Showing papers on "Fuzzy number published in 2023"
TL;DR: In this article , a generalized (m,n)-Fuzzy set is introduced to deal with issues that require different importances for the degrees of membership and non-membership and cannot be addressed by the fuzzification tools existing in the published literature.
Abstract: Orthopairs (pairs of disjoint sets) have points in common with many approaches to managing vaguness/uncertainty such as fuzzy sets, rough sets, soft sets, etc. Indeed, they are successfully employed to address partial knowledge, consensus, and borderline cases. One of the generalized versions of orthopairs is intuitionistic fuzzy sets which is a well-known theory for researchers interested in fuzzy set theory. To extend the area of application of fuzzy set theory and address more empirical situations, the limitation that the grades of membership and non-membership must be calibrated with the same power should be canceled. To this end, we dedicate this manuscript to introducing a generalized frame for orthopair fuzzy sets called “(m,n)-Fuzzy sets”, which will be an efficient tool to deal with issues that require different importances for the degrees of membership and non-membership and cannot be addressed by the fuzzification tools existing in the published literature. We first establish its fundamental set of operations and investigate its abstract properties that can then be transmitted to the various models they are in connection with. Then, to rank (m,n)-Fuzzy sets, we define the functions of score and accuracy, and formulate aggregation operators to be used with (m,n)-Fuzzy sets. Ultimately, we develop the successful technique “aggregation operators” to handle multi-criteria decision-making problems in the environment of (m,n)-Fuzzy sets. The proposed technique has been illustrated and analyzed via a numerical example.
18 citations
TL;DR: This work studies the univariate fuzzy fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasi-interpolation arctangent-algebraic-Gudermannian-generalized symmetrical activation function relied fuzzy neural network operators.
Abstract: Here we study the univariate fuzzy fractional quantitative approximation of fuzzy real valued functions on a compact interval by quasi-interpolation arctangent-algebraic-Gudermannian-generalized symmetrical activation function relied fuzzy neural network operators. These approximations are derived by establishing fuzzy Jackson type inequalities involving the fuzzy moduli of continuity of the right and left Caputo fuzzy fractional derivatives of the involved function. The approximations are fuzzy pointwise and fuzzy uniform. The related feed-forward fuzzy neural networks are with one hidden layer. We study also the fuzzy integer derivative and just fuzzy continuous cases. Our fuzzy fractional approximation result using higher order fuzzy differentiation converges better than in the fuzzy just continuous case.
11 citations
TL;DR: In this paper , the authors proposed a new multiobjective optimization approach for designing a self-generated interpretable fuzzy logic system (FLS), where the types of fuzzy sets can be constructed automatically by self-organizing method, so as to form a hybrid fuzzy system.
Abstract: This paper proposes a new multiobjective optimization approach for designing a self-generated interpretable fuzzy logic system (FLS). The types of fuzzy sets can be constructed automatically by self-organizing method, so as to form a hybrid fuzzy system. Different from the existing evolutionary type-1 fuzzy system, which is full of type-1 fuzzy sets, and the evolutionary interval type-2 fuzzy system, which is full of interval type-2 fuzzy sets, there are both type-1 fuzzy sets and interval type-2 fuzzy sets in the hybrid fuzzy system. A new transparency-oriented objective function is defined, and the constraint of the footprint of uncertainty (FOU) of the interval type-2 (IT2) fuzzy set (FS) is considered for the first time. A new FS merging criterion focusing on the proximity of the cores of fuzzy sets is proposed, which is easy to calculate and maintains the characteristics of classical similarity measures. Combined with the new merging criterion, the online cluster and fuzzy set updating (OCFU) algorithm is employed to initialize the reference rule base and the type of fuzzy sets, as it is assumed that no training data are collected in advance. Based on the reference rule base, the advanced multiobjective front-guided continuous ant colony optimization (AMO-FCACO) algorithm is introduced to optimize all the free parameters of the FLS. With the operation mentioned above, the self-generated FLSs achieve a good balance between interpretability and performance. The effectiveness of the proposed method is verified by three nonlinear system tracking problems.
