Iranian journal of fuzzy systems
Volume:15 Issue: 3, May-June 2018

This work applies fuzzy sets to the integration of purchasing, manufacturing and assembling of production planning decisions with multiple suppliers, multiple components and multiple machines in remanufacturing systems. The developed fuzzy multi-objective linear programming model (FMOLP) simultaneously minimizes total costs, total $\text{CO}_2$ emissions and total lead time with reference to customer demand, due date, supplier/manufacturer capacity, lot-size release and machine yield. The proposed FMOLP model provides a recoverable remanufacturing framework that facilitates fuzzy decision-making, enabling the decision maker (DM) to adjust interactively the membership function or parameters during the solution procedure to obtain a preferred and satisfactory solution. To test the model, it was implemented in various scenarios with a remanufacturing production system. The analytical results in this work can help planner by enabling systematic analysis of the cost-effectiveness of remanufacturing systems and their potential for improving $\text{CO}_2$ emissions and lead time in terms of remanufacturing planning. Future investigations may apply the related patterns of non-linear membership functions to develop an actual remanufacturing planning decision.

In this paper, we study fuzzy calculus in two main branches differential and integral. Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating $gH$-derivative of a composite function. Two techniques namely, Leibniz's rule and integration by parts are introduced for fuzzy integrals. Furthermore, we prove three essential theorems such as a fuzzy intermediate value theorem, fuzzy mean value theorem for integral and mean value theorem for $gH$-derivative. We derive a Bolzano's theorem, Rolle's theorem and some properties for $gH$-differentiable functions. To illustrate and explain these rules and theorems, we have provided several examples in details.

Intervals are related to the representation of uncertainty. In this sense, we introduce an integral of Gould type for an interval-valued multifunction relative to an interval-valued set multifunction, with respect to Guo and Zhang order relation. Classical
and specific properties of this new type of integral are established and several examples and applications from multicriteria decision making problems are provided.

We study here $T_{0}$-$Q$-bitopological spaces and sober $Q$-bitopological spaces and their relationship with two particular Sierpinski objects in the category of $Q$-bitopological spaces. The epireflective hulls of both these Sierpinski objects in the category of $Q$-bitopological spaces turn out to be the category of $T_0$-$Q$-bitopological spaces. We show that only one of these Sierpinski objects is sober $Q$-bitopological space and its epireflective hull in the category of $T_0$-$Q$-bitopological spaces turns out to be the category of saturated $T_{0}$-$Q$-bitopological spaces.

The main purpose of this paper is to use a new way to extend fuzzy implications $I$ from a generalized sublattice $M$ to a bounded lattice $L$, such that the extended implications preserve many of the considered properties of fuzzy implications on $M$.
Furthermore, as a special case, we investigate the extension of $(S,N)-$implications. Results indicate that the extended implications preserve many of the considered properties of $(S,N)$-implications.

In this paper, an adaptive fuzzy tracking control approach is proposed for a class of single-input single-output (SISO) nonlinear systems in which the unknown continuous functions may be nonlinearly parameterized. During the controller design procedure, the fuzzy logic systems (FLS) in Mamdani type are applied to approximate the unknown continuous functions, and then, based on the minimal learning parameters (MLP) algorithm and the adaptive backstepping dynamic surface control (DSC) technique, a new adaptive fuzzy backstepping control scheme is developed. The main advantages of our approach include: (i) unlike the existing results which deal with the nonlinearly parameterized functions by using the separation principle, the nonlinearly parameterized functions are lumped into the continuous functions which can be approximated by using the FLS, (ii) only one parameter needs to be adjusted online in controller design procedure, which reduces the online computation burden greatly, and our development is able to eliminate the problem of ''explosion of complexity" inherent in the existing backstepping-based methods. It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound. Finally, two examples are used to show the effectiveness of the proposed approach.

Fuzzy risk analysis, as a powerful tool to address uncertain information, can provide an appropriate method for risk analysis. However, the previous fuzzy risk analysis methods still have some weaknesses. To overcome the weaknesses of existing fuzzy risk analysis methods, a novel method for ranking generalized fuzzy numbers is proposed for addressing fuzzy risk analysis problems. In the proposed method, a new value of ranking score is obtained based on ordered weighted averaging (OWA) operator. The proposed method takes into consideration of the different importance of the three scoring factors defuzzified value, height and spread. Comparing to some existing methods, the new method can get more reasonable results in some situations.

The main purpose of this study is to discuss the uniform boundedness principle in fuzzifying topological linear spaces. At first the concepts of uniformly boundedness principle and fuzzy equicontinuous family of linear operators are proposed, then the relations between fuzzy equicontinuous and uniformly bounded are studied, and with the help of net convergence, the characterization of fuzzy equicontinuous is proved. Finally, the famous theorem of the uniform boundedness principle is presented in fuzzifying topological linear spaces.

This paper deals with the problem of testing statistical hypotheses when the available data are fuzzy. In this approach, we first obtain a fuzzy test statistic based on fuzzy data, and then, based on a new signed distance between fuzzy numbers, we introduce a new decision rule to accept/reject the hypothesis of interest. The proposed approach is investigated for two cases: the case without nuisance parameters and the case with nuisance parameters. This method is employed to test the hypotheses for the mean of a normal distribution with known/unknown variance, the variance of a normal distribution, the difference of means of two normal distributions with known/unknown variances, and the ratio of variances of two normal distributions.