Volume 18, Issue 4 , July and August 2021
O. Pavlacka; M. Pavlackova
Volume 18, Issue 4 , July and August 2021, Pages 1-17
Abstract
Weighted average with normalized weights is a widely used aggregation operator that takes into account the varying degrees of importance of the numbers in a data set. It possesses some important properties, like monotonicity, continuity, additivity, etc., that play an important role in practical applications. ...
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Weighted average with normalized weights is a widely used aggregation operator that takes into account the varying degrees of importance of the numbers in a data set. It possesses some important properties, like monotonicity, continuity, additivity, etc., that play an important role in practical applications. The inputs of the aggregation as well as the normalized weights are usually not known precisely. In such a case, their values can be expressed by fuzzy numbers, and the fuzzy weighted average of fuzzy numbers with normalized fuzzy weights needs to be employed in the model. The aim of the paper is to reveal whether and in which way the properties of the weighted average operator can be observed also for its fuzzy extension. It is shown that it possesses three conditions characteristic for aggregation operators -- identity, monotonicity and boundary conditions, and besides that, also compensation, idempotency, stability for linear transformation, 1-lipschitzianity, and continuity. Furthermore, it is proved that it preserves strict monotonicity in case of positive fuzzy weights, and symmetry in case of equal fuzzy weights, although it does not coincide with the fuzzy arithmetic mean operator in such a case. One of the most valuable result of the study is the fact that in contrast to the crisp weighted average operator, it is not additive. The importance of the obtained results is discussed and illustrated by several illustrative examples.
A. Tripathi; S. P. Tiwari; I. Perfilieva
Volume 18, Issue 4 , July and August 2021, Pages 19-36
Abstract
This work aims to study F-transforms based on general implicators and to investigate their basic properties. Interestingly, we show that some of the properties of F-transforms fail to hold in the case of implicators, such as S- and QL-implicators. {Further, we establish an equivalence between L-fuzzy ...
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This work aims to study F-transforms based on general implicators and to investigate their basic properties. Interestingly, we show that some of the properties of F-transforms fail to hold in the case of implicators, such as S- and QL-implicators. {Further, we establish an equivalence between L-fuzzy transformation systems and F-transforms}.
R. A. Aliev; B. G. Guirimov; O. H. Huseynov; R. R. Aliyev
Volume 18, Issue 4 , July and August 2021, Pages 37-49
Abstract
The notion of consistency is used to estimate the quality of preference knowledge and its stability for reliable evaluation of decision alternatives. It is well-known that a set of strict consistency conditions are used to keep the rationality of preference intensities between compared elements. These ...
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The notion of consistency is used to estimate the quality of preference knowledge and its stability for reliable evaluation of decision alternatives. It is well-known that a set of strict consistency conditions are used to keep the rationality of preference intensities between compared elements. These requirements are not achievable in the real situations when decision maker has limited rationality and partially reliable preferences. In this study, we propose an approach to deriving consistency-driven preference degrees for such kind of situations. A preference degree is described by a Z-number to reflect imprecision and partial reliability of preference knowledge. An optimization problem with Z-number valued variables is used to formulate design of consistent preferences. A real-world decision making problem is considered to illustrate application of the proposed method and conduct comparison with an existing technique.
J. Dombi; T. Jonas
Volume 18, Issue 4 , July and August 2021, Pages 51-68
Abstract
Dombi and Baczy\'{n}ski presented a new approach to the problem of implication operation by introducing the preference implication, which has very advantageous properties. In this paper, it is presented how the preference implication is connected with soft inequalities and with sigmoid functions. ...
