Iranian Journal of Fuzzy Systems
https://ijfs.usb.ac.ir/
Iranian Journal of Fuzzy Systemsendaily1Wed, 01 Dec 2021 00:00:00 +0330Wed, 01 Dec 2021 00:00:00 +0330cover 18-6 December 2021
https://ijfs.usb.ac.ir/article_6342.html
End-point linear functions
https://ijfs.usb.ac.ir/article_6329.html
Positive homogeneity is represented as a constraint 0-homogeneity and generalized into z-homogeneity, called also z-end point linearity. Several special z-homogeneous aggregation functions are studied, in particular semicopulas, quasi-copulas, copulas, overlap functions, etc.Adaptive control design for fixed-time synchronization of fuzzy stochastic cellular neural networks with discrete and distributed delay
https://ijfs.usb.ac.ir/article_6330.html
This paper studies the fixed-time synchronization problem of fuzzy stochastic cellular neural networks (FSCNNs) with discrete and distributed delay. Compared with the finite-time synchronization in the existing literature, the fixed-time synchronization of FSCNNs is studied for the first time, and the convergence time obtained does not depend on the upper bound of the initial value of the system. In addition, two kinds of control are designed, one is feedback control and the other is adaptive control. Besides, it is the first time to achieve fixed-time synchronization of FSCNNs via adaptive control. Finally, two numerical examples are also proposed to illustrate the practicability and validity of the results we proposed.Calculation of centroid of high dimensional fuzzy number and application
https://ijfs.usb.ac.ir/article_6331.html
In this paper, the conception of centroid of $n$-dimensional fuzzy number is introduced viaregarding its membership function as the density function on its support set, and some properties of it are obtained. Compared with the mean of the multi dimensional fuzzy number, the centroid takes into account the overall relationship between the edge membership functions of the membership function of the multi dimensional fuzzy number. Therefore, it can approximate (characterize) the fuzzy number more objectively and reasonably than using the mean of the multi dimensional fuzzy number. The most important work of this paper is that for two special kinds of multi dimensional fuzzy numbers (fuzzy $n$-cell numbers and fuzzy $n$-ellipsoid numbers), we respectively give calculation formulas, which can be used conveniently in application since the formulas are based on a definite integral of the level set functions of the multi dimensional fuzzy number on the unit interval $[0,1]$, rather than the multiple integral of the membership function of the multi dimensional fuzzy number itself on its support set. Then, by using the calculation formulas, we obtain another special property of the centroid for fuzzy $n$-cell number and fuzzy $n$-ellipsoid number. Finally, as an example of application, by using the centroid of multi dimensional fuzzy number, we define a fuzzy order on $n$-dimensional fuzzy number space, which can be used to rank uncertain or imprecise multichannel digital information.Structural topology in a category
https://ijfs.usb.ac.ir/article_6332.html
Several fuzzy topologies are defined and studied by different authors. In this article, we unify five of the most common fuzzy topologies existing in the literature, as well as the standard topology. This is done by introducing the notion of structural topology on objects in a category and proving that topologies on a set as well as fuzzy topologies on fuzzy sets and fuzzy topologies on fuzzy subsets are all structural topologies. We also introduce the notion of structural continuity and we show that the fuzzy continuity defined in the literature in all the above mentioned cases, as well as the standard continuity are structural.A new definition of fuzzy k-pseudo metric and its induced fuzzifying structures
https://ijfs.usb.ac.ir/article_6333.html
In this paper, a new definition of a fuzzy $k$-pseudo metric is introduced and its induced fuzzifying structures are constructed,&nbsp;such as a fuzzifying neighborhood system, a fuzzifying topology,&nbsp;a fuzzifying closure operator,&nbsp;a fuzzifying uniformity.Besides, it is shown that there is a one-to-one correspondence between fuzzy $k$-pseudo metrics and nests of crisp $k$-pseudo metrics.Different classes ratio and Laplace summation operator based intuitionistic fuzzy rough attribute selection
https://ijfs.usb.ac.ir/article_6334.html
In real-world data deluge, due to insignificant information and high dimension, irrelevant and redundant attributes reduce the ability of experts both in predictive accuracy and speed, respectively. Attribute selection is the notion of selecting those attributes that are essential as well as enough to specify the target knowledge preferably. Fuzzy rough set-based approaches play a crucial role in selecting relevant and less redundant attributes from a high-dimensional dataset. Intuitionistic fuzzy set-based approaches can handle uncertainty as it gives an additional degree of freedom when compared to fuzzy approaches. So, it has a more flexible and practical ability to deal with vagueness and noise available in the information system. In this paper, we introduce two new robust approaches for attribute selection based on intuitionistic fuzzy rough set theory using the concepts of Different Classes ratio and Laplace Summation operator. Firstly, Different Classes ratio and Laplace Summation operator based lower andupper approximations are established based on intuitionistic fuzzy rough set concept. Moreover, we present algorithms and illustrative examples for a better understanding of our approaches. Finally, experimental analysis is performed on some real-valued datasets for attribute selection and classification accuracies.A fuzzy approach to review-based recommendation: Design and optimization of a fuzzy classification scheme based on implicit features of textual reviews
