_2$ sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice $L$ (e.g., the real interval $[0; 1]_mathbb{R}$). In this paper, we combine the Ershov Hierarchy and fuzzy set theory, by introducing and investigating the Fuzzy Ershov Hierarchy. In particular, we focus on the fuzzy $n$-c.e. sets which form the finite levels of this hierarchy. Intuitively, a fuzzy set is $n$-c.e. if its membership function can be approximated by changing monotonicity at most $n-1$ times. We prove that the Fuzzy Ershov Hierarchy does not collapse; that, in analogy with the classical case, each fuzzy $n$-c.e. set can be represented as a Boolean combination of fuzzy c.e. sets; but that, contrary to the classical case, the Fuzzy Ershov Hierarchy does not exhaust the class of all $Delta^0_2$ fuzzy sets.
Ranking of intuitionsitic fuzzy number plays a vital role in decision making and other intuitionistic fuzzy applications. In this paper, we propose a new ranking method of intuitionistic fuzzy number based on distance measure. We first define a distance measure for interval numbers based on Lp metric and further generalize the idea for intuitionistic fuzzy number by forming interval with their respective value and ambiguity indices. Finally, some comparative results are given in tabular form.
This paper presents a method to compute the degree of similarity between two aggregated fuzzy numbers from intervals using the Interval Agreement Approach (IAA). The similarity measure proposed within this study contains several features and attributes, of which are novel to aggregated fuzzy numbers. The attributes completely redefined or modified within this study include area, perimeter, centroids, quartiles and the agreement ratio. The recommended weighting for each feature has been learned using Principal Component Analysis (PCA). Furthermore, an illustrative example is provided to detail the application and potential future use of the similarity measure.
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