نشریه سیستم های فازی و کاربردها
سال ششم شماره 1 (پیاپی 12، بهار و تابستان 1402)

In many optimization problems, all decision-makers are not on the same level, but decision-makers may be placed in a hierarchical structure.‏ ‎Also, it is possible that the parameters of the problem are not stated crisp, but are presented in different types of fuzzy or interval. ‎In this study‎, ‎we considered ‎two‎ ‎‎‎state of the bilevel linear programming problems with ambiguity uncertainty.‎‏‎ In one of the problems, ‎all‎ the parameters were trapezoidal intuitionistic fuzzy numbers, and in the other, ‎all‎ the parameters were triangular intuitionistic fuzzy numbers. By using the proposed ranking method, we obtain the ‎‎‎bilevel linear programming problem corresponding to each state, which is solved by the usual methods.

The interpretation of logical connectives in continuous t-norm based fuzzy logics are not necessarily continuous. Recently two topologies are introduced on the sets [0,1] and [0,1]^2 where the interpretation of all logical connective under these topologies are continuous. In this paper, firstly we study some of the properties of these topologies and then besides the ideas of the first-order continuous logic, we introduce first-order continuous fuzzy logic based on a continuous t-norms and finally it is shown that the interpretation of any formula in this logic is a continuous function.

In this paper, we introduce and study the different concepts of graded fuzzy absorbing hyperideals in a commutative multiplicative hyperring such as graded fuzzy 2-absorbing hyperideals, graded fuzzy strongly 2-absorbing hyperideals, graded fuzzy weakly completely 2-absorbing hyperideals and graded fuzzy $k$-2-absorbing hyperideals. we obtain some basic properties and new results of this case of structures. Also, we present the telative between graded fuzzy multiplicative hyperrings and graded multiplicative hyperrings by level sets and state the quotient set of a graded commutative multiplicative hyperring over fuzzy hyperideal with conditions is a graded multiplicative hyperring.

In this paper, first the notion of (⊗,)−𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛𝑠 on 𝐸𝑄−𝑎𝑙𝑔𝑒𝑏𝑟𝑎𝑠 where ∈{~,→} is introduced and then they are characterized, in this way, the function 𝑑:𝐸→𝐸 on 𝐸𝑄−𝑎𝑙𝑔𝑒𝑏𝑟𝑎 𝐸 with the bottom element 0 is a (⊗,~)((⊗,→))−𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛 if and only if 𝑑(𝑥)=1 ,𝑥~𝑦=1, for all 𝑥,𝑦∈𝐸. Thus 𝑑 is an isotone, homomorphism, and closure derivation. Furthermore, (⊗,∧)−𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛𝑠 on 𝐸𝑄−𝑎𝑙𝑔𝑒𝑏𝑟𝑎𝑠 are investigated and some related results are discussed. Indeed it is shown that if 𝑑:𝐸→𝐸 be a (⊗,∧)−𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛 on an 𝐸𝑄−𝑎𝑙𝑔𝑒𝑏𝑟𝑎 𝐸 such that for all 𝑥∈𝐸, 𝑑(1)⨂𝑥≤𝑑(𝑥), so 𝑑 is an isotone derivation. Then by studying on (⊗,∨)−𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛𝑠 on 𝑙𝑎𝑡𝑡𝑖𝑐𝑒−𝑜𝑟𝑑𝑒𝑟𝑒𝑑 𝐸𝑄−𝑎𝑙𝑔𝑒𝑏𝑟𝑎𝑠, semi-dual closure derivation is introduced and it is proved that for 𝑎∈𝐸, 𝑑𝑎(𝑥)=𝑥⨂𝑎, for all 𝑥∈𝐸, is a semi-dual closure (⊗,∨)−𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛 on 𝐸. Finally, by proving a property of 𝐸𝑄−𝑎𝑙𝑔𝑒𝑏𝑟𝑎𝑠, some conditions are found under which the set of fixed points in (⊗,∨)−𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑜𝑛𝑠 on 𝑙𝑎𝑡𝑡𝑖𝑐𝑒−𝑜𝑟𝑑𝑒𝑟𝑒𝑑 𝐸𝑄−𝑎𝑙𝑔𝑒𝑏𝑟𝑎𝑠, also is a 𝑙𝑎𝑡𝑡𝑖𝑐𝑒−𝑜𝑟𝑑𝑒𝑟𝑒𝑑 𝐸𝑄−𝑎𝑙𝑔𝑒𝑏𝑟a.

This research presents a new method of coarse-tuning the fuzzy reinforcement learning architecture using agent-environment interactive data. This method solves two main challenges the fuzzy reinforcement learning: the low-speed training process and determining the input membership functions of the fuzzy structure. First, the agent interacts with the environment to gather training data. Then, the transition probability matrix and the expected return matrix are calculated by applying a clustering algorithm due to the continuous space. Each cluster is a state of the environment, and an approximation of the transition probability from one cluster to another is calculated using the gathered data. Finally, the parameters of the fuzzy system are adjusted using the modified value iteration method of dynamic programming for the continuous space. The proposed method is fully described with an example. This method increases the learning speed and adjusts the input membership functions of the fuzzy system.