https://ijfs.usb.ac.ir/article_6335.html
In the design of recommender systems, it is believed that the set of reviews written by a user can somehow reveal his/her interests, and the content of an item can also be implied from its corresponding reviews. The present study attempts to model both the users and the items via extracting key information from the existing textual reviews. Based on this information, a fuzzy rule-based classifier is designed and tuned, which aims to predict whether a typical user will be interested in a typical item or not. For this purpose, the set of all reviews belonging to a user are mapped to a vector representing the user's interests. Similarly, the set of reviews written by different users over an item are merged and mapped to a vector representing the item. By conjoining these two vectors, a longer vector is obtained which will be used as the input of the classifier. To optimize the classifier, an adaptive approach is suggested and rule-weight learning is carried out, accordingly. The performance of the proposed fuzzy recommender system was evaluated on the Amazon dataset. Experimental results narrate from the promising classification ability of the proposed recommender system compared to state of the art.Design and analysis of acceptance sampling plans based on intuitionistic fuzzy linguistic terms
https://ijfs.usb.ac.ir/article_6336.html
Acceptance sampling plans (ASPs) offer inspection of a small set of items from a lot within a predefined plan to procure a certain output quality level with minimum cost in terms of time, effort, and damage to the inspected items. Although traditional ASPs use crisp plan parameters, quality characteristics of the incoming items or human evaluations about inspection process may contain uncertainties and may not always be defined as crisp values in real life problems. The fuzzy set theory (FST) is one of the most popular techniques to model these uncertainties by defining plan parameters as fuzzy numbers. Despite the advantages, traditional fuzzy sets are not flexible enough to model all kinds of uncertainties. For example, it has some disadvantages because of defining the status of any item based on defectiveness or non-defectiveness conditions and presuming the parts as non-defective whose defectiveness is not indeed determined. New extensions of FST can improve the quality of uncertainty modeling of ASPs. Intuitionistic Fuzzy Sets (IFSs) allow slackness for non-determination about the membership and give more sensitive modeling opportunity in human-related evaluations by the help of this ability. Since the inspection procedure of the ASPs depends on human-related judgements, IFSs have been used to define the defectiveness degree of the items in this study. ASPs based on interval-valued IFSs (IVIFSs) have also been designed and some characteristic functions of ASPs, such as acceptance probability ($P_a$), average sample number ($ASN$) and average total inspection ($ATI$) have been reformulated. Intuitionistic binomial and Poisson distributions have been defined to be able to formulate the ASPs. Additionally, the defectiveness of the items has been represented by using linguistic terms to overcome the difficulty of quantifying the verbal evaluation results as numerical measures. The $\alpha$-cut technique has been combined with the linguistic approach to allow defining with multiple $\alpha$ values for different product segments. Finally, some numerical examples have been presented to analyze the effectiveness of proposed ASPs and discuss the obtained results.A normalized distribution mechanism under multi-criteria situations and fuzzy behavior
https://ijfs.usb.ac.ir/article_6337.html
In general, agents always face an increasing need to focus on multiple aims efficiently under their operational processes. However, agents might take different activity levels to participate and might represent administrative areas of different scales. Therefore, this paper proposes a normalized index considering multi-criteria situations and supreme-utilities among fuzzy activity level (decision, strategy) vectors. Three existing notions of traditional game theory are reinterpreted in the framework of multi-criteria fuzzy transferable utility games. First, the normalized index could be represented as an alternative formulation in terms of excess functions. Second, an axiomatic result is proposed to present the rationality of this normalized index based on the reduced game and related consistency. Finally, two dynamic processes are introduced to illustrate that this normalized index could be reached by agents who start from an arbitrary efficient payoff vector and make successive adjustments.A novel fuzzy sliding mode control approach for chaotic systems
