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The main objective of this research was to determine the synoptic and thermodynamic conditions accompanying the development of two severe thunderstorms that caused significant damage in Warsaw. The storm events of 17 June and 4 September 2016 were analysed. Materials used in the research included meteorological, aerological and radar data, as well as the Fire Service interventions database. These data allowed the conditions for the formation of the storms and their spatial variations in terms of intensity to be determined. It was shown that damage in Warsaw was caused by phenomena associated with supercell storms that developed in a moderate CAPE environment and a strong shear. It was confirmed that the geometry of the city increased the wind speed and modified its direction locally. In addition, it was found that the data on the number of Fire Service interventions clearly reflected the spatial variations in storm intensity by corresponding radar signatures to the high intensity of meteorological phenomena.

The statistical hadronization model ThermalFist was applied to numerous hadron yields measured in p+p collisions at √S = 8.8s=8.8, 12.3 and 17.3 GeV, including recently published yields of ϕ-mesons, measured by the NA61/SHINE Collaboration. We consistently used the energy-dependent widths of Breit-Wigner mass distributions of hadronic resonances, as this approach was generally found to provide better agreement with experimental data. The well-established experimental ϕ meson yields are consequently accounted for (although neglecting this particle was found to improve the fit quality). The canonical treatment of particles with open strangeness with the grand canonical approach for non-strange particles gave a moderately reasonable agreement with the measured yields, only when the volume of strange particles was allowed to vary freely. In all the studied cases this volume is found to be greater than the canonical one.

In March 2019 the HADES experiment recorded 14 billion Ag+Ag collisions at √sNN = 2.55 GeV as a part of the FAIR phase-0 physics program. In this contribution, we present and investigate our capabilities to reconstruct and analyze weakly decaying strange hadrons and hypernuclei emerging from these collisions. The focus is put on measuring the mean lifetimes of these particles.

Identifying potential healthy and unsound customers is an important task. The reduction of loans granted to companies of questionable credibility can influence banks’ performance. A prior identification of factors that affect the condition of companies is a vital element. Among the most commonly used methods we can enumerate discriminant analysis (DA), scoring methods, neural networks (NN), etc. This paper investigates the use of different structure NN and DA in the process of the classification of banks’ potential clients. The results of those different methods are juxtaposed and their performance compared.

The main goal of this paper is a discussion on the correct choice of annualized return rate. Selected return rate should be appropriate for the multiannual comparative analysis of bank deposits and investment funds. The whole discussion was based on theoretical considerations and a numerical experiment.

The behavioural present value is defined as a fuzzy number assessed under the impact of chosen behavioural factors. The first formal model turned out to be burdened with some formal defects which are finally corrected in the presented article. In this way a new modified formal model of a behavioural present value is obtained. New model of the behavioural present value is used to explain the phenomenon of market equilibrium on the efficient financial market remaining in the state of financial imbalance. These considerations are illustrated by means of extensive numerical case study.

The statistical hadronization model ThermalFist was applied to numerous hadron yields measured in p+p collisions at √s = 8.8, 12.3, and 17.3 GeV, including recently published yields of ф and K0 S-mesons, measured by the NA61/SHINE Collaboration. We consistently used the energydependent widths of Breit--Wigner mass distributions of hadronic resonances. The canonical treatment of particles with open strangeness combined with the grand canonical approach for non-strange particles gave a moderately reasonable agreement with the measured yields, quantified by χ2/NDF ≈ 2-7, only when the volume of strange particles was allowed to vary freely. This volume is found to be greater than the one for non-strange matter for all the studied energies. The predicted yields of some of not yet measured particles are provided. [ABSTRACT FROM AUTHOR]

The return rate is considered here as a fuzzy probabilistic set. Then the expected return is obtained as a fuzzy subset in the real line. This result is a theoretical foundation for new investment strategies. All considered strategies result of comparison profit fuzzy index and limit value. In this way we obtain an imprecise investment recommendation. Financial equilibrium criteria are a special case of comparison of the profit index and the limit value. The following criteria are generalized here: the Sharpe's Ratio, the Jensen's Alpha and the Treynor's Ratio. Moreover, the safety-first criteria are generalized here for the fuzzy case. The Roy Criterion, the Kataoka Criterion and the Telser Criterion are also generalized. Obtained results show that proposed theory is useful for the investment applications.

The article discussesd the impact of chosen behavioural factors on the imprecision of present value assessment. The formal model of behavioural present value is offered as a result of this discussion. The behavioural present value is described here as an intuitionistic fuzzy set. The significance of the replacement of a fuzzy set by an intuitionistic fuzzy set is proved.