In this article, the hypothesis test and confidence interval for the fuzzy coefficients in the fuzzy weighted regression model with precise inputs and fuzzy outputs are discussed. By applying the weighted estimation method in estimating the coefficients and using the conventional fuzzy hypotheses in the fuzzy environment,, We are trying to determine the distribution of the available estimators, based on the bootstrap method so that we can decide to accept or reject the existing hypotheses. Therefore, at first, the required test statistics are calculated based on the bootstrap method. Then, by comparing the probability value and the given significance level, as in the classical method, the null hypothesis is accepted or rejected. Also, from another point of view, hypothesis testing based on bootstrap confidence intervals is also discussed. At the end, by analyzing a practical example with real data in housing, the approach investigated in hypothesis testing and confidence interval for the coefficients of the fuzzy regression model has been analyzed.

Due to the change in the output characteristic of photovoltaic units under changes in radiation, temperature, load size and also the angle of placement of the panels, these systems rarely automatically turn on around the maximum power point. So far, various methods such as increasing conductivity, parasitic capacitor, neural network and fuzzy logic controller have been presented to track the maximum power point of photovoltaic systems, which have disadvantages such as high cost, high complexity. And they have low reliability. In this article, a fuzzy controller is designed to track the maximum power point so that the maximum power point tracking can be extracted under the conditions of changing temperature and radiation. In order to increase the accuracy of the proposed controller and considering the nature of temperature and radiation changes, the gray wolf optimization algorithm has been used to adjust the limits of the fuzzy functions to obtain a robust controller, and a proportional integral controller has also been used on the load side Its parameters are also calculated by GWO algorithm to set the optimal voltage. In order to validate the proposed mechanism, this structure has been implemented in the Simulink environment of MATLAB software, and the results show the optimal efficiency of the optimized fuzzy controller in tracking the maximum power point of photovoltaic sources.

In this paper, the level of carbon dioxide in blood is studied as a model of fuzzy differential equations, which is designed based on Hukuhara difference. First, a linear system consisting of independent second-order difference equations is studied and the sufficient conditions of existence of it,s general solution is found. Then, the systematic convergence of the fuzzy difference equation under study is proposed and sufficient conditions for its systematic convergence is provided.

Information transmitters in wireless sensor networks have limited storage and energy. One of the most critical issues in the design of these networks is the optimal use of energy since it is almost impossible to charge or replace batteries in sensor nodes. In order to solve energy limitations in sensor networks, the use of clustering algorithms can play an effective role. In fact, these algorithms help to balance the network load with proper clustering and selection of optimal cluster heads, which will reduce energy consumption and subsequently increase the network's lifespan. Accordingly, in this article, in order to select the best nodes as cluster heads, a new method based on the fruit fly algorithm and fuzzy logic is proposed. In the proposed protocol, fuzzy logic is used to calculate the odor intensity parameter in the fruit fly algorithm. Candidate nodes for clustering use the three parameters of the distance to the sink, the amount of remaining battery energy, and the distance to the center of the cluster as fuzzy logic input (to calculate the smell intensity). By simulating the proposed method and comparing it with the well-known AFSRP protocol, it can be seen that the proposed protocol has a much better performance in terms of energy consumption, data transmission delay, media access delay, and signal-to-noise ratio than AFSRP.

Decision‐making in conditions of uncertainty, especially in the diagnosis of diseases, has always been  a challenging task in the field of research, which has been the focus of many researchers. Due to the successful performance of intuitionistic fuzzy numbers in covering the uncertainty related to medical  problems, the main focus of this article is on this type of numbers. The theory of sizes as a  complementary and efficient tool in combination with disease diagnosis processes is a great help in  final decision‐making in order to speed up the treatment process. Although various measures have  been proposed for intuitionistic fuzzy numbers, however, by changing the attitudes, it is possible to  complete  the  measures  from  other  dimensions.  Choosing  a  suitable  size  can  cause  a  special  improvement in the final result or reduce the amount of calculations. Our main motivation for this  article is a new perspective on some of the prominent sizes and reducing the volume of their  operations. In this way, the rewriting and extension of some of the proposed measures are presented  based on a conceptual model. In some numerical examples from the literature of the research, a  comparative analysis is given for the new measures in comparison with other measures. In addition,  discussions on the effectiveness of the mentioned measurements are expressed using the findings  obtained from its application in the medical diagnosis problem.

The main aim of this paper is to find an optimal interval control law for quadratic linear problems under interval uncertainty. For this purpose, using Bellman's optimality principle and interval Hamilton-Jacobi-Bellman inequalities, the interval optimal control problem is transformed into a system of interval differential inequalities. These inequalities are called Riccati's differential inequalities, which is a result of the dynamic programming method. To solve this system of inequalities, we use inclusion relations and interval arithmetic. By this method, we can obtain the upper and lower bounds of the solutions. We also use Hokuhara's generalized difference to reduce errors in the interval arithmetic. We apply the presented method for solving some interval quadratic linear optimal control problems by using MATLAB software. The obtained results show the efficiency of the proposed method.

In this paper, bipolar inverse fuzzy graphs are introduced. Several operations are made on such graphs and whether these operations result in a bipolar inverse fuzzy graph is investigated. A type of bipolar inverse fuzzy graphs called strong bipolar inverse fuzzy graphs have been studied. The complement graph and dependent threshold of a bipolar inverse fuzzy graph are introduced and it is concluded that the complement of a bipolar inverse fuzzy graph is a strong bipolar inverse fuzzy graph. An inclusion condition regarding threshold graphs corresponding to two bipolar inverse fuzzy graphs with special conditions will result.