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Dombi and Baczy\'{n}ski presented a new approach to the problem of implication operation by introducing the preference implication, which has very advantageous properties. In this paper, it is presented how the preference implication is connected with soft inequalities and with sigmoid functions. Utilizing this connection the preference implication-based preference measure for two fuzzy numbers is introduced and its key properties, including the reciprocity, are described. Then, the exact expression for computing the new preference measure for trapezoidal fuzzy numbers is presented. Here, using the new preference measure, two crisp relations over trapezoidal fuzzy numbers are introduced. It is shown that one of them is a strict (but not a total) order relation, and the other one is an equivalence relation. The strict order relation can be used to rank comparable fuzzy numbers, while the equivalence relation, which we call the indifference relation, expresses that the order of some fuzzy numbers is indifferent. These two crisp relations can be used to rank a collection of trapezoidal fuzzy numbers. Lastly, the proposed ranking method is compared with some well-known existing fuzzy number ranking methods.
D. Jardon; I. Sanchez
Volume 18, Issue 4 , July and August 2021, Pages 69-78
Abstract
Given a metric space X, we consider the family of all normal upper semicontinuous fuzzy sets on X, denoted by $\mathcal{F}(X)$, and a discrete dynamical system $(X,f)$. In this paper, we study when $(\mathcal{F}(X), \widehat{f})$ is (strongly) sensitive, where $\widehat{f}$ is the Zadeh's extension of ...
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Given a metric space X, we consider the family of all normal upper semicontinuous fuzzy sets on X, denoted by $\mathcal{F}(X)$, and a discrete dynamical system $(X,f)$. In this paper, we study when $(\mathcal{F}(X), \widehat{f})$ is (strongly) sensitive, where $\widehat{f}$ is the Zadeh's extension of f and $\mathcal{F}(X)$ is equipped with different metrics: The uniform metric, the Skorokhod metric, the sendograph metric and the endograph metric. We prove that the sensitivity in the induced dynamical system $(\mathcal{K}(X),\overline{f})$ is equivalent to the sensitivity in $ \widehat{f} :\mathcal{F}(X)\to \mathcal{F}(X) $ with respect to the uniform metric, the Skorokhod metric and the sendograph metric. We also show that the following conditions are equivalent:\item {\rm a)} $(X,f)$ is strongly sensitive;\item {\rm b)} $(\mathcal{F}(X), \widehat{f})$ is strongly sensitive, where $\mathcal{F}(X)$ is equipped with the uniform metric;\item {\rm c)} $(\mathcal{F}(X), \widehat{f})$ is strongly sensitive, where $\mathcal{F}(X)$ is equipped with the Skorokhod metric;\item {\rm d)} $(\mathcal{F}(X), \widehat{f})$ is strongly sensitive, where $\mathcal{F}(X)$ is equipped with the sendograph metric.
S. Kanakalakshmi; R. Sakthivel; L. Susana Ramya; A. Parivallal; A. Leelamani
Volume 18, Issue 4 , July and August 2021, Pages 79-93
Abstract
The robust stabilization problem for singular fractional order time delay T-S fuzzy systems with nonlinearities and unknown external disturbances is addressed in this paper. An equivalent-input-disturbance (EID) estimator is used to estimate the impact of external disturbances and nonlinearities on the ...
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The robust stabilization problem for singular fractional order time delay T-S fuzzy systems with nonlinearities and unknown external disturbances is addressed in this paper. An equivalent-input-disturbance (EID) estimator is used to estimate the impact of external disturbances and nonlinearities on the system output. Based on this EID approach, a dynamic compensator is designed to solve the stabilization problem of the considered system. Moreover, by considering a relevant Lyapunov-Krasovskii functional candidate and by using Lyapunov technique, the stability conditions in terms of LMIs are acquired for the considered closed-loop system. At last, to validate the effectiveness of the proposed result, two numerical examples are provided.
F. Khalili Goudarzi; H. R. Maleki; S. Niroomand
Volume 18, Issue 4 , July and August 2021, Pages 95-112
Abstract
In this paper, a new fuzzy multi-objective multi-product pipeline scheduling problem is introduced. The system consists of a single refinery, a unique distribution center, and a multi-product pipeline. Restrictions such as batchsizing, discharging rate, forbidden sequences, batch volumetric, etc. ...