In previous research, the Extended Order Scale (EOS) dedicated to risk assessment was analysed. It was characterised by a Numerical Order Scale (NOS) evaluated by trapezoidal oriented fuzzy numbers (TrOFNs). However, the research showed that EOS with two-stage orientation phases, was too complicated. Therefore, the main aim of our paper is to simplify a Complete Order Scale (COS) to a zero- or one-stage order scale and a hybrid approach. For this purpose, a way to calculate the scoring function is presented. The results show that changes in the COS structure influence the values of a scoring function. Replacing just one linguistic indicator gives different results. Another finding of the research is the method's flexibility that allows an expert to individually choose the most suitable COS. The research proves that the boundary between various linguistic labels cannot be precisely defined. However, knowledge of a formal COS structure allows it to be transformed into a less complex one. [ABSTRACT FROM AUTHOR]

Following the recent measurement of several hadron yields by NA61/SHINE collaboration, the unified set of yields of particles produced in proton–proton collisions at = 17.3 GeV (laboratory beam momentum 158 GeV/c) is evaluated, combining the results of the NA49 and NA61/SHINE collaborations at the CERN SPS. With the statistical hadronization code Thermal-Fist we confirm the unacceptably high value of χ2, both in the canonical and grand canonical—strangeness canonical approach, and the common volume for all the hadrons. The use of the energy-dependent width of the Breit–Wigner parametrization for the mass distributions of unstable particles improves the quality of the description of particle yields only slightly. We confirm the observation that exclusion of the ϕ meson yield makes the fit result more reasonable. The complete experimental data set of particle yields can be also reasonably fitted if the canonical volumes of hadrons without and with open strangeness are allowed to vary independently. The canonical volume of strangeness was found to be larger than that for non-strange hadrons. The femtoscopy measurements with kaon pairs and pion pairs at 27.4, 63 and 900 GeV are not precise enough to confirm or reject this observation. The model with the best-fit parameters allows to predict the yields of several not yet measured particles emitted from p + p at = 17.3 GeV. [ABSTRACT FROM AUTHOR]

Preferential information may be visualized in many different ways, and this constitutes an important issue in the principal-agent decision-making context, e.g., in representative negotiations. In the INSPIRE negotiation support system, the principal's preferences are visualized by circles with different radii. Agents evaluate the principal's preferences in such a manner that they digitize these preferences using numbers directly proportional to the size of the circles, drawn by the principal. The manner, in which an agent understands the concept of the circle size is unknown. The main goal of this paper is to propose such an image of principal's preferences, which is independent of an individual agent's evaluation. Individual negotiators may differ in their understanding of this concept. This means that the notion of "circle size" is a linguistic variable that may be described by a fuzzy set. The empirical studies referred to show that the size of the circle is a value between the radius and the area of this circle. In this paper, the principal's preferences are defined as a fuzzy preorder between fuzzy "circle sizes". We distinguish here two kinds of the INSPIRE method. All considerations are illustrated by means of a short case study based on INSPIRE data. [ABSTRACT FROM AUTHOR]

This study documents atmospheric conditions, development, and evolution of a severe weather outbreak that occurred on 11 August 2017 in Poland. The emphasis is on analyzing system morphology and highlighting the importance of a mesovortex in producing the most significant wind damages. A derecho-producing mesoscale convective system (MCS) had a remarkable intensity and was one of the most impactful convective storms in the history of Poland. It destroyed and partially damaged 79 700 ha of forest (9.8 million m3 of wood), 6 people lost their lives, and 58 were injured. The MCS developed in an environment of high 0–3-km wind shear (20–25 m s−1), strong 0–3-km storm relative helicity (200–600 m2 s−2), moderate most-unstable convective available potential energy (1000–2500 J kg−1), and high precipitable water (40–46 mm). Within the support of a midtropospheric jet, the MCS moved northeast with a simultaneous northeastward inflow of warm and very moist air, which contributed to strong downdrafts. A mesocyclone embedded in the convective line induced the rear inflow jet (RIJ) to descend and develop a bow echo. In the mature stage, a supercell evolved into a bookend vortex and later into a mesoscale convective vortex. Swaths of the most significant wind damage followed the aforementioned vortex features. A high-resolution simulation performed with initial conditions derived from GFS and ECMWF global models predicted the possibility of a linear MCS with widespread damaging wind gusts and embedded supercells. Simulations highlighted the importance of cloud cover in the preconvective environment, which influenced the placement and propagation of the resulting MCS. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the application potential of ordered fuzzy numbers (OFN) to support evaluation of negotiation offers. The Simple Additive Weighting (SAW) and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods are extended to the case when linguistic evaluations are represented by OFN. We study the applicability of OFN for linguistic evaluation negotiation options and also provide the theoretical foundations of SAW and TOPSIS for constructing a scoring function for negotiation offers. We show that the proposed framework allows us to represent the negotiation information in a more direct and adequate way, especially in ill-structured negotiation problems, allows for holistic evaluation of negotiation offers, and produces consistent rankings, even though new packages are added or removed. An example is presented in order to demonstrate the usefulness of presented fuzzy numerical approach in evaluation of negotiation offers. [ABSTRACT FROM AUTHOR]

We consider the obvious thesis that the present value of a portfolio is equal to the sum of the present values of its components. The main goal of this paper is the implementation of this thesis in the case when present values are determined by trapezoidal ordered fuzzy numbers. We apply the revised sum of ordered fuzzy numbers. The associativity of such a revised sum is investigated here. In addition, we show that the multiple revised sum of a finite sequence of trapezoidal ordered fuzzy numbers depends on the ordering of its summands. Without any obstacles, the results obtained can be generalized to the case of any ordered fuzzy numbers. [ABSTRACT FROM AUTHOR]

