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The mathematical understanding ability is one of the abilities that must be mastered by students in mathematics learning. One of the actions that can be taken to improve the mathematical understanding ability is to use Learning Cycle 7E Model. The 7E stands for Elicit, Engage, Explore, Explain, Elaborate, Evaluate, and Extend. This research was to examine whether the students' mathematical understanding ability who learned using Learning Cycle 7E Model was better than those who learned using conventional learning. The research method used was quantitative with a quasi-experimental design, the detail was a non-equivalent post-test only group design. The population of this research was students in 7th grade, which consisted of 7A, 7B, and 7C in SMP PGRI 400 Tangerang, Indonesia. The selected samples were 7A and 7B by cluster random sampling. This research was used a test instrument with essay form about mathematical understanding ability in Algebraic Count Operations. The data analysis used was an independent sample t-test, the result showed that the t-calculated value (7.093) is greater than the t-table value (1.665) at an alpha of 0.05. Based on this result, it can be concluded that the students' mathematical understanding ability who learned using Learning Cycle 7E Model was better than those who learned using conventional learning. [ABSTRACT FROM AUTHOR]

One of the most effective techniques for determining the best choice among the several is to use a fuzzy TOPSIS. This paper proposes a novel intuitionistic fuzzy entropy measure to deal with a MCDM problem by using fuzzy TOPSIS. To express rating of each option and weighting of each criteria, this method uses an intuitionistic fuzzy number. An actual example has given to show how the fuzzy TOPSIS approach may utilized to address a MCDM problem in which we compare the three universities Guru Nanak Dev University; Panjab University and Punjabi University while choosing on the most desired choice, the decision maker uses the seven criterion by using real data from https://naac.gov.in. At the last, we show the distinction between the suggested fuzzy TOPSIS approach and the classic fuzzy approach. The suggested fuzzy TOPSIS method uses intuitionistic fuzzy numbers to introduce objective entropy weights into an intuitionistic fuzzy environment, while the classic fuzzy TOPSIS method uses intuitionistic fuzzy numbers to introduce criterion weights into a fuzzy environment. This shows that the alternatives' closeness coefficient values are quantitative and change depending on the criteria, and can used to show the degree to which one alternative is better than the other one. [ABSTRACT FROM AUTHOR]

Due to perceivedflexibilty in dealing with uncertainity Intuitionistic fuzzy set (IFS) notions are proven to be one of the highly effective tool in many application fields than existing fuzzy set. This research paper describes a modified intuitionistic fuzzy information measure and application to decision-making problem based on fuzzy TODIM methodwhen there is a partial information of weight. Initially we discuss the fundamental concepts and operating rules of IFSs. Secondly, model is developed based on novel entropyand applied to a real-world case study examining supplier rankings. [ABSTRACT FROM AUTHOR]

In this article, we establish a new fuzzy divergence measure along with its proof of existence. Further, we have developed some effective properties on the new recognized fuzzy divergence measure and that particular properties are proved for it. Index terms: Fuzzy divergence measure,Fuzzy set, Fuzzy set theory. [ABSTRACT FROM AUTHOR]

A distance measure is crucial for computing the similarity or difference between two objects. Earlier studies proposed various distance measures between the two Intuitionistic Fuzzy Sets (IFSs), but measuring the distance between IFSs is a complex topic that requires substantial research. In this study, a three-dimensional distance measure for IFSs has been suggested. It is often proclaimed that for IFSs, the three-dimensional distance function is not obligatory because the two-dimensional distance function describes the distance between two IFSs in a straightforward and incisive manner. However, this research confirms that the hesitancy degree is a significant contributing element for IFSs. In addition, the difference between the membership functions and the difference between the non-membership functions are other essential factors in calculating the distance between two IFSs. The inclusion of these terms produced outperforming results, and the shortcomings of prevailing distance measures are overcome. The introduced distance measure expression satisfies the axiom definition of the distance measure. Some mathematical characteristics of the suggested distance measure have been discussed. Some numerical examples have been employed to confirm the validity and effectiveness of the proposed measure. Moreover, the suggested distance measure is suitable for medical diagnostic problems, pattern recognition, and decision-making processes. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to solve the real world problems using trapezoidal fuzzy number in a different approach. We will use new technique to solve the fuzzy numbers and generate the result in a successful way. The numerical description discussed at the end shows the stability of the proposed method and shows the optimal result than those obtained by the widely used methods. [ABSTRACT FROM AUTHOR]

