Iranian journal of fuzzy systems
Volume:19 Issue: 4, Jul-Aug 2022

Recently in cite{DvZa5,DvZa6}, new algebras, called weak pseudo EMV-algebras, wPEMV-algebras for short, were introduced generalizing pseudo MV-algebras, generalized Boolean algebras and pseudo EMV-algebras. For these algebras a top element is not assumed a priori. For this class of algebras, we define a state as a finitely additive mapping from a wPEMV-algebra into the real interval $[0,1]$ which preserves a partial addition of two non-interactive elements and attaining the value $1$ in some element. It can happen that some commutative wPEMV-algebras are stateless, e.g. cancellative ones.\%The paper is divided into two parts. Part I deals with basic properties of states and state-morphisms which are wPEMV-homomorphisms from a wPEMV-algebra into the real interval $[0,1]$ endowed as a commutative wPEMV-algebra. We show that there is a one-to-one correspondence between the set of state-morphisms and the set of maximal and normal ideals having a special property.In Part II, we present an analogue of the Krein-Mil'man theorem applied to the set of states. We characterize the space of the state-morphisms of a wPEMV-algebra without top element as a Hausdorff locally compact space in the weak topology of states and we present its Alexandroff's one-point compactification. Moreover, we give an integral representation of any (finitely additive) state by a unique regular Borel $sigma$-additive probability measure.

Recently in cite{DvZa5,DvZa6}, new algebras, called weak pseudo EMV-algebras, wPEMV-algebras for short, were introduced generalizing pseudo MV-algebras, generalized Boolean algebras and pseudo EMV-algebras. For these algebras a top element is not assumed a priori. For this class of algebras, we define a state as a finitely additive mapping from a wPEMV-algebra into the real interval $[0,1]$ which preserves a partial addition of two non-interactive elements and attaining the value $1$ in some element. It can happen that some commutative wPEMV-algebras are stateless, e.g. cancellative ones.The paper is divided into two parts. Part I deals with basic properties of states and state-morphisms which are wPEMV-homomorphisms from a wPEMV-algebra into the real interval $[0,1]$ endowed as a commutative wPEMV-algebra. We show that there is a one-to-one correspondence between the set of state-morphisms and the set of maximal and normal ideals having a special property.In Part II, we present an analogue of the Krein-Mil'man theorem applied to the set of states. We characterize the space of the state-morphisms of a wPEMV-algebra without top element as a Hausdorff locally compact space in the weak topology of states and we present its Alexandroff's one-point compactification. Moreover, we give an integral representation of any (finitely additive) state by a unique regular Borel $sigma$-additive probability measure.

On account of the idea of maximum fuzzy entropy and  symmetric implicational mechanism under the environment of intuitionistic fuzzy sets,  we come up with the intuitionistic fuzzy entropy derived symmetric implicational (IFESI) algorithm.  Above all, novel symmetric implicational principles are presented, and the unified solutions of the IFESI algorithm are  acquired for IFMP (intuitionistic fuzzy modus ponens) and IFMT (intuitionistic fuzzy modus ponens), which build upon in view of residual intuitionistic implications. Thereafter, the reductive properties and continuity of the  IFESI algorithm are validated for IFMP and IFMT. In addition, the IFESI algorithm is extended to the $alpha$-IFESI algorithm, and the unified solutions of the $alpha$-IFESI algorithm are obtained for IFMP and IFMT. Finally, two examples of fuzzy classification for the $alpha$-IFESI algorithm are presented to demonstrate the detailed computing process of the IFESI algorithm.

In this paper we study the aggregation of fuzzy preferences on non-necessarily finite societies. We characterize in terms of possibility and impossibility a family of models of strongly-connected preferences in which the transitivity is defined for any t-norm. For that purpose, we have described each model by means of some crisp binary relations and we have applied the results obtained by Kirman and Sondermann about ultrafilters and Arrovian models.

The performance assessment of companies in terms of sustainability requires to find a balance between multiple and possibly conflicting criteria. We here rely on composite metrics to rank a set of companies within an industry considering environmental, social and corporate governance criteria. To this end, we connect intuitionistic fuzzy sets and composite programming to propose novel composite metrics. These metrics allow to integrate important environmental, social and governance principles with the gradual membership functions of fuzzy set theory. The main result of this paper is a sustainability assessment method to rank companies within a given industry. In addition to consider multiple objectives, this method integrates two important social principles such as maximum utility and fairness. A real-world example is provided to describe the application of our sustainability assessment method within the motor industry. A further contribution of this paper is a multicriteria generalization of the concept of magnitude of a fuzzy number.

Both fuzzy set theory and probability theory could handle uncertainty, and researchers have always compared the two to try to figure out which is better. Meanwhile, fuzzy decision tree algorithms represent classification knowledge more naturally to the way of human thinking. However, most generalizations of fuzzy decision tree algorithms focus only on numerical fine-tuning and interpretability of the algorithms. In order to make full use of the information of data sets and improve the performance of fuzzy decision trees. In this paper, we apply prior probability knowledge to the construction of fuzzy decision tree. Therefore, first of all, based on prior probability knowledge, for a certain feature variable, we present a concept of feature value's class contribution level which shows the different roles the same feature values play  in different classes. Then, on the basis of feature value's class contribution level, we put forward a new algorithm called Feature Contribution Fuzzy Decision Tree (FCFDT). FCFDT algorithm has good classification results especially on data set with outliers. And it also maintains the interpretability of the fuzzy decision tree algorithms. The proposed algorithm is implemented and validated with seven state-of-the-art decision tree algorithms on 15 real-life data sets coming from the UCI Repository of machine learning. The experimental results obtained clearly indicate the superiority of the proposed scheme over the baseline methods.