9 citations
TL;DR: In this paper , the Hermite-Hadamard-, Fejér-, and Pachpatte-type inequalities for up and down fuzzy-ordered relations between two fuzzy numbers are proven using the fuzzy fractional operator.
Abstract: In this study, we apply a recently developed idea of up and down fuzzy-ordered relations between two fuzzy numbers. Here, we consider fuzzy Riemann–Liouville fractional integrals to establish the Hermite–Hadamard-, Fejér-, and Pachpatte-type inequalities. We estimate fuzzy fractional inequalities for a newly introduced class of ℏ-preinvexity over fuzzy-number valued settings. For the first time, such inequalities involving up and down fuzzy-ordered functions are proven using the fuzzy fractional operator. The stated inequalities are supported by a few numerical examples that will be helpful to validate our main results.
6 citations
TL;DR: In this article , the authors considered the well-known fuzzy Hermite-Hadamard (HH) type and associated inequalities, and with the help of fuzzy Aumann integrals and the newly introduced fuzzy number valued up and down convexity (𝑈𝒟-convexity), they increase this mileage even further.
Abstract: The topic of convex and nonconvex mapping has many applications in engineering and applied mathematics. The Aumann and fuzzy Aumann integrals are the most significant interval and fuzzy operators that allow the classical theory of integrals to be generalized. This paper considers the well-known fuzzy Hermite–Hadamard (HH) type and associated inequalities. With the help of fuzzy Aumann integrals and the newly introduced fuzzy number valued up and down convexity (𝑈𝒟-convexity), we increase this mileage even further. Additionally, with the help of definitions of lower 𝑈𝒟-concave (lower 𝑈𝒟-concave) and upper 𝑈𝒟-convex (concave) fuzzy number valued mappings (ℱ𝒩𝒱ℳs), we have gathered a sizable collection of both well-known and new extraordinary cases that act as applications of the main conclusions. We also offer a few examples of fuzzy number valued 𝑈𝒟-convexity to further demonstrate the validity of the fuzzy inclusion relations presented in this study.
5 citations
TL;DR: In this article , a generalized version of the q-linear Diophantine fuzzy set (q-LDFS) is proposed for decision-making problems, which is known as spherical Q-linear DDFS.
Abstract: The main goal of this article is to reveal a new generalized version of the q-linear Diophantine fuzzy set (q-LDFS) named spherical q-linear Diophantine fuzzy set (Sq-LDFS). The existing concepts of intuitionistic fuzzy set (IFS), q-rung orthopair fuzzy set (q-OFS), linear Diophantine fuzzy set (LDFS), and spherical fuzzy set have a wide range of applications in decision-making problems, but they all have strict limitations in terms of membership degree, non-membership degree, and uncertainty degree. We moot the article of the spherical q-linear Diophantine fuzzy set (Sq-LDFS) with control factors to alleviate these limitations. A Spherical q-linear Diophantine fuzzy number structure is independent of the selection of the membership grades because of its control parameters in three membership grades. An Sq-LDFS with a parameter estimation process can be extremely useful for modeling uncertainty in decision-making (DM). By using control factors, Sq-LDFS may classify a physical system. We highlight some of the downsides of q-LDFSs. By using algebraic norms, we offer some novel operational laws for Sq-LDFSs. We also introduced the weighted average and weighted geometric aggregation operators and their fundamental laws and properties. Furthermore, we proposed the algorithms for a multicriteria decision-making approach with graphical representation. Moreover, a numerical illustration of using the proposed methodology for Sq-LDF data for emergency decision-making is presented. Finally, a comparative analysis is presented to examine the efficacy of our proposed approach.
2 citations
01 Jan 2023
TL;DR: In this paper , a decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives.