This paper introduces a new picture fuzzy information measure dependent on Tsallis information measure. In addition, some basic concepts and few elegant mathematics properties are given. Besides, An illustrative model is created to show the legitimacy and dependability of the proposed approach and contrasted the outcomes and few current methodologies. The proposed approach is more appropriate than the current ones to manage questionable and uncertain data. The comparison with already existing methodologies shows the flexibility and effectiveness of proposed information measure. [ABSTRACT FROM AUTHOR]

Multiple Criteria Decision Making (MCDM) is a decision-making method in which we decide the right decision from a range of viable options based on the comparative or context of specific of a defined system of interrelated or impartial parameters. By giving preferred evidence in the form of an actual real number or a range, a suitable solution may be selected. Therefore, given ambiguous or inaccurate facts, desire info in actual life could be analyzed directly. In certain instances, uncertainty is generated by creators who are ambiguous or inaccurate. Such feature provided researchers with a strong incentive to apply MCDM methods in an uncertain environment. In recent times, TOPSIS is often known about MCDM in several areas. The fuzzy TOPSIS (technique for order preference by similarity to ideal solution) approach and several basic principles are discussed in this paper. The major aim of this paper is to create a novel intuitionistic fuzzy set decision-making method based on a novel fuzzy entropy measure. To begin, create a novel intuitionistic fuzzy entropy measure as well as innovative weighting techniques for intuitionistic multi-criterion decision making by using the attribute values based mostly on the fuzzy based measure. In addition, it develops an intuitionistic fuzzy TOPSIS method for ranking options, and a practical example is provided in which we compare the four universities LPU, Amity University, Chitkara University, and Chandigarh University for the purpose of selecting the best one for admission by using the real data. [ABSTRACT FROM AUTHOR]

The main problem in coding theorem is to transfer the message on noiseless medium and length of code should be selected in such a way that average code length is minimized. Therefore, a new approach of generalization of Renyi's entropy of parameter β has been discussed in this paper. We have also considered a number of its characteristics in comparison with Shannon and other existing entropies. Thereafter, we discussed the monotonous behavior of MCWL (Mean Code Word Length) using the noiseless coding theorem with the different values of β. We also proved that entropy function is lower bound of average code word length i.e. average code word length is upper bound of entropy value. Additionally, we proposed a new information measure for fuzzy set and proved its validation. To demonstrate the better results attained by proposed measure, numerical examples are also provided. Further, comparison has been given with other entropies which shows the reliability and supremacy of proposed measure. [ABSTRACT FROM AUTHOR]

Fuzzy entropy measure is preferred for characterization and quantification of fuzzy uncertainty and vagueness. We proposed a new parametric exponential entropy measure on fuzzy set, along with some properties that make it flexible for application. [ABSTRACT FROM AUTHOR]

Sugeno introduced the concept of fuzzy integral on a regular fuzzy measure space and its generalization was pioneered by Ralescu, Adams and Wang. In this note, Wavelet Fractional Integrals for Fuzzy Boehmians and its property are addressed by fuzzy integrals. [ABSTRACT FROM AUTHOR]

Spherical fuzzy soft sets (SFSSs) generalize fuzzy soft sets, and are more flexible and reliable than existing other soft set models. In this work, a similarity measure and a corresponding weighted similarity measure between two SFSSs are proposed and some of their basic properties are discussed. Finally, the proposed similarity measure is applied to determine whether or not a patient may have a disease. [ABSTRACT FROM AUTHOR]