This study builds a new forecasting model for time series based on some important improvements.  First, we choose  the universal set to be the  percentage variation of the series. This universal set is divided to clusters by the automatic algorithm.  The suitable  number of cluster  depends on the similar level of elements in the universal set.   Second, a principle to find the relationship of each element in the series to the found clusters is established. Finally, we propose the forecasting rule from the established fuzzy relationships. The proposed model is illustrated in detail by the numerical examples, and can be quickly applied to real data by the established Matlab procedure.  Comparing many series with the differences about the number of elements, fields, and characteristics, the proposed model has shown the outstanding advantages.  Using the proposed model, we forecast the salty peak  for a coastal province  in Vietnam to illustrate for application of this study.

In this work, we develop a reasoning mechanism under uncertainty for a typical class of decision making problems based on the theory of fuzzy soft set. Accordingly, we consider a logic of fuzzy soft sets. In the sequel, implication operations dealing with fuzzy soft sets over different universal sets and different sets of parameters have been studied extensively. An algorithm for rule based reasoning has been developed for a modus ponens type rule of inference using the proposed logical structure. The entire proposal is illustrated with an example. Results of application of our proposed inference are compared with those obtained by Mondal and Raha on the problem of management of hypertension using a medical diagnostic support system.

In this paper, a new concept of the fuzzy logic controller is presented.The proposed concept is called fuzzy ontology controller and it's based on an ontology description of the Fuzzy Logic Controller (FLC).In this concept, the SPARQL query sent to the ontology replaced the fuzzification process, fuzzy interface, and rules of the fuzzy controller while defuzzification is done on an obtained response.Fuzzy ontology is designed with Prot'{e}g'{e} and hosted in the Virtuoso database on a remote server.Simulation results obtained with the proposed fuzzy ontology controller are compared to ones obtained with the classical fuzzy logic controller.Both controllers obtained the same simulation results due to the same membership function and defuzzification process.The results showed that this concept can be used as a part of some IoT solution within the vision of Industry 4.0.Also, results confirmed that the ontology-based controller works properly and gives the same output as FLC.The experiment is carried out on a heat exchange process controlled with a PLC.Modbus TCP protocol is used for communication between the server PC and a PLC.Experimental results show that only slow processes are controllable for now due to slow communication between PLC and server and the time needed for execution of SPARQL queries.

The focus of this paper is to investigate the modularity equation involving uninorms and Mayor's aggregation operators.  Necessary and sufficient conditions are established for this equation. And, it finds that themodularity equation of a Mayor's aggregation operator over a uninorm is reduced to the modularityof a commutative semi-t-norm over a uninorm and the modularity equation of a uninorm over a Mayor's aggregation operator is reduced to the modularity equation of a uninorm over a commutative semi-t-conorm. Among them, the cases of a uninorm which is locally internal on the boundary are studied in cite{Su_Riera_Aguilera_Torrens_2019}. In this paper, we consider whether the neutral element $e$ of the uninorm is idempotent element of the Mayor's aggregation operator in modularity equation to get solutions in the corresponding cases.

In this paper, we discussed the conjunctivenormal form, disjunctive normal form, duality principle, equality of two setsand a semi Boolean algebra of complex fuzzy sets (CFSs). We established somebasic results and particular examples with respect to standard complex fuzzyintersection, standard complex fuzzy union and standard complex fuzzycomplement functions with the same function for determining the phase term. Weused CFSs in signals and systems because the behavior of CFSs is similar toFourier transforms in certain cases. Moreover, we developed a new algorithmusing a Cartesian product of complex fuzzy sets for applications in signalsand systems by which we identified a reference signal out of the large numberof signals detected by a digital receiver.

In this work, we consider the joint distribution function as well as the copula of $(X+Z,Y)$ where the random vector $(X, Y, Z)$  is characterized by a copula $C_{X,Y,Z}$. We use this copula to analyze a Berkson measurement error model. By presenting a general form of a Berkson measurement error model with copula-dependent random variables, we investigate some of its special cases. Some theoretical results, several examples as well as a simulation study, are proposed for illustration.

This study presents a new method of damage detection using a combination of the second-order gradient Levenberg-Marquardt algorithm (SOGLMA) and fuzzy logic (FL) to solve the nonlinear damage detection equation for space frame structures. For damage detection in structures with a large number of degrees of freedom using the second-order gradient Levenberg-Marquardt algorithm, it is necessary to perform an iterative process of analysis and solving a set of simultaneous nonlinear equations that requires a lot of time. Therefore, the computation time and the number of iterations are reduced by using the proposed method "Combination of the second-order gradient Levenberg-Marquardt algorithm and fuzzy logic (SOGLMA-FL)". Acceleration response in sensor nodes obtained at different time steps from dynamic analysis are considered as input values for fuzzification. The output values of the proposed method after defuzzification are the damage extent of structural elements. The results show that the proposed damage detection method (SOGLMA-FL) has faster convergence, lower numbers of iteration and reduced computation time than the damage detection method (SOGLMA) for space frame structures.