Abstract: Intuitionistic fuzzy numbers incorporate the membership and non-membership degrees. In contrast, Z-numbers consist of restriction components, with the existence of a reliability component describing the degree of certainty for the restriction. The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers, namely intuitionistic Z-numbers (IZN). The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are characterized by the membership and non-membership functions, exhibiting the degree of the hesitancy of decision-makers. This paper presents the application of such numbers in fuzzy multi-criteria decision-making problems. A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives. The proposed model is then implemented in a supplier selection problem. The obtained ranking is compared to the existing models based on Z-numbers. The results show that the ranking order is slightly different from the existing models. Sensitivity analysis is performed to validate the obtained ranking. The sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80% to 100% consistency despite the drastic change of criteria weights. Intuitionistic Z-numbers play a very important role in describing the uncertainty in the decision makers’ opinions in solving decision-making problems.
2 citations
TL;DR: In this article , a new weighted aggregated operator, namely, nth power root fuzzy weighted power average (nPR-FWPA), was developed to deal with choice information and show some of their basic properties.
Abstract: An nth power root fuzzy set is a useful extension of a fuzzy set for expressing uncertain data. Because of their wider range of showing membership grades, nth power root fuzzy sets can cover more ambiguous situations than intuitionistic fuzzy sets. In this article, we present several novel operations on nth power root fuzzy sets, as well as their various features. Besides, we develop a new weighted aggregated operator, namely, nth power root fuzzy weighted power average (nPR-FWPA) over nth power root fuzzy sets to deal with choice information and show some of their basic properties. In addition, we define a scoring function for nth power root fuzzy sets ranking. Furthermore, we use this operator to determine the optimal location for constructing a home and demonstrate how we may choose the best alternative by comparing aggregate outputs using score values. Finally, we compare the nPR-FWPA operator outcomes to those of other well-known operators.
2 citations
TL;DR: In this paper , the authors proposed a novel fuzzy entropy named as the exponential probabilistic hesitant fuzzy entropy for the P-HFEs, which not only observes the basic property of fuzzy entropy, but also has the same characteristics and change tends with the existing fuzzy entropy proposed and studied by other scholars.
Abstract: The probabilistic hesitant fuzzy sets (P-HFSs) allow experts to express their preferences regarding different membership degrees with probabilistic information. Fuzzy entropy is an important concept to measure the uncertainty of probabilistic hesitant fuzzy information. In this paper, we propose a novel fuzzy entropy named as the exponential probabilistic hesitant fuzzy entropy for the P-HFEs. This novel fuzzy entropy not only observes the basic property of fuzzy entropy, but also has the same characteristics and change tends with the existing fuzzy entropy proposed and studied by other scholars. Then, based on the cardinal reconciliation method and TODIM(Tomada de decisao interativa multicriterio) method, we propose a multi-criteria decision-making (MCDM) problem, where the attribute weight is determined by the exponential probabilistic hesitant fuzzy entropy of the integration results. Finally, a application case in green building is given for the sake of illustrating the efficiency of the MCDM problem. Numerical and theoretical results show that a MCDM problem based on the proposed novel fuzzy entropy and the TODIM method have a wide range of application.
2 citations
02 Dec 2022
TL;DR: In this article , the authors proposed six new variants of score functions for effective ranking of interval-valued Fermatean fuzzy sets, and used a TOPSIS-based multi-criteria decision-making (MCDM) problem.
Abstract: Fermatean fuzzy sets (FFSs), an orthopair fuzzy set proposed by Senapati and Yager (Journal of Ambient Intelligence and Humanized Computing 11:663–674, 2020, [24]), can handle the situation with ambiguous and incomplete information in a more effective manner than the Pythagorean fuzzy sets presented by Yager (Pythagorean fuzzy subsets, 2013 Joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS), pp 57–61, 2013, [2]) and the intuitionistic fuzzy sets presented by Atanassov (Fuzzy Sets and Systems 20:87–96, 1986, [3]). Sergi et al. (Journal of Intelligent & Fuzzy Systems 42:365–376, 2022, [40]) initiated interval-valued Fermatean fuzzy sets (IVFFSs) and established IVFFS ordering, as well as some mathematical operations. In addition, Jeevraj (Expert Systems with Applications 185:1–20, 2021, [37]) introduced the concept of a score and accuracy function for IVFFSs. The main objective of this chapter is to suggest some score functions for acceptable ranking of IVFFSs, as well as the interval-valued Fermatean fuzzy TOPSIS method for solving multi-criteria decision making problems. Here, we have proposed six new variants of score functions for effective ranking of interval-valued Fermatean fuzzy sets. Depending on various types of score functions, we have used a TOPSIS-based multi-criteria decision making (MCDM) problem in which decision makers’ (DMs’) preference knowledge is summarized in the pattern of interval-valued Fermatean fuzzy sets. To illustrate the usefulness of the proposed method, a computational paradigm has been considered. Finally, concluding remarks and future scope of research have been mentioned.