LQ45 is one of many Indeks Harga Saham (IHS) which is included in Bursa Efek Indonesia (BEI). IHS is used by investors to predict the stock prices. The motion of IHS is unpredictable causes the investors in quandary situation. Stochastic model is probabilistic model based on an event which is characterized with parameters value and time-variant. IHS fluctuate causes unpredictable effect that is also the feature of stochastic process. The uncertainty can be measured by fuzzy then the composite of both is fuzzy stochastic. On fuzzy, membership value used as parameter approach is fuzzy linguistic summary (FLS). FLS has not examined chance of fluctuation the stock prices motion, so that Markov chain's combination is used as the approach of parameter r. The r parameter has five state, those are the steady, rising, most rising, falling, and most falling. There are three kinds of stocks return, which are the positive return, negative return, and no return. The clustering process uses fuzzy c-means results the positive return clusters and negative return clusters. This research results interval on five sorted interval clusters −5.17 ≤ x ≤ 1.17 when IHS is most falling, −1.17 < x < 0 when IHS is falling, 0 when IHS is steady, 0 < x < 1.2 when IHS is rising, dan 1.2 ≤ x ≤ 3.73 when IHS is most rising and stochastic model obtained is X (n + 1) = X (n)er along r is the parameter of five states, rsteady = 0, 0001, rrising = 0, 0106, rmostrising = 0, 0135, rfalling = 0, 0072 and rmost falling = 0, 0104. The fuzzy stochastic model with those parameters on five states has MAPE value 0,49% therefore the model has great forecasting capability. [ABSTRACT FROM AUTHOR]

Multi-fuzzy set theory is an extension of fuzzy set theory, which deals with the multi dimensional fuzziness. It was introduced by S. Sebastian and T.V. Ramakrishnan in 2010. Thenceforth, the theory is developing through many angles. This paper proposes the notion of distance measure of multi-fuzzy sets. Furthermore, the paper explores some results related to this concepts. [ABSTRACT FROM AUTHOR]

Nowadays, in different fields there are many systems whose processes are described by queueing models. In this paper, the L-R method is computing performance measures of fuzzy queues. Basing on this technique, we find the number of customers and the waiting time of a queue M/Ek/1 in the fuzzy environment, it is essentially based on L-R fuzzy arithmetic. The L-R method has the advantage of being convenient, flexible and short compared to other methods. A numerical example is a model proposed to shows the validity of this approach. [ABSTRACT FROM AUTHOR]

In providing service or products to people, queuing system could influence the customer’s satisfaction. However, queuing system used in most organization unable to explain linguistic terms existed in nature of arrival rate and service rate. Therefore, fuzzy is used as it can be best in describing the linguistic variables. In this study, calculation and comparison on queuing performance measures for multi-server traditional and fuzzy queuing model are carried out. Queuing performance measures involve in this study are average number of customers in the queue (Lq), average number of customers in the system (L), average waiting time of a customer in the queue (Wq) and average waiting time of customer in the system (W). Dong, Shah & Wong (DSW) algorithm is used to define the membership function of performance measures in fuzzy queuing model. The results show that the performance measures of traditional queuing model give a single value while for fuzzy queuing model in range of values. The performance measures of traditional queuing model obtained lie in the range of performance measures of fuzzy queuing model computed. Hence, the results obtained are consistent. [ABSTRACT FROM AUTHOR]

In this work, the parameterized degree of compactness of a lattice valued fuzzy soft set is described in a fuzzy soft topological space. The extended versions of the basic compactness properties known in general topology are investigated for the given notion and some other characterizations of parameterized degree of compactness are specified. Further, a generalized version of Tychonoff Theorem is proved in the product fuzzy soft topological space. [ABSTRACT FROM AUTHOR]

In the present communication, parametric exponential fuzzy information measure is introduced and defined in axiomatic way of entropy. Anshu Ohlan [1] defined entropy on fuzzy set and we generalize this entropy on intuitionistic fuzzy set. To verify that our proposed measure is valid entropy, we have analyzed some properties of this measure. [ABSTRACT FROM AUTHOR]

