scispace - formally typeset
Search or ask a question

Showing papers on "Fuzzy number published in 2022"


Journal ArticleDOI
TL;DR: In this paper , three continuous review economic order quantity models for time-dependent deterioration using preservation technology were developed for a finite time horizon, incorporating promotional effort and full backorder, and the optimal solutions were derived for the number of orders, preservation technology cost and the fraction of a cycle with positive stock.
Abstract: This paper studies three continuous review economic order quantity models for time-dependent deterioration using preservation technology. First, a crisp model is developed and the model is extended into a fuzzy model to include the imprecise nature of demand. It is further extended to analyze the impact of the learning effect under the fuzzy environment. All models are developed for a finite time horizon, incorporating promotional effort and full backorder. The optimal solutions are derived for the number of orders, preservation technology cost, and the fraction of a cycle with positive stock. Three algorithms are developed to find the optimal solution for three models. Numerical analysis is performed to demonstrate the application, followed by a sensitivity analysis of the important parameters. The crisp model leads to the lowest total cost followed by fuzzy learning and fuzzy model. Even though the optimal number of orders is found to be the same for the three models, order quantity is more for the fuzzy model and less for the crisp model. The order quantity increases step-wise with an increase in preservation factor.

35 citations


Journal ArticleDOI
TL;DR: In this paper , a new class of orthopair fuzzy sets called (2,1)-Fuzzy sets are introduced, which are good enough to control some real-life situations.
Abstract: Abstract Orthopair fuzzy sets are fuzzy sets in which every element is represented by a pair of values in the unit interval, one of which refers to membership and the other refers to non-membership. The different types of orthopair fuzzy sets given in the literature are distinguished according to the proposed constrain for membership and non-membership grades. The aim of writing this manuscript is to familiarize a new class of orthopair fuzzy sets called “(2,1)-Fuzzy sets” which are good enough to control some real-life situations. We compare (2,1)-Fuzzy sets with IFSs and some of their celebrated extensions. Then, we put forward the fundamental set of operations for (2,1)-Fuzzy sets and investigate main properties. Also, we define score and accuracy functions which we apply to rank (2,1)-Fuzzy sets. Moreover, we reformulate aggregation operators to be used with (2,1)-Fuzzy sets. Finally, we develop the successful technique “aggregation operators” to handle multi-criteria decision-making (MCDM) problems in the environment of (2,1)-Fuzzy sets. To show the effectiveness and usability of the proposed technique in MCDM problems, an illustrative example is provided.

22 citations


Journal ArticleDOI
TL;DR: This manuscript familiarizes a new type of extensions of fuzzy sets called square-root fuzzy sets (briefly, SR-Fuzzy sets), and discovers the essential set of operations for the SR-Korean fuzzy sets along with their several properties.
Abstract: An intuitionistic fuzzy set is one of the efficient generalizations of a fuzzy set for dealing with vagueness/uncertainties in information. Under this environment, in this manuscript, we familiarize a new type of extensions of fuzzy sets called square-root fuzzy sets (briefly, SR-Fuzzy sets) and contrast SR-Fuzzy sets with intuitionistic fuzzy sets and Pythagorean fuzzy sets. We discover the essential set of operations for the SR-Fuzzy sets along with their several properties. In addition, we define a score function for the ranking of SR-Fuzzy sets. To study multiattribute decision-making problems, we introduce four new weighted aggregated operators, namely, SR-Fuzzy weighted average (SR-FWA) operator, SR-Fuzzy weighted geometric (SR-FWG) operator, SR-Fuzzy weighted power average (SR-FWPA) operator, and SR-Fuzzy weighted power geometric (SR-FWPG) operator over SR-Fuzzy sets. We apply these operators to select the top-rank university and show how we can choose the best option by comparing the aggregate outputs through score values.