https://ijfs.usb.ac.ir/article_6338.html
The purpose of this paper is to study the stabilization problem for a class of uncertain chaotic systems against unknown dynamics and disturbances, based on fuzzy sliding mode controller approaches. To fulfill this aim, the first- and the second-orders sliding mode controllers and an adaptive variable universe fuzzy sliding mode controller are combined to a set of linguistic rules, to design some novel approaches for improving the performance of the control action and eliminating the chattering issue. The stability analysis of the closed-loop system is proved via the Lyapunov stability theorem, and also the convergence of the tracking error to zero in finite-time is guaranteed. The new proposed control laws contribute the control actions to outperform the conventional one in terms of chattering reduction and elimination, along with lessening in the reaching time. Moreover, some numerical simulations are provided to depict that the proposed control laws are not only robust with respect to uncertainties and external disturbances, which lead the system to the desired state, but also can significantly eliminate the chattering effect.Interval discrete fractional calculus and its application to interval fractional difference equations
https://ijfs.usb.ac.ir/article_6339.html
In this work, we present some useful results of discrete fractional calculus for \ivf s. The composition rules for interval fractional operators are introduced, which are used to construct the general form of the solutions to nonlinear interval fractional difference equations. An illustrative example is provided in which the method of recursive iterations is applied to obtain explicit formulas for the solutions of linear interval fractional difference equations.A visual social network group consensus approach with minimum adjustment based on Pythagorean fuzzy set
https://ijfs.usb.ac.ir/article_6340.html
People's demand for the decision-making space of opinion expression is getting higher, and the methods to determine the threshold value of current consensus still remain elusive. To deal with large and diverse information of users and discuss deeply the threshold in social networks, we establish a new consistency model with a new preference structure. In this paper, the Pythagorean fuzzy numbers (PFNs) are introduced into social network group decision-making for the expression of decision-makers' preference (DMs) and the concepts definition of the distance measurements, consensus index, and threshold indifference curves, respectively. In addition, we establish a Pythagorean fuzzy group consensus model with minimum adjustment through determining the setting rule of threshold value before reaching the consensus. Finally, we use the proposed model to solve the selection of square cabin hospitals.Fuzzy arithmetic with product t-norm
https://ijfs.usb.ac.ir/article_6341.html
Fuzzy arithmetic performed with the product t-norm is the focus of this paper. The subject is handled from both practical and theoretical perspectives. Explicit formulas for product-sum and product-multiplication of triangular fuzzy numbers are obtained. These formulas can effectively replace the computational methods proposed so far. The issue that these operations are not shape preserving is solved by the presentation of appropriate approximations. Finally, the product arithmetic is compared in detail to the arithmetic performed with the boundary t-norms, namely the minimum and drastic sum.translate 18-6 December 2021
https://ijfs.usb.ac.ir/article_6343.html
(2008-6077) Idempotent uninorms and nullnorms on bounded posets
https://ijfs.usb.ac.ir/article_6162.html
The paper deals with uninorms and nullnorms as basic semi-group&nbsp; operations which are commutative and monotone (increasing). These operations were first introduced on the unit interval and later generalized to bounded lattices. In [Kalina 2019] they were introduced on bounded posets. This contribution is a generalization and extension of the results in [Kalina 2019]. Some necessary and some sufficient conditions for the existence of idempotent uninorms and idempotent nullnorms&nbsp; on bounded posets are studied. Finally, some application examples are provided.(2007-6024) Ranking of generalized fuzzy numbers based on accuracy of comparison
https://ijfs.usb.ac.ir/article_6164.html