In the present paper, we have refined some inequalities considered in the Singh & Tomar [14], for fuzzy divergence measures. Some new inequalities have been obtained for fuzzy divergence measures therefore automatically the question of refinement arises. Hence in the present communication, we establish mainly the following refinements:- (i) DIΔ (A||B)≤2/3DhΔ (A||B)≤2DhI(A||B)≤DTJ (A||B) (ii) DIΔ (A||B)≤2/3DhΔ (A||B)≤1/2DJΔ A||B)≤1/3DTΔ (A||B)≤DTJ (A||B) [ABSTRACT FROM AUTHOR]

Evaluation of the efficiency of financial literacy promotion efforts has always been an interesting and challenging problem for both the researchers in the field as well as practitioners. Although there are several sources of measurement tools for the actual levels of financial literacy available and tested in an international setting, the overall evaluation of efficiency of actions, programmes, strategies and approaches targeted towards improving financial literacy among the general population are difficult to construct. Therefore an approach based on multi-faceted international expert panel judgment can be introduced as a source of more uniform point of view. The paper discusses the implications, possibilities and limitations of Fuzzy Delphi Method (FDM) when applied to conceptualization, inception and formation of a questionnaire-based evaluation tool targeted towards evaluating the efficiency of a multitude of financial literacy promotion efforts. Using this method a set of key efficiency appraisal instruments can be constructed and established on multiple dimensions – time, population, topics and fields. The paper demonstrates the process of initiating and forming the research structure, selecting the experts, providing feedback and collecting responses in multiple rounds. As the error level is reduced, using fuzzy sets allows for the quantification of expert opinions and variables to be more related and consistent with human socio-linguistic behaviour on an international level. The paper concludes that FDM is a valuable tool in expert opinion-gathering when the topic of interest is prone to bias, vaguely defined and may not be easily quantifiable. [ABSTRACT FROM AUTHOR]

In real life decision problems always dealt with the criteria that are mutually influences and have interactive characteristics among them. The interaction between criteria is important to consider during aggregating criteria evaluation for compute the global scores. The interdependence or interactive characteristics among criteria is not suitable to aggregate by traditional aggregation operators that based on additive measures because it is assumed that there is no interaction among the evaluated criteria or the criteria are independent. Thus, to approximate the human subjective decision making process, it would be appropriate to apply non-additive aggregation operator by taking into accounts the interaction between the subjects which is called fuzzy measures. In this paper, we proposed Maximized L-measure and Delta-measure to measure the interaction among criteria and employing the non-additive aggregation operators which is Choquet integral to obtain the overall evaluation is more suitable because this method is able to deal with interaction among subjects. [ABSTRACT FROM AUTHOR]

In this paper, multilevel fuzzy analysis method is used to making a comprehensive evaluation on the health hazards of workers exposed to electric field in 500kV substation. The five different regions of 500kV substation is identified as the first level index, according to the specific measurement substation of each area to set up the second level index. The first level weight is established according to the proportion of the retention time of the workers in the different areas, and the weight of the second level is determined according to the proportion of the measuring points. Establishing five comment sets, and carrying out the fuzzy comprehensive evaluation according to the maximum membership principle, eventually come to the conclusion: although the measured data show that a small number of electric field intensity exposure value of 500kV substation beyond the requirements of the International Commission on non-ionizing radiation protection (ICNIRP) and the requirements of the People's Republic of China(PRC), but workers have very little contact time, therefore, it cannot be explained that there is a large occupational health hazard in 500kV substation. The multilevel fuzzy analysis method can be used to evaluate the health hazards of the electric field in the substation working environment well, it avoids the subjective and limitations of the traditional methods, and can be able to make a more accurate and objective judgment of the substation [ABSTRACT FROM AUTHOR]

Markowitz in 1952 introduced the mean-variance methodology for the portfolio selection problems. His pioneering research has shaped the portfolio risk-return model and become one of the most important research fields in modern finance. This paper extends the classical Markowitz's mean-variance portfolio selection model applying the fuzzy measure to determine the risk and return. In this paper, we apply the original mean-variance model as a benchmark, fuzzy mean-variance model with fuzzy return and the model with return are modeled by specific types of fuzzy number for comparison. The model with fuzzy approach gives better performance as compared to the mean-variance approach. The numerical examples are included to illustrate these models by employing Malaysian share market data. [ABSTRACT FROM AUTHOR]

