Iranian journal of fuzzy systems
Volume:20 Issue: 2, Mar-Apr 2023

In this paper, we introduce a new optimization problem with respect to a generalized form of fuzzy relational equations (FRE) in which fuzzy equality replaces ordinary equality in the constraints (FRE-FC). Fuzzy constraints enable us to attain optimal points (called super-optima in this paper) that are better solutions than those resulted from the resolution of the similar problems with ordinary equality constraints. Some structural properties of the FRE-FC problems are studied and a new formulation is presented in which the fuzzy constraints (equations) are precisely modeled. Subsequently, a new PSO-based algorithm is proposed to solve the FRE-FC problems defined by arbitrary continuous t-norms. The proposed algorithm is tested with different test problems generated by ten well-known continuous t-norms used in the literature. Moreover, the generated solutions for these problems, are also compared with some well-known meta-heuristic methods which have been applied to many practical optimization problems. It is shown that the optimal intensity of electromagnetic radiation problem can be formed as a special case of FRE-FC problems in which fuzzy composition is defied by max-product composition.

The theory of interval-valued difference equations under $gH$-difference is an interesting topic, since it can be applied to study numerical solutions to interval-valued or fuzzy-valued differential equations. In this paper, we estimate the number of solutions to a class of first-order interval-valued difference equations under $gH$-difference, which reveals the complexity of the stability analysis in this area, as well as the difficulty for prediction and control problems. Then, based on the relative positions of initial values and equilibrium points, we provide sufficient conditions for the existence of convergent solutions. We also provide examples to illustrate the validity of our results.

The cloud model is one of the mathematical tools that realize the transformation of quantitative information from qualitative data. Therefore, cloud model theory is widely used in computer science, reliability estimation, nonlinear function approximation, controller design, etc. In general, cloud controller design is known to use Gaussian membership clouds. However, it is computationally expensive because membership cloud computing is a nonlinear operation, and it has a disadvantage that it is difficult to decompose the structure of the controller. This paper proposes a new asymmetric triangular cloud model consisting of linear operations instead of Gaussian functions and, on this basis, develops a controller design method to approximate the output of the controlled plant to the desired value. Furthermore, it is demonstrated that the proposed controller is capable of stability analysis even if the mathematical model of the plant is not given, and it is validated by simulation of electrode up and down control of ultra-high power electric arc furnace and stabilization control of inverted pendulum.

The aim of this paper is to study the completeness of L-quasi-uniform convergence spaces and L-quasi-uniform spaces. Firstly, we describe L-quasi-uniform convergence spaces as enriched categories. Then we give two kinds of completeness of L-quasi-uniform convergence spaces and show that Lawvere completeness implies Cauchy completeness. Finally, we use the Cauchy completeness of L-quasi-uniform convergence spaces to define the Cauchy completeness of L-quasi-uniform spaces, and show that Cauchy completeness is equivalent to Lawvere completeness in L-quasi-uniform spaces.

Conditional distributivity of aggregation functions, which has received wide attention from the researchers, is vital for many different fields, for example, integration theory, utility theory and so on. This article is mainly devoted to dealing with the conditional distributivity of continuous t-norms over 2-uninorms. As the first step for investigating the conditional distributivity of 2-uninorms, we give the complete characterization of all pairs $(T,\mathcal{H})$ {fulfilling} this property. Compared to the case of distributivity of continuous t-norms over 2-uniorms, which leads to the 2-uninorm must be idempotent, the results obtained in this paper demonstrate that conditional distributivity and  distributivity on this topic, are not equivalent.

Dual probabilistic linguistic term sets (DPLTSs) are more powerful compare to probabilistic linguistic term sets, probabilistic hesitant fuzzy sets, hesitant fuzzy sets and intuitionistic fuzzy sets for the reason that they deal with both belongingness grades and non-belongingness grades along with their respective probabilities. On the other hand, the generalized Dombi operators have higher flexibility due to inclusion of two parameters. MARCOS (Measurements alternatives and ranking according to compromise solution) technique was developed by utilizing the utility degrees of options using the ideal and anti-ideal solutions. Here, we combine the merits of generalized Dombi operator and MARCOS and propose a DPL-MARCOS approach under dual probabilistic linguistic setting. In this methodology, the concepts of consistency and similarity between the experts are used to calculate their weights of subjective and objective types, respectively. For aggregating experts' preferences, we propose dual probabilistic linguistic- generalized Dombi weighted averaging aggregation operator. A biomass feedstock selection problem is furnished to show the applicability of our technique. We have considered coconut shell, coffee husk and sugarcane baggage as alternatives. The result shows that coffee husk is the most suitable option. The sensitivity assessment of parameter values reveals that our technique is stable. The comparative study proves that our model is more significant and realistic compare to the existing ones.