Ranking generalized fuzzy numbers plays an important role in many applied models and, in particular, decision-making procedures. In ranking process of two generalized fuzzy numbers, it is natural to compare the sets of values in support of two the generalised fuzzy numbers. Accordingly, the comparison of a real number and a generalised fuzzy number as well as two generalised fuzzy numbers have to be considered. On the other hand, it is seen that a definitive process of comparison of a real number and a generalised fuzzy number, as well as two generalised fuzzy numbers, is not possible. So in this study, a method for comparing a real number and a generalised fuzzy number with a degree of accuracy (between a zero and one) is defined and then the method is generalized to compare two generalised fuzzy numbers. In general, an index to rank a real number and generalised fuzzy number is constructed. Eventually, this index is extended to rank two generalised fuzzy numbers based on the concept of accuracy of comparison. The advantage of our method is that it can compare two generalised fuzzy numbers with an accuracy of comparison. Also, a definition is introduced to make a definitive comparison. Finally, the proposed method is illustrated by some numerical examples.(1912-5600) Type 2 adaptive fuzzy control approach applied to variable speed DFIG based wind turbines with MPPT algorithm
https://ijfs.usb.ac.ir/article_6166.html
In this research, a Type 2 adaptive fuzzy controller approach is formulated and designed to be applied to variable speed doubly fed induction generator-based wind turbines directly connected to the grid. It brings this study to evaluate the whole operation of the system to capture the highest rate of power in the wind turbines. The controlling approach is considered to keep the stator reactive power to the ideal value. In contrast to the other researches, here the controlling technique is developed through the nonlinear systems.&nbsp; By the aim of making progress in system operation, in contrast with the Type 1 adaptive fuzzy system, type two adaptive fuzzy theory is proposed to approximate a large number of uncertainties and the dynamic nonlinearities, exists in tracking errors which may limit the system performance. Feedback linearization control approach helps us to algebraically alter the system into a linearized plant. Thanks to the Lyapunov theorem, the introduced type two adaptive fuzzy approach is proved to meet the uniformly ultimately boundness (UUB) property. On the other hand, it results better tracking function. The simulation outputs represent that the proposed technique is robust enough in presence of parameter variations and unstructured uncertainties.(2011-6272) Design and analysis of process capability indices cpm and cpmk by neutrosophic sets
https://ijfs.usb.ac.ir/article_6251.html
Process capability indices (PCIs) have been widely used to analyze capability of the process that measures how the customer expectations have been conformed. Two of the well-known PCIs, named indices $ C_{pm} $ and $ C_{pmk} $ have been developed to consider customers' ideal value that called target value ($ T $). Although, these indices have similar features of the well-known indices $ C_{p} $ and $ C_{pk} $, one of the most important differences is to consider \textit{T}. In real case problems, we need to add some uncertainties related with human's evaluations into process capability analysis (PCA). One of the uncertainty modelling methods called neutrosophic sets (NSs), have an important role in modeling uncertainty based on incomplete and inconsistent information. For this aim, the PCIs have been designed by using NSs to manage the uncertainties of systems and to increase sensitiveness, flexibility and to obtain more detailed results of PCA in this paper. For this aim, the indices $ C_{pm} $ and $ C_{pmk} $ have been performed and re-designed by using single valued neutrosophic numbers for the first time in the literature. Additionally, specification limits (SLs) have been re-considered by using NSs. The neutrosophic state of the SLs provide us to have more knowledge about the process and easily applied for engineering problems that includes uncertainty. Finally, the neutrosophic process capability indices (NPCIs) $ \widetilde{\dddot{C}}_{pm}$ and $ \widetilde{\dddot{C}}_{pmk} $ have been obtained and the main formulas of them have been produced. Additionally, the proposed $ \widetilde{\dddot{C}}_{pm} $ and $ \widetilde{\dddot{C}}_{pmk} $ have been applied on real case studies from manufacturing industry. The obtained results show that the indices $ \widetilde{\dddot{C}}_{pm} $ and $ \widetilde{\dddot{C}}_{pmk} $ include more informative and flexible results to evaluate capability of process.(2006-5936) Distributivity laws for quasi-linear means
https://ijfs.usb.ac.ir/article_6277.html
Aggregation operations play a fundamental role in a large number of disciplines, from mathematics and natural sciences&nbsp;to economics and social sciences. This paper is focused on the problem of distributivity for some special classes ofaggregation operations, and quasi-linear means. Characterization of distributivity pairs for uninorms, semi-uninorms&nbsp;and associative a-CAOA vs quasi-linear means is given.(2101-6381) A note on divisible discrete triangular norms
https://ijfs.usb.ac.ir/article_6278.html