20 citations


Journal ArticleDOI
12 May 2022
TL;DR: The Pythagorean fuzzy set, developed to overcome the limitation of intuitionistic fuzzy set in the description of decision-maker information, is extended to extend two considerable MCDM methods, namely, fuzzy decision by opinion score method and fuzzy-weighted zero inconsistency.
Abstract: In the fuzzy multicriteria decision-making approach, a committee of decision-makers is usually involved in the assessment of the suitability of different alternatives based on the evaluation criteria by using linguistic terms and their equivalent fuzzy numbers. In this context, researchers have developed the Pythagorean fuzzy set (PFS) to overcome the limitation of intuitionistic fuzzy set in the description of decision-maker information such as imposing restrictions on the representation of membership and nonmembership grades. On the one hand, PFS still does not have sufficient ability and flexibility to deal with such issues. On the other hand, multipolar technology is used to operate large-scale systems in real-life situations, especially in dealing with dissatisfaction and indeterminacy grades for the alternatives of the reference set. Thus, [Formula: see text]-polar fuzzy set is utilized and applied with other fuzzy sets because of its remarkable ability as a tool for depicting fuzziness and uncertainty under multipolar information in many circumstances. With the practical features of [Formula: see text]-polar fuzzy set in combination with PFS, this paper employs it to extend two considerable MCDM methods, namely, fuzzy decision by opinion score method and fuzzy-weighted zero inconsistency. Such extensions, called Pythagorean [Formula: see text]-polar fuzzy-weighted zero-inconsistency (Pm-PFWZIC) method and Pythagorean [Formula: see text]-polar fuzzy decision by opinion score method (Pm-PFDOSM), are formulated to weight the evaluation criteria followed by alternative ranking progressively. The research methodology is presented as follows. Firstly, the mechanisms of Pm-PFWZIC and Pm-PFDOSM are formulated and integrated into the development phase. Secondly, the description of the real-world case study of the evaluation and benchmarking of the sign language recognition systems is adapted and presented. The result of Pm-PFWZIC shows that the criterion of ‘finger movements’ has the highest weight amongst the rest of the criteria, whereas ‘misclassification error’ has the lowest weight. In the ranking results, a variation of ranking is scored by each expert, and group decision-making is applied to solve the individual ranking variety. The robustness of the formulated methods is evaluated using systematic ranking, sensitivity analysis and comparison analysis.

18 citations


Journal ArticleDOI
TL;DR: In this article, a job shop scheduling problem with the double goal of minimising energy consumption during machine idle time and minimising the project makespan is considered. But the problem is not solved by a single memetic algorithm.
Abstract: The quest for sustainability has arrived to the manufacturing world, with the emergence of a research field known as green scheduling. Traditional performance objectives now co-exist with energy-saving ones. In this work, we tackle a job shop scheduling problem with the double goal of minimising energy consumption during machine idle time and minimising the project’s makespan. We also consider uncertainty in processing times, modelled with fuzzy numbers. We present a multi-objective optimisation model of the problem and we propose a new enhanced memetic algorithm that combines a multiobjective evolutionary algorithm with three procedures that exploit the problem-specific available knowledge. Experimental results validate the proposed method with respect to hypervolume, ϵ -indicator and empirical attaintment functions.

17 citations


Journal ArticleDOI
18 Feb 2022-Symmetry
TL;DR: This paper investigates the shortcomings of picture fuzzy (PF) SMs in order to introduce a new SM in a T-spherical fuzzy (TSF) environment and proposes a newly improved SM that has a larger ground for accommodating the uncertain information with three degrees and is also responsible for the reduction of information loss.
Abstract: T-spherical fuzzy set (TSFS) is a fuzzy layout aiming to provide a larger room for the processing of uncertain information-based data where four aspects of unpredictable information are studied. The frame of picture fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs) provide limited room for processing such kinds of information. On a scale of zero to one, similarity measures (SMs) are a tool for evaluating the degrees of resemblance between various items or phenomena. The goal of this paper is to investigate the shortcomings of picture fuzzy (PF) SMs in order to introduce a new SM in a T-spherical fuzzy (TSF) environment. The newly improved SM has a larger ground for accommodating the uncertain information with three degrees and is also responsible for the reduction of information loss. The proposed SM’s validity is demonstrated mathematically and by examples. To examine the application of the suggested SM two real-life issues are discussed, including the concerns of medical diagnosis and pattern recognition. A comparison of the suggested SMs with current SMs is also made to assess the proposed work’s reliability. Since symmetric triangular fuzzy numbers are quite useful in database acquisition, we will consider the proposed SM for symmetric T-spherical triangular fuzzy numbers in the near future.

