A fractional minimal cost ow problem under linear type Belief degree based uncertainty is studied for the  rst time. This type of uncertainty is useful when no historical information of an uncertain event is available. The problem is crisped using an uncertain chance-constrained programming approach and its non-linear objective function is linearized by a variable changing approach. An illustrative example is solved to prove the e ciency of the proposed formulation.

Data Envelopment Analysis (DEA) is recognized as a robust analytical tool extensively utilized in measuring the relative e ciency of a group of Decision Making Units (DMUs) with multiple inputs and outputs. The DEA models require inputs and outputs equipped with precise information. However in real-world situations inputs and outputs may be unstable and complicated thus unable to be accurately measured. This problem resulted in the investigation of uncertain DEA models. The BCC model is studied in this paper in an uncertain environment where uncertain inputs and outputs were Belief degree-based uncertainty useful for the cases for which no historical information of an uncertain event is available. As the solution method the uncertain BCC model was converted to a crisp form using two approaches of expected value method (EV) and expected value and chance-constrained method (EVCC) separately. Finally, an applied example regarding the Iranian Banking system is presented to document the proposed models.

Objective: Anesthetic techniques like the Akinosi technique were introduced to surmount the problems of the conventional inferior alveolar nerve block (IANB) technique. This study aimed to compare the local anesthetic efficacy of IANB via the conventional and Akinosi techniques in patients presenting to the Maxillofacial Surgery Department of School of Dentistry, Shahid Beheshti University.Methods: This clinical trial was conducted on 80 candidates for bilateral extraction of mandibular molars. For each patient, local anesthesia was induced by IANB injection, which was done by the conventional technique in one side and by the Akinosi technique in the other side of the mouth. The allocation of technique to side was randomized. Time to anesthesia for the long buccal, lingual and inferior alveolar nerves (IAN), degree of pain during injection and tooth extraction and incidence of positive aspiration in the two techniques were evaluated and analyzed using Wilcoxon Signed Rank and Chi square tests.Results: The mean time to anesthesia for the IAN was 2.82 minutes in the conventional and 3.05 minutes for the Akinosi technique. These values were 1.47 and 1.55 minutes, respectively for the lingual nerve and 1.43 and 1.56 minutes, respectively for the long buccal nerve. Four patients in the Akinosi technique and 12 patients in the conventional technique had positive aspiration. During anesthetic injection with the Akinosi technique, 72.5% were pain free, 18.8% experienced mild, 5% experienced moderate and 3.8% experienced severe pain. These values in the conventional technique were 51.3%, 27.5%, 11.3% and 10%, respectively.Conclusion: Considering the lack of a significant difference between the success rate of conventional and Akinosi IANB techniques, Akinosi technique seems to be a suitable alternative to the conventional technique since it is less painful and has lower risk of positive aspiration.