Triangular norms and conorms on [0, 1] as well as on finite chains are characterized by 4 independent properties, namely&nbsp;by the associativity, commutativity, monotonicity and neutral element being one of extremal points of the considered&nbsp;domain (top element for t-norms, bottom element for t-conorms). In the case of [0, 1] domain, earlier results of Mostert&nbsp;and Shields on I-semigroups can be used to relax the latest three properties significantly, once the continuity of the&nbsp;underlying t-norm or t-conorm is considered. The aim of this short note is to show a similar result for finite chains,&nbsp;we significantly relax 3 basic properties of t-norms and t-conorms (up to the associativity) when the divisibility of a&nbsp;t-norm or of a t-conorm is considered.(2103-6531) Monte Carlo statistical test for fuzzy quality
https://ijfs.usb.ac.ir/article_6279.html
Testing the capability of a productive process on the basis of the flexible fuzzy quality using Yongting's index is proposed&nbsp;in this paper by the Monte Carlo simulation. The theoretical approach and detailed steps of an algorithm are givento simulate the critical-value-based and also p-value-based approaches to statistical testing fuzzy quality. Also, the&nbsp;probability of type II error of the quality test simulated by Monte Carlo approach. Moreover, a real-world case studyis provided to show the performance of the proposed algorithm for triangular and trapezoidal fuzzy qualities.(2010-6217) Solvability of fuzzy fractional stochastic Pantograph differential system
https://ijfs.usb.ac.ir/article_6280.html
In this paper, a new type of equation namely fuzzy fractional stochastic Pantograph delay differential system (FSPDDS)&nbsp;is proposed. In our previous work, a first extension of fuzzy stochastic differential system into fuzzy fractional stochasticdifferential system by using Granular differentiability has been established. Here we study the existence and uniqueness&nbsp;results for the fuzzy FSPDDS which are obtained by using generalized Granular differentiability and contraction principlewith weaker conditions. This kind of equation is used in many real world problems. Finally, we provide two numerical&nbsp;examples for the effectiveness of the theoretical results.(2011-6287) A fuzzy non-parametric time series model based on fuzzy data
https://ijfs.usb.ac.ir/article_6281.html
Parametric time series models typically consists of model identification, parameter estimation, model diagnostic checking,&nbsp;and forecasting. However compared with parametric methods, nonparametric time series models often providea very flexible approach to bring out the features of the observed time series. This paper suggested a novel fuzzy&nbsp;nonparametric method in time series models with fuzzy observations. For this purpose, a fuzzy forward fit kernel-basedsmoothing method was introduced to estimate fuzzy smooth functions corresponding to each observation. A simple&nbsp;optimization algorithm was also suggested to evaluate optimal bandwidths and autoregressive order. Several common&nbsp;goodness-of-fit criteria were also extended to compare the performance of the proposed fuzzy time series method compared&nbsp;to other fuzzy time series model based on fuzzy data. Furthermore, the effectiveness of the proposed method was&nbsp;illustrated through two numerical examples including a simulation study. The results indicate that the proposed model&nbsp;performs better than the previous ones in terms of both scatter plot criteria and goodness-of-fit evaluations.(2103-6517) Arithmetic operations and ranking of hesitant fuzzy numbers by extension principle
https://ijfs.usb.ac.ir/article_6282.html
A hesitant fuzzy number (HFN) is important as a generalization of the fuzzy number for hesitant fuzzy analysis and takes&nbsp;some applications that were discussed in recent literature. In this paper, we develop the hesitant fuzzy arithmetic, which&nbsp;is based on the extension principle for hesitant fuzzy sets. Employing this principle, standard arithmetic operations on&nbsp;fuzzy numbers are extended to HFNs and we show that the outcome of these operations on two HFNs are an HFN.Also we use the extension principle in HFSs for the ranking of HFNs, which may be an interesting topic. In this paper,&nbsp;we show that the HFNs can be ordered in a natural way. To introduce a meaningful ordering of HFNs, we use a newlattice operation on HFNs based upon extension principle and defining the Hamming distance on them. Finally, the&nbsp;applications of them are explained on optimization and decision-making problems.(2102-6487) Ordinal sum constructions for aggregation functions on the real unit interval
https://ijfs.usb.ac.ir/article_6286.html
We discuss ordinal sums as one of powerful tools in the aggregation theory serving, depending on the context, both&nbsp;as a construction method and as a representation, respectively. Up to recalling of several classical results dealing with&nbsp;ordinal sums, in particular dealing, e.g., with continuous t-norms, copulas, or recent results, e.g., concerning uninorms&nbsp;with continuous underlying functions, we present also several new results, such as the uniqueness of the link between&nbsp;t-norms or t-conorms, and related Archimedean components, problems dealing with the cardinality of the considered&nbsp;index sets in ordinal sums, or infinite ordinal sums of aggregation functions covering by one type of ordinal sums both&nbsp;t-norms and t-conorms ordinal sums.( 2003-5778) Stability problem for Pexiderized Cauchy-Jensen type functional equations of fuzzy number-valued mappings
