and Applied Analysis 3 is Cauchy. If each Cauchy sequence is convergent, then the fuzzy norm is said to be complete, and the fuzzy normed space is called a fuzzy Banach space. Let X,N be a fuzzy normed space and Y,N ′ a fuzzy Banach space. For a given mapping f : X → Y , we use the abbreviation Df ( x, y ) : f ( 2x y ) f ( 2x − y 2f x − fx y − fx − y − 2f 2x , 2.1 for all x, y ∈ X. Recall Df ≡ ...

The research work presented in this paper proposes a data-driven modeling method for bearings remaining useful life estimation based on Takagi-Sugeno (T-S) fuzzy inference system (FIS). This allows identifying the parameters of classic T-S FIS, starting with small quantity data. In work, we used vibration signals data from number over an entire period run-to-failure. FIS model inputs are featur...

In this paper, a type of fuzzy system structure is applied to heuristic dynamic programming (HDP) algorithm to solve nonlinear discrete-time Hamilton–Jacobi–Bellman (DT-HJB) problems. The fuzzy system here is adopted as a 0-order T–S fuzzy system using triangle membership functions (MFs). The convergence of HDP and approximability of the multivariate 0-order T–S fuzzy system is analyzed in this...

Combining both kinds of fuzzy logic forms including fuzzy T-S model and adaptive fuzzy logic systems, this paper presents an adaptive control scheme for a class of nonlinear systems. Firstly, the fuzzy T-S model is used to approximate the nonlinear systems, and the fuzzy control law of the fuzzy model is derived by the linear matrix inequality. Secondly, the adaptive fuzzy logic systems are con...

In this paper, the notion of an interval valued intuitionistic fuzzy subsemiring (ideal) of a semiring with respect to t−norm T and s−norm S is given and the characteristic properties are described. The homomorphic image and inverse image are investigated. In particular, by the help of the congruence relations on semirings, new interval valued intuitionistic (S, T )−fuzzy subsemirings (ideals) ...

In this paper we have introduced a non interactive model for fuzzy rule based systems A critical aspects of this non interactive model is the introduction of a new set of rules with fewer parameters and without considering the interaction between the functionality of inputs The new non interactive model of the fuzzy rule based system represents the output as a linear combination of the non line...

Among the computational intelligence techniques employed to solve classification problems, Fuzzy Rule-Based Classification Systems (FRBCSs) are a popular tool because of their interpretable models based on linguistic variables, which are easier to understand for the experts or end-users. The aim of this paper is to enhance the performance of FRBCSs by extending the Knowledge Base with the appli...

compositional rule of inference to a fuzzy input X* E F ( X ) we obtain a fuzzy output Y* E F(Y): We propose an enhancement of MamY * = X * o T R , (1) dani fuzzy controllers. We tested it on l.e., a simple control task and verified that it outperforms the traditional approach. VY E Y : Y*(Y) = SUPT(X*(X),R(X,Y)) , (2) xEX

See the abstract for Chapter D1. Relatively early in neural network research there emerged an interest in analyzing and designing layered, feedforward networks augmented by some formalism stemming from the theory of fuzzy sets. One of B2.3 the first approaches was the fuzzification of the binary McCulloch–Pitts neuron (Lee and Lee 1975). B1.2 Then, several researchers looked at a typical feedfo...

This presentation may look like a glossary of the fusion rules and we also introduce new ones presenting their formulas and examples: Conjunctive, Disjunctive, Exclusive Disjunctive, Mixed Conjunctive-Disjunctive rules, Conditional rule, Dempster's, Yager's, Smets' TBM rule, Dubois-Prade's, Dezert-Smarandache classical and hybrid rules, Murphy's average rule, Inagaki-Lefevre-Colot-Vannoorenberg...