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...

In this note, we study an approximation property of regular fuzzy neural network(RFNN). It is shown that any fuzzy-valued measurable function can be approximated by the four-layer RFNN in the sense of fuzzy integral norm for the finite sub-additive fuzzy measure on R.

The goal of this paper is to consider properties of the composition of interval-valued fuzzy relations which were introduced by L.A. Zadeh in 1975. Fuzzy set theory turned out to be a useful tool to describe situations in which the data are imprecise or vague. Interval-valued fuzzy set theory is a generalization of fuzzy set theory which was introduced also by Zadeh in 1965. This paper generali...

Using order relations on the space of fuzzy numbers, we define the levels of fuzzy number valued mappings and we present some topologicals and geometrics properties. We use this concept to locate points and the set of points that solve a problem of fuzzy optimization. Consequently we obtain a necessary condition, for means of fuzzy integrals, for fuzzy global optimality.

The intuitionistic linguistic set (ILS) is an extension of linguisitc variable. To overcome the drawback of using single real number to represent membership degree and non-membership degree for ILS, the concept of interval-valued intuitionistic linguistic set (IVILS) is introduced through representing the membership degree and non-membership degree with intervals for ILS in this paper. The oper...

A fuzzy logic controller with interval-valued inference mechanism is presented for the control of distributed parameter system (DPS). Interval-valued fuzzy set, a special case of type-2 fuzzy set, is innovatively designed to cope with the spatial information of distributed parameter systems. The proposed fuzzy logic controller is composed of six modules: fuzzifier, fuzzy composition, rules, inf...

In this paper we study the relationships existing between total measurability in variation and Gould type fuzzy integrability (introduced and studied in [21]), giving a special interest on their behaviour on atoms and on finite unions of disjoint atoms. We also establish that any continuous real valued function defined on a compact metric space is totally measurable in the variation of a regula...

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the arithmetic and geometric aggregation operators with interval-valued dual hesitant fuzzy linguistic information. Then, motivated by the ideal of traditional arithmetic operation, we have developed some aggregation operators for aggregating interval-valued dual hesitant fuzzy linguistic information: i...

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued (∈,∈ ∨ q)-fuzzy filters of pseudo BL-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these ge...