1 citations
TL;DR: In this paper , the authors presented TI-fuzzy β-neighborhood measures, which are FMs and generalized CIs, to deal with granularity reduction and decision making in a fuzzy β-covering approximation space.
TL;DR: In this article , the authors employed a novel ranking function to solve the transportation problem, where fuzzy triangular numbers represent the fuzzy demand and supply (DAS) and the fuzzy model is transformed and compressed to a crisp model (CM), and the results are compared using the northwest corner method and the least cost method.
Abstract: The transportation problem (TP) is employed in many different situations, such as scheduling, performance, spending, plant placement, inventory control, and employee scheduling. When all variables, including supply, demand, and unit transportation costs (TC), are precisely known, effective solutions to the transportation problem can be provided. However, understanding how to investigate the transportation problem in an uncertain environment is essential. Additionally, businesses and organizations should seek the most economical and environmentally friendly forms of transportation, considering the significance of environmental issues and strict environmental legislation. This research employs a novel ranking function to solve the transportation problem (TP), where fuzzy triangular numbers represent the fuzzy demand and supply (DAS). The fuzzy model is transformed and compressed to a crisp model (CM), and the results are compared using the northwest corner method and the least cost method. In addition, a numerical example of the fuzzy transportation model (FTM) is shown.
TL;DR: In this article , the second-order fuzzy homogeneous differential equation is transformed into a more special simplest form under the condition that the solution of the boundary value problem of the equation exists and is unique.
Abstract: In this paper, the second-order fuzzy homogeneous differential equation is transformed into a more special simplest form under the condition that the solution of the boundary value problem of the equation exists and is unique. Then the eigenvalues of the boundary value problem of the second-order simplest fuzzy homogeneous differential equation are studied and the theorems that make the eigenvalues exist are proposed and then illustrated with examples. Finally, it is proved that when the second-order fuzzy coefficient p ˜ ( t ) in the second-order fuzzy homogeneous differential equation is a fuzzy number, the solution set of its corresponding second-order granular homogeneous differential equation becomes larger, that is, the solution set of fuzzy differential equations with real numbers is a subset of the solution set with fuzzy coefficients as fuzzy numbers.
TL;DR: In this article , the authors proposed a low complexity method for the calculation of fuzzy measures that have been applied to Choquet integral for the fusion of deep learning models across different application domains for increasing the accuracy of the overall model.
Abstract: This paper studies the high complexity of the calculation of fuzzy measures which can be used in fuzzy integrals to combine the decisions of different learning algorithms. To this end, this paper proposes an alternative low complexity method for the calculation of fuzzy measures that have been applied to Choquet integral for the fusion of deep learning models across different application domains for increasing the accuracy of the overall model. The paper shows that the Dempster-Shafer (DS) belief structure provides partial information about the fuzzy measures associated with a variable, and the paper devises a method to use this partial information for the calculation of fuzzy measures. An infinite number of fuzzy measures is associated with the DS belief structure. This paper proposes a theorem to calculate the general form of a specific set of fuzzy measures associated with the DS belief structure. This specific set of fuzzy measures can be expressed as a weighted summation of the basic assignment function of the DS belief structure. The main advantage of expressing the fuzzy measures in this format is that the monotonic condition which needs to be maintained during the calculation of the fuzzy measure can be avoided and only the basic assignment function needs to be evaluated. The calculation of the basic assignment function is formulated using a method inspired by the Monte Carlo approach used to calculate Value Functions in Markov Decision Process.
