Membership function

About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.

Isomorphic Multiplicative Transitivity for Intuitionistic and Interval-Valued Fuzzy Preference Relations and Its Application in Deriving Their Priority Vectors

Abstract: Intuitionistic fuzzy preference relations (IFPRs) are used to deal with hesitation, while interval-valued fuzzy preference relations (IVFPRs) are for uncertainty in multicriteria decision making (MCDM) This paper aims to explore the isomorphic multiplicative transitivity for IFPRs and IVFPRs, which builds the substantial relationship between hesitation and uncertainty in MCDM To do that, the definition of the multiplicative transitivity property of IFPRs is established by combining the multiplication of intuitionistic fuzzy sets and Tanino's multiplicative transitivity property of fuzzy preference relations It is proved to be isomorphic to the multiplicative transitivity of IVFPRs derived via Zadeh's extension principle The use of the multiplicative transitivity isomorphism is twofold: 1) to discover the substantial relationship between IFPRs and IVFPRs, which will bridge the gap between hesitation and uncertainty in MCDM problems; and 2) to strengthen the soundness of the multiplicative transitivity property of IFPRs and IVFPRs by supporting each other with two different reliable sources, respectively Furthermore, based on the existing isomorphism, the concept of multiplicative consistency for IFPRs is defined through a strict mathematical process, and it is proved to satisfy the following several desirable properties: weak transitivity, max–max transitivity, and center-division transitivity A multiplicative consistency-based multiobjective programming (MOP) model is investigated to derive the priority vector from an IFPR This model has the advantage of not losing information, as the priority vector representation coincides with that of the input information, which was not the case with the existing methods, where crisp priority vectors were derived as a consequence of the modeling transitivity just for the intuitionistic membership function and not for the intuitionistic nonmembership function Finally, a numerical example concerning green supply selection is given to validate the efficiency and practicality of the proposed multiplicative consistency MOP model

Using statistical viewpoint in developing correlation of intuitionistic fuzzy sets

Abstract: In this paper, we propose a method to calculate the correlation coefficient of intuitionistic fuzzy sets by means of mathematical statistics. This value obtained from our formula tell us not only the strength of relationship between the intuitionistic fuzzy sets, but also whether the intuitionistic fuzzy sets are positively or negatively related. This approach looks better than previous methods which only evaluate the strength of the relation. Furthermore, we extend the proposed method to interval-valued intuitionistic fuzzy sets. The value of the correlation coefficient between interval-valued intuitionistic fuzzy sets lies in the interval [-1, 1], as computed from our formula.

Input-to-State Stabilization of Interval Type-2 Fuzzy Systems Subject to Cyberattacks: An Observer-Based Adaptive Sliding Mode Approach

Abstract: This paper focuses on the sliding mode control (SMC) problem of interval type-2 (IT2) fuzzy systems subject to the unmeasurable state and cyberattacks. A key issue is how to design a state observer under the constraint that only the bounds of membership functions are known. To this end, this paper introduces two weighting factors to construct a new membership function. Besides, the concept of input-to-state stability (ISS) is utilized to deal with the residual term resulting from the cyberattacks and external disturbances. The sufficient condition is established such that the sliding mode dynamics and the estimated error dynamics are input-to-state stable. Furthermore, by online estimating the unknown parameters in upper bounds of cyberattacks and external disturbances, an adaptive sliding mode controller is synthesized such that the reachability of the prescribed sliding surface can be guaranteed and the effect of cyberattacks on the system performance can be effectively attenuated. Finally, the validity of the proposed method is illustrated by a mass–spring–damper system.