16 citations


Proceedings ArticleDOI
TL;DR: In this paper , the authors proposed some distance and knowledge measures for Fermatean fuzzy sets using t-conorms, and demonstrated the application of the suggested measures in pattern analyis and multicriteria decision-making.
Abstract: Fermatean fuzzy sets are more powerful than fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets in handling various problems involving uncertainty. The distance measures in the fuzzy and non-standard fuzzy frameworks have got their applicability in various areas such as pattern analysis, clustering, medical diagnosis, etc. Also, the fuzzy and non-standard fuzzy knowledge measures have played a vital role in computing the criteria weights in the multicriteria decision-making problems. As there is no study concerning the distance and knowledge measures of Fermatean fuzzy sets, so in this paper, we propose some novel distance measures for Fermatean fuzzy sets using t-conorms. We also discuss their various desirable properties. With the help of suggested distance measures, we introduce some knowledge measures for Fermatean fuzzy sets. Through numerical comparison and linguistic hedges, we establish the effectiveness of the suggested distance measures and knowledge measures, respectively, over the existing measures in the Pythagorean/Fermatean fuzzy setting. At last, we demonstrate the application of the suggested measures in pattern analyis and multicriteria decision-making.

14 citations


Journal ArticleDOI
23 Feb 2022-Axioms
TL;DR: The modification significantly improved the capacity of the LMAW method to consider uncertainty in decision making and showed that the model could tolerate smaller errors in defining the weight coefficients of criteria, and it provided stable results.
Abstract: The Logarithm Methodology of Additive Weights (LMAW) method is a very young method and in its basic form is defined for crisp values. In this paper, the LMAW method was improved by being modified with triangular fuzzy numbers. The modification significantly improved the capacity of the LMAW method to consider uncertainty in decision making. The special importance of the method is reflected in a relatively simple mathematical apparatus due to which it is possible to define, with high quality, weight coefficients of criteria and rank alternative solutions in uncertain environments. The method was tested in solving the problem of the location selection for a landing operations point (LOP) in combat operations of the army. The validation of the obtained results was performed: (1) by means of comparison with the Fuzzy Simple Additive Weighting (FSAW) Method, the Fuzzy Multi-Attributive Border Approximation area Comparison (FMABAC), the fuzzy Višekriterijumsko KOmpromisno Rangiranje (FVIKOR), the fuzzy COmpressed PRoportional ASsessment (FCOPRAS), and the fuzzy Multi Attributive Ideal-Real Comparative Analysis (FMAIRCA); (2) by means of sensitivity analysis by changing the weight coefficients of criteria; and (3) using simulation software. In comparison with other methods, the quality of the ranking of alternative solutions was confirmed, which highlighted the special importance of the fuzzy LMAW method relative to that of certain standard methods, respectively, the ones that are often used and confirmed in practice. On the other hand, the sensitivity analysis, including the changing of the weight coefficients of criteria, showed that the model could tolerate smaller errors in defining the weight coefficients of criteria, and it provided stable results. Finally, the validation of results achieved with the use of simulation software confirmed the obtained output results. The output results confirmed the quality of the modified method.

14 citations


Journal ArticleDOI
TL;DR: A multiple attribute decision-making (MADM) model with 3,4-quasirung fuzzy data is developed that enables the decision-makers to exploit additional spaces while applying to MADM problems.

13 citations


Journal ArticleDOI
25 Aug 2022-Axioms
TL;DR: In this article , Z-numbers were used together with the fuzzy LMAW (Logarithm Methodology of Additive Weights) method and fuzzy CRADIS (Compromise Ranking of Alternatives from Distance to Ideal Solution) method.
Abstract: The goal of this research was to find a selection of green suppliers (GSS) that will, in the best way, help agricultural producers to apply green agricultural production using uncertainty in decision making. In order to avoid the possibility of uncertainty in the expert decision making, Z-numbers were used together with the fuzzy LMAW (Logarithm Methodology of Additive Weights) method and fuzzy CRADIS (Compromise Ranking of Alternatives from Distance to Ideal Solution) method. By applying Z-numbers and the fuzzy LMAW method, the weighting coefficients of the criteria were determined, where the experts, in addition to the criteria ratings, also defined the degrees of certainty in the criteria ratings they gave. The obtained results indicated that the criteria related to price and qualities are the most important during the selection process. To select the best alternative, the CRADIS method modified with Z-numbers and fuzzy numbers was applied. The results obtained by applying this method showed that suppliers A2 and A3 have the best characteristics and are the first choice for the procurement of raw and production materials. As part of the paper, the validation of the results and the sensitivity analysis of the model were carried out by conducting the procedure of comparing the obtained results with the results obtained by other MCDM methods and changing the weighting coefficients of the criteria. These analyses indicated that the model presented provides stable results. The conducted research showed how Z-numbers can be used to reduce uncertainty in decision making and how Z-numbers can be used with other fuzzy methods to perform GSS.