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In this paper, a new fuzzy multi-objective multi-product pipeline scheduling problem is introduced. The system consists of a single refinery, a unique distribution center, and a multi-product pipeline. Restrictions such as batchsizing, discharging rate, forbidden sequences, batch volumetric, etc. are considered. Due to the uncertain nature of real-world problems, some parameters of the system are considered as fuzzy values. Tardiness and earliness penalties are considered with a time dependent non-linear function. The basic aim of this scheduling problem is to achieve the optimal sequence for pumping batches of oil products to maximize the financial benefit and simultaneously satisfies the customers with on-time delivery as a multi-objective problem. To tackle this problem, a two-stage methodology is proposed. In the first stage, the fuzzy formulation is converted to its equivalent crisp form by a credibility-based chance-constrained programming approach. In the second stage, the multi-objective crisp formulation is solved by some well-known approaches in the literature. Some test problems are generated and solved by the proposed approaches and the obtained Pareto-optimal solutions are analyzed and compared using some distance-based comparison metrics.
Y. M. Tang; G. Q. Bao; J. J. Chen; W. Pedrycz
Volume 18, Issue 4 , July and August 2021, Pages 113-129
Abstract
A novel fuzzy reasoning method called the SQI (symmetric quintuple implicational) methodis put forward, which is a generalization of the QIP (quintuple implication principle) method. First of all, the symmetric quintuple implicational principles are presented, which are distinct from the ones of the ...
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A novel fuzzy reasoning method called the SQI (symmetric quintuple implicational) methodis put forward, which is a generalization of the QIP (quintuple implication principle) method. First of all, the symmetric quintuple implicational principles are presented, which are distinct from the ones of the QIP method. Then unified optimal solutions of the SQI method are obtained for FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens), meanwhile corresponding reversible properties are verified. Furthermore, focusing on the case of multiple rules, optimal solutions of the SQI method are achieved, which involves two general approaches, i.e., FITA (first-infer-then-aggregate) and FATI (first-aggregate-then-infer). Equivalence relation of continuity and interpolation is analyzed for both FITA and FATI under the environment of the SQI method. Finally, one computing example arising in the field of affective computing is given for the SQI method with FATI. It is found that the SQI method preserves the same properties as the QIP method.
J. Chachi; A. Kazemifard; M. Jalalvand
Volume 18, Issue 4 , July and August 2021, Pages 131-148
Abstract
Most of the fuzzy regression approaches proposed in the literature adopted a single objective function in the generation of fuzzy regression models.These approaches mostly being criticized by their weak performances analysis and their sensitivity to outliers.Therefore, this paper develops a new multi-objective ...
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Most of the fuzzy regression approaches proposed in the literature adopted a single objective function in the generation of fuzzy regression models.These approaches mostly being criticized by their weak performances analysis and their sensitivity to outliers.Therefore, this paper develops a new multi-objective two-stage optimization and decision technique for fuzzy regression modeling problems in order to handle both of the criticisms.To handle the outlier problems, in the first stage, dynamic robust to outlier objective functions is considered in the estimation problem.The estimation problem is solved by running an algorithm which generates a set of fuzzy regression models.Then, in the next stage, we design a decision schema by employing Multi-Attribute Decision Making (MADM) problem.Here, the VIKOR method is employed as a proper means to provide a design to rank the generated fuzzy regression models by the first stage to introduce the most desirable model.We include simulation numerical results and a real-world house price problem in order to highlight the advantages of the proposed method in a comparison study.The results demonstrate the effectiveness of the proposed multi-objective optimization method to handle outlier detection problem while the prediction accuracy of the model is improved.
R. Verma; A. Aggarwal
Volume 18, Issue 4 , July and August 2021, Pages 149-167
Abstract
In real-world decision-making problems, experts often prefer to express their views, regarding problem parameters, in a natural language rather than precise numerical form. Linguistic representation models have been widely used to solve many decision-making problems with qualitative information. Game ...
