نشریه سیستم های فازی و کاربردها
سال ششم شماره 2 (پیاپی 13، پاییز و زمستان 1402)

In today's world, we are faced with a huge amount of growing information and uncertainty. Uncertainty in information has different types of ambiguity, possibility, probability, inaccuracy, etc., which make the use of information a challenge. Fuzzy logic, as a solution to deal with uncertainty, only deals with a certain part of these uncertainties and does not consider other aspects. In 2011, Zadeh proposed the concept of Z numbers, which consist of two components, the limit and the reliability of the limit, to cover possible and probable uncertainties.In this review article, the study of the background of Z numbers and its mathematical foundations will be discussed first. Then, the most important researches conducted in the applied fields of Z numbers include decision making, ranking, word calculations, machine learning, medical diagnosis, risk assessment, regression analysis, and review control. Examining the results of the articles indicates that the use of Z numbers can significantly improve the amount of error and accuracy. But the complexity of the calculations and the learning process in these structures are among the upcoming challenges in this field. Also, the use of Z numbers in some areas such as forecasting and optimization is among the future horizons.​

One of the methods of solving multi-objective programming problems is the use of ideal programming problems, in which the decision maker considers an ideal level for each objective function. In real-life problems, several ideal levels may be available for an objective function, or these ideal levels are of fuzzy type, in which case fuzzy multi-choice ideal programming problems arise. In this article, the introduction and solution of fuzzy multi-choice ideal programming problems are discussed, so that first the problem becomes a fuzzy multi-choiceprogramming problem in which there are several choices for the right side of the constraints, then using fuzzy binarypolynomials and polynomials Fuzzy linear least squares is a classic linear programming problem, which is solved using Lingo software. The described algorithm is used to solve a practical example in the field of fuzzy multi-choice ideal programming problems, and the previous results are compared and analyzed with the results obtained from this method.

This article deals with the problem of planning an energy hub connected to the distribution network. The problem in question is a multi-objective problem with the goals of minimizing the cost of operation and minimizing the emission of pollutants.Demand response and renewable energy sources are used in order to achieve the mentioned goals. In order to model demand response, a price-based model called load transfer has been used. Solar power plant and wind turbine have been used as renewable resources. Since the uncertainty of some parameters causes problems in the operation of the distribution network; In this article, uncertainty modeling has been considered. The IEEE 33-bus standard network is considered as the test network and the nonlinear problem is stated, implemented and solved in GAMS software environment. To solve the multi-objective problem, the weighted summation method is used, and the fuzzy satisfactory method is used to select the best solution. The results of numerical studies show the effect of demand response, renewable energy sources and uncertainty on the cost of operation and the amount of emission of environmental pollutants.

Many human decision-making processes such as competition, hostility, partnership, etc. are based on bipolar or two-sided thinking, which are positive on one side and negative on the other. Binary logic only includes zero and one, and fuzzy logic is a tool for representing ambiguity and uncertainty, but both have shortcomings in modeling bipolar relationships, as they are limited to the range from zero to one, which is suitable for representing unipolar models in nature. Bipolar fuzzy sets are actually a combination of ambiguity and its polarity, which is a tool for representing subjects of nature that have both positive or negative poles. Therefore, in this article, we will introduce bipolar fuzzy sets and numbers, and then, by defining addition and scalar multiplication for triangular bipolar fuzzy numbers, we will introduce a new ranking based on the centroid for this category of numbers, and prove the properties of the new method by stating several theorems and propositions. Finally, numerical examples demonstrate the practical applications of the proposed ranking.

In this article, an approach for fitting a fuzzy linear regression model based on support vectors is presentedwhen the response variable, model parameters and errors are considered as fuzzy numbers.In this method, the objective function is based on the sum of the absolute values ​​of the distances of the hypothetical points to the non-parallel border hyperplanes. The presented model has good robustness to the presence of outlier data. The proposed model has been compared with some other models based on three goodness of fit indices.

In this paper, we introduce three types of (f, g)-derivations suchas one, two and three (f, g)-derivations of residuated lattices and investigate someproperties of them. Then we show that if d is a (f, g)- derivation preserving, thend is isotone. We prove a formula for n-th (f, g)-derivations of type one. Finally,we show that the set of all (f, g)-derivation preserving ⊙ on residuated lattices, isa semi- group.