Introduction: Selecting suitable crops for cultivation in a non-certain environment is considered as an important management topic in the agricultural sector. Despite the multiple application of probability theory in quantifying uncertainty in the form of risk programming, validity of this theory depends on the existence of frequency for uncertain variable. For events that cannot be measured by frequency, the only solution is to use subjective judgment of persons in the domain field rather than historical data. Some experts have mistakenly considered subjective judgmentl as a subjective probability and thus used the probability theory to quantify subjective judgmental. But based on existing evidence, the quantification of subjective judgment should be carried out in another theory called the uncertainty theory. In uncertainty theory, in addition to using the Belief degree rather than frequency for calculating mathematical moments, the expected value of multiplicative variables will be different with their corresponding relations in the probability theory. Considering these conditions and having in mind that the agricultural sector is always faced with uncertain variables such as price of crops and weather conditions like rainfall, in this study the revenue uncertainty measures of major crops in the Goharbaran region of Sari have been calculated and compared. There are different measures for uncertainty, which in the present study variance and Tail Value at Risk (TVaR) have been used. Materials and Methods: The first step in the application of the uncertainty theory is the elicitation of the Belief degree or subjective judgments of the farmers about the crop's price and rainfall during the crop season. To elicit the uncertainty distribution of these variables based on the subjective judgments of farmers, 120 farmers were randomly selected in 2018. After eliciting the farmers' Beliefs about uncertain rainfall and prices in the cdf method, it was necessary to select the number of Belief degree which current practice was based on previous studies in this field. After calculating the above subjective judgments, while assuming linear, zigzag, normal and normal forms for uncertainty distribution, the parameters of each function were calculated using the least squares method. Among the forms of uncertainty distribution functions, the best form of the uncertainty distribution for each crop's price and rainfall was selected by comparing the RMSE indexes. Subsequently, by calculating a causal relationship between rainfall and crop yield, inverse uncertainty distribution of yield was also extracted. Given the inverse uncertainty distribution functions of crop price and yield, required parameters such as expected revenue, variance and TVaR of revenue at 95% confidence were calculated based on operational laws of uncertainty theory and probability theory. Eviews and Matlab software were used to estimate the yield response function and the uncertainty distribution functions, respectively. Results and Discussion: In this study, after collecting the Belief degree of farmers in the studied area about different levels of price and rainfall, three groups of comprehensive Beliefs about prices and rainfall were determined by goodness of fit test. Then, according to the relationship between crop yield and rainfall, the inverse function uncertainty distribution is also calculated. With the uncertainty distribution function of crops price and yield, the expected revenue, variance (standard deviation) and TVaR measure for revenue per hectare of crops were calculated and compared with the uncertainty theory as well as probability theory. Based on the results of this study, the amount of the above measures varied in different Belief degree groups, which is due to differences in the uncertainty distribution parameters. Also, based on the results of this study in all groups of Beliefs for all crops, the probability theory compared to the uncertainty theory has estimated the variance approximately more than 30% less, which is a significant result. In other words, applying probability theory to Belief modeling will lead to erroneous and misleading results. In the case of the TVaR measure in binary multiplicative variable conditions, the use of probability theory and uncertainty theory in calculating TVaR does not yield conflicting results. Conclusion: The purpose of this study was to compare the results of applying probability theory for modeling Belief degree rather than uncertainty theory in order to illustrate the necessity of using uncertainty theory in Belief degree modeling. Studying the effect of probability theory in modeling the Belief degree also suggests that the application of probability theory in the presence of two uncertain variables has no significant effect on expected values and TVaR but has a significant effect on variance size. Based on the results of the present study, assuming the binary multiplicative variable, in calculating higher mathematical moments such as variance, the results of probability theory and uncertainty theory make a considerable difference. This demonstrates the need to promote the uncertainty theory in Belief degree modeling. In other words, basic training in the Belief degree modeling method should be considered.

In modern times many militant atheist thinkers and activists have tried to promote the idea that religions, as well as religious ways of life, are one of the main, if not the main source of evil in the social arena. Some other non-believer scholars, while taking a respectful approach towards religions and religious people, maintaining that it is more rational for people and communities to adopt a non-religious outlook on life and become members of the community of non-believers. In this paper, I do not take issue with the militant non-believers. The reason is that their approach to religion is so ideologically driven that it leaves not much room for proper rational discussions; it only invites some polemical replies. My aim here is, instead, to enter into a dialogue with those non-believer scholars who view religion in a measured and rational way. My intention is to critically assess the claims of this latter group of scholars and explain why, contrary to what they suggest, certain interpretations of religion, and in particular, the Islamic faith, can provide them with better alternatives than their atheist outlooks. The arguments of this paper are mostly in reply to the views expressed by Professor Shearmur in his paper on critical rationalism and religion.

The Web has become the most important information source for most of us. Unfortunately, there is no guarantee for the correctness of information on the Web. Moreover, different websites often provide conflicting information on a subject. Several truth discovery methods have been proposed for various scenarios, and they have been successfully applied in diverse application domains. In this paper, we have attempted to answer the question whether the truth is relevant. We conducted an experimental study in which we analyzed and compared the results of two different truth discovery methods: Relevance-based sources ranking and Majority vote. We have found that the truth is not always held by the most relevant sources on the web. Sometimes the truth is given by the majority vote of the crowd. In addition, we have proposed a method of presenting the results of truth discovery with gradual degrees of Belief. A method that allows to configure and target the desired level of trust.

Recently two new degree concepts have been defined in graph theory: ev-degree and ve-degree. Also the ev-degree and ve-degree Zagreb and Randić indices have been defined very recently as parallel of the classical definitions of Zagreb and Randić indices. It was shown that ev-degree and ve-degree topological indices can be used as possible tools in QSPR researches [2]. In this paper, we define the ve-degree and ev-degree Narumi– Katayama indices, investigate the predicting power of these novel indices and extremal graphs with respect to these novel topological indices. Also we give some basic mathematical properties of ev-degree and ve-degree Narumi-Katayama and Zagreb indices.