TL;DR: In this paper , the authors investigated the universal approximation of multi-input single-output hierarchical fuzzy system (HFS) and developed the construction algorithms of universal approximators using the semi-tensor product of matrices.
Abstract: As an important branch of fuzzy systems, hierarchical fuzzy system (HFS) has a wide range of applications in system science, medical science and engineering. Using the semi-tensor product of matrices, this paper investigates the universal approximation of multi-input single-output HFSs, and develops the construction algorithms of universal approximators. Initially, based on the fuzzy relation matrices of fuzzy logic units with Mamdani-type fuzzy rules, the algebraic formulation of HFSs consisting of fuzzy logic units is proposed. After that, the universal approximation of HFSs is explored via the algebraic formulation, and some effective algorithms are presented to construct the universal approximators of HFSs with respect to different scenarios of approximated functions. Finally, the effectiveness of obtained results is verified by the on-ramp metering of freeway.
TL;DR: In this article , two new computational methods for solving linear programming problem under trapezoidal and triangular fuzzy uncertainties with equality constraints are proposed, where the coefficients of the constraints and the objective functions are assumed to be crisp.
Abstract: This paper proposes two new computational methods for solving linear programming problem under trapezoidal and triangular fuzzy uncertainties with equality constraints. The coefficients of the constraints and the objective functions are assumed to be crisp. However, the decision variables and the right-hand side vector of the constraints are considered as uncertain in nature. The concepts of fuzzy addition and subtraction have been used to develop the proposed methods. In the first method, the coefficients are considered as non-negative, whereas mixed coefficients (i.e. both negative and non-negative) are considered in the second method. The obtained results are compared with Behera et al. [D. Behera, K. Peters and S. A. Edalatpanah, Alternative methods for linear programming problem under triangular fuzzy uncertainty, Journal of Statistics and Management Systems, 25 (2022) 521–539; D. Behera, K. Peters, S. A. Edalatpanah and D. Qiu, New methods for solving imprecisely defined linear programming problem under trapezoidal fuzzy uncertainty, Journal of Information and Optimization Sciences, 42 (2021) 603–629], and Saati et al. [S. Saati, M. Tavana, A. Hatami-Marbini and E. Hajiakhondi, A fuzzy linear programming model with fuzzy parameters and decision variables, International Journal of Information and Decision Sciences, 7 (2015) 312–333.] for the validation.
TL;DR: In this paper , a new definition of quartic fuzzy sets with intuitionistic, Pythagorean, and Fermatean fuzzy sets is presented and compared with existing intuitionistic fuzzy sets.
TL;DR: In this paper , the concept of q-spherical fuzzy rough set (q-SFRS) was introduced, which avoids the complications of more recent ideas like the intuitionistic fuzzy rough sets, Pythagorean fuzzy rough Set, and q-rung orthopair fuzzy Rough Set.
Abstract:
This article's purpose is to investigate and generalize the concepts of rough set, in addition to the q-spherical fuzzy set, and to introduce a novel concept that is called q-spherical fuzzy rough set (q-SFRS). This novel approach avoids the complications of more recent ideas like the intuitionistic fuzzy rough set, Pythagorean fuzzy rough set, and q-rung orthopair fuzzy rough set. Since mathematical operations known as "aggregation operators" are used to bring together sets of data. Popular aggregation operations include the arithmetic mean and the weighted mean. The key distinction between the weighted mean and the arithmetic mean is that the latter allows us to weight the various values based on their importance. Various aggregation operators make different assumptions about the input (data kinds) and the kind of information that may be included in the model. Because of this, some new q-spherical fuzzy rough weighted arithmetic mean operator and q-spherical fuzzy rough weighted geometric mean operator have been introduced. The developed operators are more general. Because the picture fuzzy rough weighted arithmetic mean (PFRWAM) operator, picture fuzzy rough weighted geometric mean (PFRWGM) operator, spherical fuzzy rough weighted arithmetic mean (SFRWAM) operator and spherical fuzzy rough weighted geometric mean (SFRWGM) operator are all the special cases of the q-SFRWAM and q-SFRWGM operators. When parameter q = 1, the q-SFRWAM operator reduces the PFRWAM operator, and the q-SFRWGM operator reduces the PFRWGM operator. When parameter q = 2, the q-SFRWAM operator reduces the SFRWAM operator, and the q-SFRWGM operator reduces the SFRWGM operator. Besides, our approach is more flexible, and decision-makers can choose different values of parameter q according to the different risk attitudes. In addition, the basic properties of these newly presented operators have been analyzed in great depth and expounded upon. Additionally, a technique called multi-criteria decision-making (MCDM) has been established, and a detailed example has been supplied to back up the recently introduced work. An evaluation of the offered methodology is established at the article's conclusion. The results of this research show that, compared to the q-spherical fuzzy set, our method is better and more effective.