13 citations


Journal ArticleDOI
TL;DR: In this article , a fuzzy linear singular differential equation under granular differentiability is investigated in which the coefficients and initial conditions are as fuzzy numbers, and some new notions such as fuzzy nilpotent matrix, fuzzy linearly independent vectors, fuzzy eigenvectors, rank, index and fuzzy Jordan canonical form of a fuzzy matrix are introduced.


Journal ArticleDOI
TL;DR: In this paper , a criterion-oriented three-way ranking and clustering strategy is proposed, which can solve the qualitative clustering and ranking problems of all alternatives from the perspective of criterion fuzzy sets.
Abstract: Faced with any decision-making problems with fuzzy multicriteria information, decision-makers generally set a minimum requirement on each criterion for satisfying their own preferences, thereby forming a fuzzy set on the criterion universe, which is called the criterion fuzzy set. From the perspective of realistic decision, the final decision of all alternatives should be determined according to this criterion fuzzy set. In view of this, this article proposes the criterion-oriented three-way ranking and clustering strategies, which can solve the qualitative clustering and ranking problems of all alternatives from the perspective of criterion fuzzy sets. First, we define a criterion fuzzy set as a criterion-oriented fuzzy concept and propose a criterion-oriented relative risk loss model and discuss related properties accordingly. Meanwhile, we use the generalized fuzzy rough lower (upper) approximation to estimate the absolute (relative) conditional probability between the binary fuzzy class of the alternative and the criterion-oriented fuzzy concept. Then, a criterion-oriented absolute (relative) three-way clustering strategy is proposed, which can perform qualitative analysis on all alternatives. Furthermore, based on the three-way semantics and global cost function, we recommend a criterion-oriented absolute (relative) three-way ranking strategy, which can rank all alternatives. Finally, through numerical example, comparative analysis and sensitivity analysis, we test the feasibility and effectiveness of the proposed criterion-oriented three-way ranking and clustering strategies.

Journal ArticleDOI
TL;DR: In this paper , the dynamic multiple attribute decision making (DMADM) approach with complex q-rung Orthopair fuzzy (CQROF) information has been introduced.
Abstract: The q-rung Orthopair fuzzy set (QROFS) is one of the fuzzy structures which can introduce more fuzzy information than other fuzzy frames proposed by Ronald R. Yager. In this article, the dynamic multiple attribute decision making (DMADM) approach with complex q-rung Orthopair fuzzy (CQROF) information has been introduced. The ideas of CQROF variable and uncertain CQROF variables are defined and introduced new dynamic weighted averaging (DWA) operators called dynamic complex q-rung Orthopair fuzzy weighted average (DCQROFWA) operator and uncertain dynamic complex q-rung Orthopair fuzzy weighted average (UDCQROFWA) operator. For the moment, a procedure has been developed based on DCQROFWA and CQROFWA operator to solve DMADM problems where all attribute information are used in complex q-rung Orthopair fuzzy numbers (CQROFNs) collected at distinct periods, and another procedure is developed based on UDCQROFWA and CIVQROFWA operators to solve uncertain DMADM problems for interval uncertainty in which all attribute information takes in the form of complex interval-valued q-rung Orthopair fuzzy numbers (CIVQROFNs) collected at distinct periods. Finally, a comprehensive comparative analysis has been made for the proposed approach for testing its applicability and efficiency by considering a numerical example.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a statistical estimation approach for handling Pythagorean fuzzy information under the risk attitude of decision-makers (DMs), where the DMs are partitioned by risk attitudes (hesitancy degrees) into subgroups.
Abstract: As loss in decision sample information occurs during large-scale group decision-making (LSGDM), this paper proposes a statistical estimation approach for handling Pythagorean fuzzy information under the risk attitude of decision-makers (DMs). The DMs are partitioned by risk attitudes (hesitancy degrees) into subgroups. A five-number summary for the subgroups from the incomplete decision information given by the DMs is obtained. The Cornish–Fisher expansion is then applied to estimate the mean, standard variance, and skewness of the decision sample information from the five-number summary. The confidence interval constructed by the skewness is used to obtain the interval-valued Pythagorean fuzzy number (IVPFN) evaluation information of the subgroups. An optimization model based on minimizing the conflicts between the subgroups and the overall group is used to derive the weights of the subgroups. A sorting function of the IVPFNs is used to rank the alternatives. A case study on green credit and a comparison analysis are applied to validate the proposed method.

