For discrete-time Takagi–Sugeno (TS) fuzzy systems, we propose an state-feedback fuzzy controller associated with a fuzzy weighting-dependent Lyapunov function. The controller, which is designed via parameterized linear matrix inequalities (PLMIs), employs not only the current-time but also the one-step-past information on the time-varying fuzzy weighting functions. Appropriately selecting the ...

In this study, we apply a recently developed idea of up and down fuzzy-ordered relations between two fuzzy numbers. Here, consider Riemann–Liouville fractional integrals to establish the Hermite–Hadamard-, Fejér-, Pachpatte-type inequalities. We estimate inequalities for newly introduced class ?-preinvexity over fuzzy-number valued settings. For first time, such involving functions are proven u...

Recently, the study of fuzzy integral inequalities has gained much attention. The most popular method is using the Sugeno integral 1 . The study of inequalities for Sugeno integral was initiated by Román-Flores et al. 2, 3 and then followed by the others 4–11 . Now, we introduce some basic notation and properties. For details, we refer the reader to 1, 12 . Suppose that Σ is a σ-algebra of subs...

The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity....

evaluative and comparative analysis among educational projects remains an issue for administration, program directors, instructors, and educational institutes. this study reports a fuzzy complexity model for educational projects, which has two primary aspects (technical aspects and transparency aspects). these aspects may not be measured precisely due to uncertain situations. therefore, a fuzzy...

In the process of decision making, the decision makers usually provide inconsistent fuzzy preference relations, and it is unreasonable to get the priority from an inconsistent preference relation. In this paper, we propose a method to derive the multiplicative consistent fuzzy preference relation from an inconsistent fuzzy preference relation. The fundamental characteristic of the method is tha...

This paper further investigates the data compression of fuzzy relation information systems. First, we introduce an algorithm for constructing the homomorphism between fuzzy relation information systems. Then, we discuss that how to compress the dynamic fuzzy relation information systems by utilizing the compression of the original systems. Afterwards, several illustrative examples are employed ...

We prove necessary and sufficient conditions for the validity of Jensen type inequalities for generalized Sugeno integral. Our proofs make no appeal to the continuity of neither the fuzzy measure nor the operators. For several choices of operators, we characterize the classes of functions for which the corresponding inequalities are satisfied.

One of the important application areas of information theoretic measures is the development of some inequalities frequently used in information theory. The present communication deals with the development of such important inequalities through the maximization of entropy measures, especially while dealing with fuzzy distributions.

This paper deals with the joint verification of the inequalities of Modus Ponens and Modus Tollens in Fuzzy Logic. Although the case of Modus Ponens was partially considered before, the case of Modus Tollens and the joint satisfaction of both inequalities are studied by the first time. The cases of R-implications, Simplications, Q-implications and MamdaniLarsen implications are separatedly cons...