https://ijfs.usb.ac.ir/article_6308.html
We investigate the stability problems of the n-dimensional Cauchy-Jensen type and the n-dimensional Pexiderized&nbsp;Cauchy-Jensen type fuzzy number-valued functional equations in Banach spaces by using the metric defined on a fuzzynumber space. Under some suitable conditions, some properties of the solutions for these equations such as existence&nbsp;and uniqueness are discussed. Our results can be regarded as important extensions of stability results corresponding tosingle-valued functional equations and set-valued functional equations, respectively.(2102-6510) Constructing t-norms and t-conorms by using interior and closure operators on bounded lattices, respectively
https://ijfs.usb.ac.ir/article_6321.html
In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms)&nbsp;on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods byErtugrul, Karacal, Mesiar [15] and Cayli [8] as results. Also, we give some illustrative examples. Finally, we show that&nbsp;the introduced construction methods can not be generalized by induction to a modified ordinal sum for t-norms andt-conorms on bounded lattices. This paper has further constructed the t-norms and t-conorms on bounded lattices from&nbsp;a mathematical viewpoint.(2012-6359) An approach based on -cuts and max-min technique to linear fractional programming with fuzzy coefficients
https://ijfs.usb.ac.ir/article_6359.html
This paper presents an efficient and straightforward method with less computational complexities to address the linear fractional programming with fuzzy coefficients (FLFPP). To construct the approach, the concept of &alpha;-cut is used to tackle the fuzzy numbers in addition to rank them. Accordingly, the fuzzy problem is changed into a bi-objective linear fractional programming problem (BOLFPP) by the use of interval arithmetic. Afterwards, an equivalent BOLFPPis defined in terms of the membership functions of the objectives, which is transformed into a bi-objective linear programming problem (BOLPP) applying suitable non-linear variable transformations. Max-min theory is utilized to alter the BOLPP into a linear programming problem (LPP). It is proven that the optimal solution of the LPP is an ϵ-optimal solution for the fuzzy problem. Four numerical examples are given to illustrate the method and comparisonsare made to show the efficiency.(2010-6244) An identifi cation model for a fuzzy time based stationary discrete process
https://ijfs.usb.ac.ir/article_6374.html
A new approach of fuzzy processes, the source of which are expert knowledge reflections on the states on Stationary Discrete Extremal Fuzzy Dynamic System (SDEFDS) in extremal fuzzy time intervals, are considered. A fuzzy-integral representation of a stationary discrete extremal fuzzy process is given. A method and an algorithm for identifying the transition operator of SDEFDS are developed. The SDEFDS transition operator is restored by means of expert knowledge reflections on the states of SDEFDS. The regularization condition for obtaining of the quasi-optimal estimatorof the transition operator is represented by the theorem. The corresponding calculating algorithm is provided. The results obtained are illustrated by an example in the case of a finite set of SDEFDS states.(2104-6613) Construction of 2-uninorms on bounded lattices
https://ijfs.usb.ac.ir/article_6375.html
Uninorms and nullnorms are special 2-uninorms. In this work, we construct 2-uninorms on bounded lattices. Let L be a bounded lattice with a nontrivial element d. Given two uninorms U1 and U2, defined on sublattices [0, d] and [d, 1], respectively, this paper presents two methods for constructing binary operators on L which extend both U1 and U2. We show that our&nbsp; first construction is a 2-uninorm on L if and only if U2 is conjunctive and our second construction is a 2-uninorm on L if and only if U1 is disjunctive. Moreover, we prove that the two 2-uninorms are, respectively, the weakest and the strongest 2-uninorm among all 2-uninorms, the restrictions of which on [0, d]2 and [d, 1]2 are respectively U1 and U2.(2011-6276) Spherical fuzzy soft sets: Theory and aggregation operator with its applications
https://ijfs.usb.ac.ir/article_6376.html
The aim of this paper is to redefine the notion of spherical fuzzy soft sets as a more general concept to make them more functional for solving multi-criteria decision-making problems. We first define the set operations under the new spherical fuzzy soft set environment and obtain some fundamental properties of them. Then, we construct the spherical fuzzy soft aggregation operator which allows establishing a more efficient and useful method to solve the multi-criteriadecision-making problems. We establish an algorithm for the decision-making process which is more useful, simple, and easier than the existing methods. After constructing the method for solving the decision-making problem, we give a numerical example based on linguistic terms to show that the validity of the proposed technique. Finally, we analyze the reliability of the results of this method with the help of the comparative studies by applying this to a real-time dataset and using the existing methods.