Journal ArticleDOI
TL;DR: In this article , a double parametric fuzzy homotopy analysis approach with Shehu transform for the non-linear fuzzy time-fractional generalized Fisher's equation (FTFGFE) was designed and analyzed.

Journal ArticleDOI
TL;DR: An SEIQR model with fuzzy parameters is presented and a fuzzy non-standard finite difference (FNSFD) method for the model is developed, which preserves all the essential features of a continuous dynamical system.
Abstract: This current work presents an SEIQR model with fuzzy parameters. The use of fuzzy theory helps us to solve the problems of quantifying uncertainty in the mathematical modeling of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been derived focusing on a model in a specific group of people having a triangular membership function. Moreover, a fuzzy non-standard finite difference (FNSFD) method for the model is developed. The stability of the proposed method is discussed in a fuzzy sense. A numerical verification for the proposed model is presented. The developed FNSFD scheme is a reliable method and preserves all the essential features of a continuous dynamical system.

Proceedings ArticleDOI
TL;DR: In this article , the authors proposed some distance and knowledge measures for Fermatean fuzzy sets using t-conorms, and demonstrated the application of the suggested measures in pattern analyis and multicriteria decision-making.
Abstract: Fermatean fuzzy sets are more powerful than fuzzy sets, intuitionistic fuzzy sets, and Pythagorean fuzzy sets in handling various problems involving uncertainty. The distance measures in the fuzzy and non-standard fuzzy frameworks have got their applicability in various areas such as pattern analysis, clustering, medical diagnosis, etc. Also, the fuzzy and non-standard fuzzy knowledge measures have played a vital role in computing the criteria weights in the multicriteria decision-making problems. As there is no study concerning the distance and knowledge measures of Fermatean fuzzy sets, so in this paper, we propose some novel distance measures for Fermatean fuzzy sets using t-conorms. We also discuss their various desirable properties. With the help of suggested distance measures, we introduce some knowledge measures for Fermatean fuzzy sets. Through numerical comparison and linguistic hedges, we establish the effectiveness of the suggested distance measures and knowledge measures, respectively, over the existing measures in the Pythagorean/Fermatean fuzzy setting. At last, we demonstrate the application of the suggested measures in pattern analyis and multicriteria decision-making.

Journal ArticleDOI
05 Oct 2022-Axioms
TL;DR: Rough set models based on three-way fuzzy sets, which extend the existing fuzzy rough set models in both complete and incomplete information systems are presented and a novel method for the issue of MCDM is presented.
Abstract: Recently, the notion of a three-way fuzzy set is presented, inspired by the basic ideas of three-way decision and various generalized fuzzy sets, including lattice-valued fuzzy sets, partial fuzzy sets, intuitionistic fuzzy sets, etc. As the new theory of uncertainty, it has been used in attribute reduction and as a new control method for the water level. However, as an extension of a three-way decision, this new theory has not been used in multi-criteria decision making (MCDM for short). Based on the previous work, in this paper, we present rough set models based on three-way fuzzy sets, which extend the existing fuzzy rough set models in both complete and incomplete information systems. Furthermore, the new models are used to solve the issue of MCDM. Firstly, three-way fuzzy relation rough set and three-way fuzzy covering rough set models are presented for complete and incomplete information systems. Because almost all existing fuzzy rough set models are proposed under complete information, the new proposed models can be seen as a supplement to these existing models. Then, a relationship between the three-way fuzzy relation rough set and the three-way fuzzy covering rough set is presented. Finally, a novel method for the issue of MCDM is presented under the novel three-way fuzzy rough set models, which is used in paper defect diagnosis.

