Endpoint results are presented for multi{valued cyclic contraction mappings on complete metric spaces (X; d). Our results extend previous results given by Nadler (1969), Da er{Kaneko (1995), Harandi (2010), Moradi and Kojasteh (2012) and Karapinar (2011).

Introducing more types of integrals will provide more choices to deal with various types of objectives and components in real problems. Firstly, in this paper, a (T) fuzzy integral, in which the integrand, the measure and the integration result are all multi-valued, is presented with the introduction of T-norm and T-conorm. Then, some classical results of the integral are obtained based on the properties of T-norm and T-conorm mainly. The presented integral can act as an aggregation tool which is especially useful in many information fusing and data mining problems such as classication and programming.

In this paper, a fractional multi-objective multiproduct solid transportation problem with interval costs, supply, demand, and conveyances is investigated based on fuzzy programming approach. To minimize the problem, the order relations that represent the decision maker's (DM) performance between interval costs, supply, demand and conveyances are defined by the right limit, and the left limit. Through the deterministic problem is obtained, a fuzzy programming approach is applied by defining membership functions. A linear membership function is being used for obtaining optimal compromise solution. Finally, a numerical example is given to the utility of the approach.

Extremely efficient successor and predecessor circuits are suggested in this article using 4 CNTFETs. They have much less interconnections and complexity compared to the best previous circuits. The proposed circuits are designed by combining digital and analog techniques for the first time. They can be expanded for all MVLs like ternary, quaternary, pentaternary, and so on. The proposed designs for quaternary logic reduce the transistor count from 25 to 4 in comparison with the best previous works. Interestingly, in MVLs with more level logics, this difference will increase dramatically. This advantage leads to low complexity and costs. The accurate operation and great performance of introduced circuits are illustrated and their superiority is proved. Additionally, a quaternary half adder is founded on the presented successor and predecessor. The simulation results, which are acquired by comprehensive simulations utilizing Synopsys HSPICE and the 32 nm plenary CNTFET model of Stanford, show that proposed successor and predecessor circuits with only four transistors work accurately. According to these outcomes, in the proposed half-adder, not only the transistor count reduces 32%, but also it has 40% better PDP and 42.05% better EDP in comparison with the best previous work. Also it is more stable against process variation and robust in a wide range of temperature variation.

In this article, we delve into the concept of convexity within fuzzy metric spaces and delve into their structural characteristics. We present several theorems concerning the existence of coincidence points in fuzzy convex metric spaces. Furthermore, we introduce the notion of star-shaped subsets within fuzzy convex metric spaces. Within these star-shaped subsets, we showcase various fixed point theorems for mappings of the non-expansive type that commute. In the final section, we expand the definition of fuzzy convex metric spaces and provide a significant example of such a space. Additionally, we uncover specific fixed point theorems applicable to multi-valued mappings that are non-expansive.