Harmonics in power systems produce unsuitable effects such as saturation of iron cores of transformers and electrical machines, improper operation of protection relays and increase in losses, so they should be reduced. Moreover , a low power factor leads to occupying the capacity of lines with reactive power, which leads to additional costs in the system. This issue causes the regional power companies to consider penalties for subscribers who have a low power factor. Reducing THD and increasing power factor are two important goals in improving power quality. A capacitor can be used to compensate the power factor, as there is a possibility of resonance occurring in this situation. In order to achieve the mentioned targets, a hybrid power filter is proposed, which consists of a passive filter and an active filter. The active filter includes three parts: identification, modulation and inverter. To reduce the power rating of the active filter inverter, a passive filter is used with it. The elements of the passive filter should be determined in such a way that both the THD and power factor is optimized, so this work should be done with a multi-objective meta-heuristic algorithm, which SPEA-II algorithm is used in this manuscript. At the end, the efficiency of the proposed hybrid filter will be illustrated by simulation in MATLAB software.

In this paper, the concepts of fuzzy filter and fuzzy sub-algebra on BI-algebras are introduced. Then some of their properties are investigated. Fuzzy sub-algebras and fuzzy filters are classified according to level sets and equivalent definitions for fuzzy filters are provided. It has also been proven that in every distributive BI-algebra, every filter is a sub-algebra and we have shown that in a group of BI-algebras, every subset contains 1 is a sub-algebra and every fuzzy subset that satisfies the first condition of the filter is a fuzzy filter. Moreover, it is proved that the set of all fuzzy filters on BI-algebras is a complete lattice. The relation of congruence and quotient BI-algebra produced by fuzzy filters is also investigated.

In this article, multi-objective linear programming problems with interval coefficients in objective functions are investigated. By using the acceptance index, the concepts of different answers corresponding to such problems are presented. In order to achieve such answers, a new solution method is introduced. Characteristics of the answer/answersobtained from the new solution method are also expressed. For example, the unique optimal solution resulting from thenew solution method is a strict A-efficient solution of the multi-objective linear programming problem with interval coefficients in the objective functions. In order to better understand the presented concepts and solution method, numerical examples are also examined.

One of the significant aspects of fuzzy group theory is the classification of the fuzzy subgroups of finite groups. The main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of the semi-dihedral group of order 8n in particular cases n=p^m and n=pq; by using the natural equivalence relation. The corresponding equivalence classes of fuzzy subgroups of the semi-dihedral group are closely connected to the chains of subgroups of the semi-dihedral group. ‎In this regard‎; Inclusion-Exclusion principle and structure of the maximal subgroups play an‎ ‎essential role and in some situations give relations which lead to explicit formulas. Finally; by the obtained results; we determine the fuzzy subgroups of all semi-dihedral groups of order less than 100.

Distance size, similarity size, and entropy size provide useful results for decision makers to make decisions about problems with uncertain data. The main focus of this research is to introduce a new measure for interval-valued intuitive fuzzy numbers. Many of the defined measures have shortcomings such as not being comprehensive, high volume of calculations and application in limited cases. Therefore, the main goal of this research is to introduce a measure of distance and similarity with a new and reduced approach for intuitive fuzzy numbers with a value interval. After presenting the structure and effective indicators in the proposed size, it can be seen that the amount of calculations is clearly reduced in the defined interval size. In addition, the proof that size properties hold for it is shown correctly. The presented size structure has the ability to be combined with the process related to multi-criteria decision making and medical diagnosis problems. For this purpose, while presenting hybrid algorithms, effective applications of it have been given by mentioning several prominent examples.

In this paper, we introduced the concept of f-derivation on equality algebra E by using the notions of inner and outer f-derivations. Then, we investigated some properties of (inner, outer) f-derivation and introduced some suitable conditions that they help us to define an f-derivation on E. We defined kernel and fixed point sets of f-derivation on E and proved that under which condition they are filters of E. Finally, we proved that under some conditions the equivalence relations on (E, →, 1) coincidewith the equivalence relations on E with derivation d_f . Also, by using the properties of equality algebra, we made two outer f-derivations and by introducing an implication operation “\ri ” on the set of all these outer f-derivations, we showed that it make a BE-algebra and dual BCK-algebra.