Flow shop scheduling is a decision making problem in production and manufacturing field which has a significant impact on the performance of an organization. When the machines on which jobs are to be processed are placed at different places, the transportation time plays a significant role in production. Further two different transport agents where 1st takes the job from 1st machine to 2nd machine and then returns back to the first machine and the 2nd takes the job from 2nd machine to 3rd machine and then returns back to the 2nd machine are also considered. We propose a method to minimize the total make span; without converting the fuzzy processing time to classical numbers by using a new type of fuzzy arithmetic and a fuzzy ranking method. A numerical example is provided to explain the proposed method. [ABSTRACT FROM AUTHOR]

Many average methods are available to aggregate a set of numbers to become single number. However these methods do not consider the interdependencies between the criteria of the related numbers. This paper is highlighting the Choquet Integral method as an alternative aggregation method where the interdependency estimates between the criteria are comprised in the aggregation process. The interdependency values can be estimated by using lambda fuzzy measure method. By considering the interdependencies or interaction between the criteria, the resulted aggregated values are more meaningful as compared to the ones obtained by normal average methods. The application of the Choquet Integral is illustrated in a case study of finding the overall academic achievement of year six pupils in a selected primary school in a northern state of Malaysia. [ABSTRACT FROM AUTHOR]

With the increasing development of fuzzy set theory in various scientific fields and the need to compare fuzzy numbers in different areas. Therefore, Ranking of fuzzy numbers plays a very important role in linguistic decision-making, engineering, business and some other fuzzy application systems. Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques has been shown to produce non-intuitive results in certain case. In this paper, we reviewed some recent ranking methods, which will be useful for the researchers who are interested in this area. [ABSTRACT FROM AUTHOR]

We analyze the high gain spontaneous parametric down-conversion in a non collinear geometry as a paradigmatic scenario to investigate the observation of nonlocal properties when the size of the system is increased while keeping fixed the measurement resolution. We observe theoretically a fast decrease in the amount of Bell's inequality violation when the number of particles is increased, due to the low resolution of the measurement apparatus. This theoretical analysis is supported by the experimental observation of macro-macro correlations with an average number of photons of about 103. Our results enlighten the practical extreme difficulty of observing non-locality by performing such a dichotomic fuzzy measurement. [ABSTRACT FROM AUTHOR]

Consequence of the accidental release of radioactivity from a nuclear power plant is assessed in terms of exposure or dose to the members of the public. Assessment of risk is routed through this dose computation. Dose computation basically depends on the basic dose assessment model and exposure pathways. One of the exposure pathways is the ingestion of contaminated food. The aim of the present paper is to compute the uncertainty associated with the risk to the members of the public due to the ingestion of contaminated food. The governing parameters of the ingestion dose assessment model being imprecise, we have approached evidence theory to compute the bound of the risk. The uncertainty is addressed by the belief and plausibility fuzzy measures. [ABSTRACT FROM AUTHOR]

This paper proposes a new location problem of competitive facilities, e.g. shops, with uncertainty and vagueness including demands for the facilities in a plane. By representing the demands for facilities as fuzzy random variables, the location problem can be formulated as a fuzzy random programming problem. For solving the fuzzy random programming problem, first the α-level sets for fuzzy numbers are used for transforming it to a stochastic programming problem, and secondly, by using their expectations and variances, it can be reformulated to a deterministic programming problem. After showing that one of their optimal solutions can be found by solving 0-1 programming problems, their solution method is proposed by improving the tabu search algorithm with strategic oscillation. The efficiency of the proposed method is shown by applying it to numerical examples of the facility location problems. [ABSTRACT FROM AUTHOR]

In a neutron polarimetry experiment mixed neutron spin phases are determined. We consider evolutions leading to purely geometric, purely dynamical and combined phases. It is experimentally demonstrated that the sum of the geometric and dynamical phases—both obtained in separate measurements—is not equal to the associated total phase as obtained from a third measurement, unless the system is in a pure state. In this sense, mixed state phases are not additive. [ABSTRACT FROM AUTHOR]