02 Dec 2022
TL;DR: In this paper , a new model of multi-objective linear fractional programming problem with triangular intuitionistic fuzzy parameters has been proposed for finding the permissible deviations in the objective values in view of the constraints under consideration.
Abstract: In the present communication, a new model of multi-objective linear fractional programming problem (MOLFPP) with triangular intuitionistic fuzzy parameters has been proposed for finding the permissible deviations in the objective values in view of the constraints under consideration. Here, ( $$\alpha , \beta )$$ -cuts of the triangular intuitionistic fuzzy numbers have been utilized in the proposed model to find out the level of satisfaction and to convert the fuzzy parameters into closed intervals. Here, such fuzzification has been incorporated to encounter the uncertainty and inexactness that arises in the available information. Using the variable transformation technique/Taylor’s series, the interval-valued fractional objectives have been mathematically estimated by the intervals of linear functions. The objective functions have also been assigned appropriate weights using the analytic hierarchy process. In order to consolidate the multiple objectives into a single objective, the weighting sum method has been applied. It may be observed that the MOLFPP in the interval-valued form has been analogously reduced to a pair of linear problems which provide the acceptable deviations in the objective values. For the sake of illustration and implementation of the proposed work, a numerical example related to a manufacturing company has been solved in detail.
TL;DR: In this article , a new Membership Score Function (MSF) for interval-valued Pythagorean fuzzy numbers has been proposed, which can overcome the drawbacks of existing familiar ranking methods.
Abstract: The main aim of the paper is to define a new Membership score function on the class of interval-valued Pythagorean fuzzy numbers which can overcome the drawbacks of existing familiar ranking methods. In this paper, firstly, we show the limitations of various ranking functions in ordering/ comparing any two arbitrary interval-valued Pythagorean fuzzy numbers in detail. Secondly, we define a new Membership score function on the class of interval-valued Pythagorean fuzzy numbers and study their properties. Then we compare our proposed method with many other different existing methods for showing the efficacy of the proposed method. Finally, we show the applicability of the proposed Membership score function in solving interval-valued Pythagorean fuzzy multi-criteria decision-making problems using a numerical example.
TL;DR: In this article , the authors proposed some new operational laws and AOs for use in a T-spherical fuzzy environment, which combine the concept of proportional distribution to provide a neutral or fair solution to the membership, abstinence, and nonmembership of T-SPFNs.
Abstract: T-spherical fuzzy sets (T-SPFSs) have gained popularity because of their ability to account for uncertainty more effectively and spanning a larger domain. The sum of the t-$ th $ power of membership grades in T-SPFSs is close to a unit interval, allowing for greater uncertainty. As a result, this set outperforms traditional fuzzy structures. The "multi-criteria decision-making" (MCDM) approach is a widely used technique that requires the use of some aggregation tools, and various such aggregation operators (AOs) have been developed over the years to achieve this purpose. The purpose of this paper is to propose some new operational laws and AOs for use in a T-spherical fuzzy environment. In this regard, we presented some new neutral or fair operational rules that combine the concept of proportional distribution to provide a neutral or fair solution to the membership, abstinence, and non-membership of T-spherical fuzzy numbers (T-SPFNs). Based on the obtained operational rules, we presented the "T-spherical fuzzy fairly weighted average operator" and the "T-spherical fuzzy fairly ordered weighted averaging operator". Compared to earlier methodologies, the proposed AOs provide more generalised, reliable, and accurate information. In addition, under T-SPFSs, an MCDM approach is developed employing suggested AOs with several decision-makers (DMs) and partial weight details. Finally, to demonstrate the applicability of the innovative technique, we give an actual case study of "food waste treatment technology" (FWTT) selection under T-SPFSs scenarios. A comparison with an existing model has also been undertaken to confirm the validity and robustness of the acquired results.