Journal ArticleDOI
04 Nov 2022-Symmetry
TL;DR: In this paper , up and down pre-invex (pre-incave) fuzzy number valued mappings (F-N-V∙Ms) are defined.
Abstract: Numerous applications of the theory of convex and nonconvex mapping exist in the fields of applied mathematics and engineering. In this paper, we have defined a new class of nonconvex functions which is known as up and down pre-invex (pre-incave) fuzzy number valued mappings (F-N-V∙Ms). The well-known fuzzy Hermite–Hadamard (𝐻𝐻)-type and related inequalities are taken into account in this work. We extend this mileage further using fuzzy Riemann integrals and the fuzzy number up and down pre-invexity. Additionally, by imposing some light restrictions on pre-invex (pre-incave) fuzzy number valued mappings, we have introduced two new significant classes of fuzzy number valued up and down pre-invexity (pre-incavity), which are referred to as lower up and down pre-invex (pre-incave) and upper up and down pre-invex (pre-incave) fuzzy number valued mappings. By using these definitions, we have amassed a large number of both established and novel exceptional situations that serve as implementations of the key findings. To support the validity of the fuzzy inclusion relations put out in this research, we also provide a few examples of fuzzy numbers valued up and down pre-invexity.

Journal ArticleDOI
TL;DR: In this article , an interval-valued intuitionistic fuzzy extension of rule base evidential reasoning is presented, which is a synthesis of fuzzy logic, the Dempster-Shafer theory of evidence (DST) and Atanassov's intuitionistic Fuzzy Sets theory redefined in the framework of DST.
Abstract: This paper presents an interval-valued intuitionistic fuzzy extension of rule base evidential reasoning which generally is a synthesis of fuzzy logic, the Dempster–Shafer theory of evidence (DST) and Atanassov’s intuitionistic fuzzy sets (A-IFS) theory redefined in the framework of DST. A lot of attention is paid to situations when in the solution of decision making problem the competing fuzzy classes with intersecting membership functions in antecedent parts of fuzzy rules, e.g., such as Low and Moderate play an important role in the problem formulation. As a result, a new mathematical object “belief interval bounded belief interval” (BIBBI) is obtained. The properties of BIBBI make it possible to use it as a more reliable representation of interval-valued intuitionistic fuzzy value than that formulated in terms of A-IFS. Using the introduced DST based definition of interval-valued A-IFS, the corresponding operations with BIBBIs and the DST representation of rule base evidential reasoning in the intuitionistic fuzzy setting, a new approach to the interval-valued intuitionistic fuzzy extension of rule base evidential reasoning is developed. To prove the correctness and applicability of this approach to the solution of decision making problems, a case study of its use for the type 2 diabetes diagnostics is analyzed.

Journal ArticleDOI
TL;DR: In this article , a new type of fuzzy covering-based rough set model over two different universes by using Zadeh's extension principle is proposed, which can be seen as a fuzzy mapping from a universe to the set of fuzzy sets on another universe.
Abstract: In this paper, we propose a new type of fuzzy covering-based rough set model over two different universes by using Zadeh’s extension principle. We mainly address the following issues in this paper. First, we present the definition of fuzzy $$\beta$$ -neighborhood, which can be seen as a fuzzy mapping from a universe to the set of fuzzy sets on another universe and study its properties. Then we define a new type of fuzzy covering-based rough set model on two different universes and investigate the properties of this model. Meanwhile, we give a necessary and sufficient condition under which two fuzzy $$\beta$$ -coverings to generate the same fuzzy covering lower approximation or the same fuzzy covering upper approximation. Moreover, matrix representations of the fuzzy covering lower and fuzzy covering upper approximation operators are investigated. Finally, we propose a new approach to a kind of multiple criteria decision making problem based on fuzzy covering-based rough set model over two universes. The proposed models not only enrich the theory of fuzzy covering-based rough set but also provide a new perspective for multiple criteria decision making with uncertainty.

Journal ArticleDOI
11 Jan 2022-Symmetry
TL;DR: A multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information to interrelate among these operators.
Abstract: Picture fuzzy sets (PFSs) can be used to handle real-life problems with uncertainty and vagueness more effectively than intuitionistic fuzzy sets (IFSs). In the process of information aggregation, many aggregation operators under PFSs are used by different authors in different fields. In this article, a multi-attribute decision-making (MADM) problem is introduced utilizing harmonic mean aggregation operators with trapezoidal fuzzy number (TrFN) under picture fuzzy information. Three harmonic mean operators are developed namely trapezoidal picture fuzzy weighted harmonic mean (TrPFWHM) operator, trapezoidal picture fuzzy order weighted harmonic mean (TrPFOWHM) operator and trapezoidal picture fuzzy hybrid harmonic mean (TrPFHHM) operator. The related properties about these operators are also studied. At last, an MADM problem is considered to interrelate among these operators. Furthermore, a numerical instance is considered to explain the productivity of the proposed operators.