Recently, Zhao et al. \cite{Zhao-2021-25} characterized the distributivity equations of null-uninorms with continuous and Archimedean underlying operators over overlap or grouping functions. Moreover, Liu et al. \cite{Liu-2020-25} studied the distributive laws of continuous t-norms over overlap functions. In this paper, we proceed with the distributivity characterization of idempotent null-uninorms over overlap or grouping functions. In order to do that, we introduce a class of weak overlap and grouping functions with weak coefficients, and obtain the full characterizations of overlap and grouping functions by considering the different values of underlying uninorms' associated functions of idempotent null-uninorms on the interval endpoints and comparing them with the weak coefficients. Obviously, idempotent null-uninorms generalize idempotent uninorms. Thus, the obtained results also generalize the distributivity of idempotent uninorms proposed as future work in

The aviation industry is a complicated, sensitive, and challenging phenomenon.  One of the major issues in the operation of streamlined processes in this industry is the management of proper decisions during the disruption of flight schedules. Such disruptions commonly reduce customer satisfaction and the profitability of the airlines. Since there are multiple reasons for the disruption of the flight schedules along with the different possible decisions, a correct decision is very difficult to make requiring the opinions of the specialist staff. In this research, an expert model using a ``fuzzy multi-criteria decision-making" method is proposed to provide a correct decision during the disruption of the flight schedules. The results show that the most important factors that make disruption of flight schedules are arrival delays and technical failure of the airline fleet. Besides, the most important possible decisions are the announcement of the delay and canceling of the flight. Thanks to utilizing the fuzzy analytical network process, the outcomes of the proposed expert model are in good alignment with the opinions of the specialist staff. The fuzzy analytical network process determines the values of 0.5124 and 0.2621 for the magnitude of the arrival delay and technical defect respectively. This method also determines the values of 0.7042 and 0.2076 for flight delay and flight canceling as the two most important possible decisions.

In this paper, in order to apply the concept of IVI-octahedron sets to MCDGM problems, we define some aggregation operators via IVI-octahedron sets and obtain some their properties. We  define some aggregation operators via IVI-octahedron sets and obtain some their properties.  We present a MCGDM method with linguistic variables in IVI-octahedron set environment. Finally, we give a numerical examples  for MCGDM problems.

Restricted equivalence function, as an effective tool for the theoretical research and practical applications of fuzzy sets and systems along with fuzzy logic, has been continuously considered by scholars since it was proposed. In particular, recently, Bustince, Campi\'{o}n, De Miguel et al. (H. Bustince, M.J. Campi\'{o}n, L. De Miguel, E. Indur\'{a}in, Strong negations and restricted equivalence functions revisited: An analytical and topological approach, Fuzzy Sets and Systems (2021), https://doi.org/10.1016/j.fss.2021.10.013.) investigated it using analytical and topological approach and proposed an open problem to ask whether the binary function $F(x,y)=T(I(x,y),I(y,x))$ obtained from a t-norm $T$ and a fuzzy implication function $I$ is a restricted equivalence function or not. In this paper, we pay attention to this problem and give positive answer of it. Specifically, first, we consider the binary functions obtained from overlap functions and fuzzy implication functions by following the construction way of $F$ and get the necessary and sufficient condition that makes such obtained $F$ to be a restricted equivalence function. Second, we introduce the so-called $\heartsuit$-functions, which are binary functions on unit closed interval with few additional axioms and obtain the necessary and sufficient condition that ensures the binary function constructed via any non-decreasing $\heartsuit$-function and fuzzy implication function as the way of $F$ to be a restricted equivalence function. Finally, we give the necessary and sufficient condition that makes $F$ to be a restricted equivalence function.

This paper focuses on the topic of ordinal sums of semigroups in the sense of A. H. Clifford - a method for constructing a new semigroup from a given system of semigroups indexed by a linearly ordered index set. We completely describe the linearly ordered index set for an ordinal sum of semigroups yielding a uninorm.

Extending and completing earlier results on lifting certain continuity properties of aggregation functions by super- and sub-additive transformations (J. Mahani Math. Res. Center 8 (2019) 37--51, and Iranian J. Fuzzy Sets 17 (2020) 2, 165--168), we prove that uniform continuity of multi-dimensional aggregation functions is preserved under super-additive transformations.

The COVID-19 pandemic has affected health, economic, and social factors and harmed the distribution and sales of agricultural products. It has become a crucial factor in agricultural development. The purpose of the present study is to design a sustainable development model in the agricultural sector under circuital circumstances (i.e., the COVID-19 pandemic). To achieve this goal of used a combined methodology of grounded theory, the Fuzzy Delphi Method (FDM), the Fuzzy decision-making trial and evaluation laboratory (FDEMATEL) method, and the Fuzzy decision-making trial and evaluation laboratory-based analytic network process (FDANP) method. The criteria of higher importance were identified using grounded theory and FDM. Then, the fuzzy DEMATEL method was carried out to identify internal relationships, effects, and dependencies of the main criteria. Finally, the weight of the main criteria of the model has been calculated with the Fuzzy DANP method. According to the results of the Fuzzy DEMATEL method, Critical circumstances (COVID-19), environmental factors, educational factors, health factors, and economic factors had the highest effects. The “critical circumstances” criterion (COVID-19) had the largest effect and strongest relationship with the other criteria. On the other hand, the results of the Fuzzy DANP method show that environmental factors (MC7), social factors (MC2), critical circumstances (COVID-19) (MC5), health factors (MC1), entrepreneurial factors (MC8), are the most important criteria of the sustainable development model of the agricultural sector under critical circumstances. Therefore, to move on the path of sustainable development in the agricultural sector, one should focus on the factors that have a higher influence and importance.