TL;DR: In this article , the problem of approximating n-dimensional fuzzy number by using α−β-knots piecewise linear fuzzy n-cell numbers is discussed. And the notions of I-nearest α− β-knows piece wise linear fuzzy approximation and II-NEarest α −β-knowss piece-wise linear approximation are introduced for a general n-dimentional fuzzy number.
TL;DR: In this article , a hybrid-type fuzzy system (HTFS) is proposed to automatically determine the types of fuzzy sets (type-1 fuzzy sets) or interval type-2 fuzzy sets(IT2-FSs) based on fuzziness.
TL;DR: In this paper , the authors employed t-conorms to suggest various Fermatean fuzzy similarity measures and created some new entropy measures for fuzzy sets using numerical comparison and linguistic hedging, and established the superiority of the suggested similarity metrics and entropy measures over the existing measures in the FermATEan fuzzy environment.
Abstract: To deal with situations involving uncertainty, Fermatean fuzzy sets are more effective than Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. Applications for fuzzy similarity measures can be found in a wide range of fields, including clustering analysis, classification issues, medical diagnosis, etc. The computation of the weights of the criteria in a multi-criteria decision-making problem heavily relies on fuzzy entropy measurements. In this paper, we employ t-conorms to suggest various Fermatean fuzzy similarity measures. We have also discussed all of their interesting characteristics. Using the suggested similarity measurements, we have created some new entropy measures for Fermatean fuzzy sets. By using numerical comparison and linguistic hedging, we have established the superiority of the suggested similarity metrics and entropy measures over the existing measures in the Fermatean fuzzy environment. The usefulness of the proposed Fermatean fuzzy similarity measurements is shown by pattern analysis. Last but not least, a novel multi-attribute decision-making approach is described that tackles a significant flaw in the order preference by similarity to the ideal solution, a conventional approach to decision-making, in a Fermatean fuzzy environment.
TL;DR: In this article , the authors proposed an efficient approximating alpha-cut operations (exACO) method by incorporating two novel treatments: logarithmic and exponential functions are used to approximate the membership functions of fuzzy priorities.
TL;DR: The theory of extensional (R,R*)-fuzzy sets defined on sets with fuzzy similarity relations with values in dual pair of semirings and power sets functors related to this theory and, at the same time, the theory of cuts with relational morphisms of these structures are presented as mentioned in this paper .
Abstract: Many of the new MV-valued fuzzy structures, including intuitionistic, neutrosophic, or fuzzy soft sets, can be transformed into so-called almost MV-valued fuzzy sets, or, equivalently, fuzzy sets with values in dual pair of semirings (in symbols, (R,R*)-fuzzy sets). This transformation allows any construction of almost MV-valued fuzzy sets to be retransformed into an analogous construction for these new fuzzy structures. In that way, approximation theories for (R,R*)-fuzzy sets, rough (R,R*)-fuzzy sets theories, or F-transform theories for (R,R*)-fuzzy sets have already been created and then retransformed for these new fuzzy structures. In this paper, we continue this trend and define, on the one hand, the theory of extensional (R,R*)-fuzzy sets defined on sets with fuzzy similarity relations with values in dual pair of semirings and power sets functors related to this theory and, at the same time, the theory of cuts with relational morphisms of these structures. Illustratively, the reverse transformations of some of these concepts into new fuzzy structures are presented.