Journal ArticleDOI
TL;DR: In this paper , the authors established the calculus for linearly correlated fuzzy number-valued functions and introduced a definition of derivative by using representation functions and a linear isomorphism when the basic fuzzy number is non-symmetric.

Journal ArticleDOI
TL;DR: In this paper , a novel approach named linguistic uncertain Z-numbers weighted averaging aggregation operator based on the rectangular coordinate system (LUZWAAORCS) is defined, and a score function considering the Minkowski distance measure and technique for order preference by similarity to an ideal solution (TOPSIS) is suggested to quantify the information in different Znumbers.

Journal ArticleDOI
TL;DR: The present article correlates with a fuzzy hybrid technique combined with an iterative transformation technique identified as the fuzzy new iterative transform method to confirm the superiority and efficiency of constructing numerical results to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.
Abstract: The present article correlates with a fuzzy hybrid technique combined with an iterative transformation technique identified as the fuzzy new iterative transform method. With the help of Atangana-Baleanu under generalized Hukuhara differentiability, we demonstrate the consistency of this method by achieving fuzzy fractional gas dynamics equations with fuzzy initial conditions. The achieved series solution was determined and contacted the estimated value of the suggested equation. To confirm our technique, three problems have been presented, and the results were estimated in fuzzy type. The lower and upper portions of the fuzzy solution in all three examples were simulated using two distinct fractional orders between 0 and 1. Because the exponential function is present, the fractional operator is nonsingular and global. It provides all forms of fuzzy solutions occurring between 0 and 1 at any fractional-order because it globalizes the dynamical behavior of the given equation. Because the fuzzy number provides the solution in fuzzy form, with upper and lower branches, fuzziness is also incorporated in the unknown quantity. It is essential to mention that the projected methodology to fuzziness is to confirm the superiority and efficiency of constructing numerical results to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.

Journal ArticleDOI
TL;DR: This paper forms the portfolio problem as a sequential decision problem and proposes an automatic trading system with three stages to determine the investment strategy at the beginning of each period, and designs a multi-objective genetic algorithm to solve the proposed model.
Abstract: This paper deals with a portfolio optimization problem with sell orders, in which the investor will immediately sell the risky assets once their prices reach the preset sell thresholds. Departing from the traditional portfolio models, the investor needs to determine not only an investment proportion but also a sell threshold for each risky asset. We formulate the portfolio problem as a sequential decision problem and propose an automatic trading system with three stages to determine the investment strategy at the beginning of each period. In Stage 1, we formulate the return of an investment strategy as an L R -power fuzzy number based on the historical data and propose a fuzzy mean–semi-variance portfolio optimization model with sell orders. In Stage 2, we design a multi-objective genetic algorithm to solve the proposed model. In Stage 3, we select an optimal investment strategy among the efficient solutions based on the fuzzy Value-at-Risk ratio. Moreover, we conduct two case studies in the real stock market to illustrate the effectiveness and practicability of the proposed model and algorithm. The comparison results show that the proposed trading system has a better out-of-sample performance than the other ones.

Journal ArticleDOI
TL;DR: In this paper , the authors proposed a new golden rule representative value for fuzzy numbers, and then, applied it to the ranking of the Z-number, which greatly retains the original information of the z-number and can overcome the shortcomings of the existing methods.
Abstract: Real-world decision-making is based on human cognitive information, which is characterized by fuzziness and partial reliability. In order to better describe such information, Zadeh proposed the concept of Z-number. Ranking the Z-number is an indispensable step in solving the decision-making problem under the Z-number-based information. Golden rule representative value is a new concept introduced by Yager to rank interval values. This article expands it and proposes a new golden rule representative value for fuzzy numbers, and then, apply it to the ranking of the Z-number. Some new rules involving the centroid and fuzziness of fuzzy numbers are constructed to capture the preference of decision-makers. The Takagi–Sugeno–Kang fuzzy model is used to implement these rules. The obtained Rep function is used to construct a new golden rule representative value fuzzy subset of the Z-number and associate this new fuzzy subset with a scalar value. This fuzzy subset not only implies the fuzzy aspect of the Z-number but also contains the information in the hidden probability distribution. The scalar value is regarded as the golden rule representative value of the Z-number to participate in the ranking. The proposed method greatly retains the original information of the Z-number and can overcome the shortcomings of the existing methods. Some numerical examples are used to describe the specific process of the proposed method. The comparative analysis and discussion with existing methods clarify the advantages of the proposed method.