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In real-world decision-making problems, experts often prefer to express their views, regarding problem parameters, in a natural language rather than precise numerical form. Linguistic representation models have been widely used to solve many decision-making problems with qualitative information. Game theory has been found successful applications in a wide range of areas. This paper presents an extensive study of matrix games with qualitative payoffs. The work uses 2-tuple intuitionistic fuzzy linguistic values (2-TIFLVs) to represent the payoffs of the matrix game. We develop the mathematical formulation and concepts of the solutions for matrix games with payoffs represented by 2-TIFLVs. Paper also shows that matrix games with payoffs of 2-TIFLVs have solutions that can be obtained by transforming the matrix game in a pair of linear/nonlinear programming problems. Finally, a real-life numerical is given to illustrate the developed method.
B. Farahbakhsh; S. H. Moosavirad; Y. Asadi; A. Amirbeigi
Volume 18, Issue 4 , July and August 2021, Pages 169-184
Abstract
Appointment scheduling for outpatient services is a challenge in the healthcare sector. For addressing this challenge, most studies assumed that patients’ unpunctuality and the duration of service have constant values or a specific probability distribution function. Consequently, there is a research ...
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Appointment scheduling for outpatient services is a challenge in the healthcare sector. For addressing this challenge, most studies assumed that patients’ unpunctuality and the duration of service have constant values or a specific probability distribution function. Consequently, there is a research gap to consider the uncertainty of both patients’ unpunctuality and the duration of service in terms of fuzzy sets. Therefore, this research aims to consider fuzzy values for both unpunctuality and duration of service have to improve an outpatient appointment scheduling (the time interval between two patients) in a referral clinic with the objective of reducing the total weight of waiting time, idle time, and overtime. Four different fuzzy linear programming models and 36 scenarios have been developed based on the show, no-show of patients, single-book, and double-book by using GAMS software. These four models are as follows: (1) probability of no-show equal to zero, (2) probability of no-show equal to 20\%, (3) probability of no-show equal to zero and with double-book factor, and (4) probability of no-show equal to 20\% and with double-book factor. The results of the first, second, third, and fourth models, respectively, present the scenarios considering 10, 5, 15, and 15 minutes for the time interval between two patients that have the minimum total weight of patient waiting times, physician idle times, and physician overtime. By considering these findings, the investigated referral clinic can improve its appointment system’s performance. Moreover, other similar clinics can apply the proposed model for improving their appointment systems' performance.
J. Mo; H. L. Huang
Volume 18, Issue 4 , July and August 2021, Pages 185-200
Abstract
Probabilistic hesitant fuzzy set represents the occurrence probabilities of elements.The probabilistic hesitant fuzzy preference relations can more effectively express thehesitant preference information of decision makers.But in the existing research, all of them are based on discrete probability distribution.In ...
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Probabilistic hesitant fuzzy set represents the occurrence probabilities of elements.The probabilistic hesitant fuzzy preference relations can more effectively express thehesitant preference information of decision makers.But in the existing research, all of them are based on discrete probability distribution.In order to give decision maker more evaluation space,continuous probability distribution is necessary to be considered.Therefore, in this paper, the continuous probability-interval valued fuzzy setis defined and its probability is represented by a probability density function.A method of converting probabilistic hesitant fuzzy set into continuous probability-interval valued fuzzy setis developed to transform discrete data into continuous data.Then, the continuous probability-interval valued fuzzy preference relations is presented.In order to consider the consistency of continuous probability-interval valued fuzzy preference relations, the multiplication consistent expected preference relations is proposed.The individual consistency index and group consensus index are also presented to determine the consistency level.And then, an algorithm is introduced for checking and improving the individual consistency level andgroup consensus level.Finally, a numerical example is shown to the effectiveness of proposed algorithm,the comparative analysis is given with the existing methods toshow the superiority of this algorithm.
Volume 18, Issue 4 , July and August 2021, Pages 201-214