Ordered fuzzy numbers are defined by Kosiński. In this way, he was going to supplement a fuzzy number by orientation. A significant drawback of Kosiński's theory is that there exist such ordered fuzzy numbers which, in fact, are not fuzzy numbers. For this reason, a fully formalized correct definition of ordered fuzzy numbers is proposed here. Also, the arithmetic proposed by Kosiński has a significant disadvantage. The space of ordered fuzzy numbers is not closed under Kosiński's addition. On the other hand, many mathematical applications require the considered space be closed under used arithmetic operations. Therefore, the Kosinski's theory is modified in this way that the space of ordered fuzzy numbers is closed under revised arithmetic operations. In addition, it is shown that the multiple revised sum of finite sequence of ordered fuzzy numbers depends on its summands ordering. [ABSTRACT FROM AUTHOR]

A multi-asset portfolio in the case of its present value estimated by a discrete trapezoidal fuzzy number has been assessed. The benefits of owning a security have been evaluated according to an expected fuzzy discount factor. The ambiguity risk has been assessed by an energy measure and indistinctness risk has been evaluated by Kosko's entropy measure. The relationship between the expected fuzzy discount factor for a portfolio and the expected fuzzy discount factors for its components has been derived. An analogous relationship between the values of the energy measure has been presented. The model has been illustrated by means of a profound numerical case study. [ABSTRACT FROM AUTHOR]

The entropy measure is predefined as a mapping, increasing with an increase in the fuzziness of evaluated set. The relation "is less fuzzy than" is strictly modeled by an inequality fulfilled by membership functions. This inequality is systematically repeated across the literature. In this paper we show that it is incorrect. We prove that the relation "is less fuzzy than" should be modeled by an inclusion. Obtained conclusions are applied in a more precise definition of entropy measure. [ABSTRACT FROM AUTHOR]

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The article discussesd the impact of chosen behavioural factors on the imprecision of present value assessment. The formal model of behavioural present value is offered as a result of this discussion. The behavioural present value is described here as an intuitionistic fuzzy set. The significance of the replacement of a fuzzy set by an intuitionistic fuzzy set is proved. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to present a modern axiomatic approach to financial arithmetic. An axiomatic theory of financial arithmetic was first proposed by Peccati, who introduced an axiomatic definition of future value. This theory has been extensively developed in recent years. The proposed approach to financial arithmetic is based on the concept of the utility of a financial flow. This utility function is defined as a linear extension of a multicriterion comparison determined by an individual's time preference and capital preference. The present value is then defined to be the utility of the financial flow. Therefore, the law of the diminishing marginal utility of wealth has been considered as an additional feature of the present value. The future value is defined as the inverse of the utility function. This definition is a generalization of Peccati's one. The net present value is given as the unique additive extension of the utility of the financial flow. Moreover, the synergy effect and the diversification effect will be discussed. At the end, the axiomatic definition of the present value will be specified in three ways. [ABSTRACT FROM AUTHOR]

The generalized fuzzy present value of a security is defined here as fuzzy valued utility of cash flow. The generalized fuzzy present value cannot depend on the value of future cash flow. There exists such a generalized fuzzy present value which is not a fuzzy present value in the sense given by some authors. If the present value is a fuzzy number and the future value is a random one, then the return rate is given as a probabilistic fuzzy subset on a real line. This kind of return rate is called a fuzzy probabilistic return. The main goal of this paper is to derive the family of effective securities with fuzzy probabilistic return. Achieving this goal requires the study of the basic parameters characterizing fuzzy probabilistic return. Therefore, fuzzy expected value and variance are determined for this case of return. These results are a starting point for constructing a three-dimensional image. The set of effective securities is introduced as the Pareto optimal set determined by the maximization of the expected return rate and minimization of the variance. Finally, the set of effective securities is distinguished as a fuzzy set. These results are obtained without the assumption that the distribution of future values is Gaussian. [ABSTRACT FROM AUTHOR]

We consider the negotiation problem, in which an agent negotiates on behalf of a principal. Our considerations are focused on the Inspire negotiation support system in which the principal's preferences are visualised by circles. In this way, the principal describes the importance of each negotiation issue and the relative utility of each considered option. The paper proposes how this preference information may be implemented by the agent for determining a scoring function used to support decisions throughout the negotiation process. The starting point of our considerations is a discussion regarding the visualisation of the principal's preferences. We assume here that the importance of each issue and the utility of each option increases with the size of the circle representing them. The imprecise meaning of the notion of "circle size" implies that in a considered case, the utility of an option should be evaluated by a fuzzy number. The proposed utility fuzzification is justified by a simple analysis of results obtained from the empirical prenegotiation experiment. A novel method is proposed to determine trapezoidal fuzzy numbers, which evaluates an option's utility using a series of answers given by the participants of the experiment. The utilities obtained this way are applied to determine the fuzzy scoring function for an agent. By determining such a common generalised fuzzy scoring system, our approach helps agents handle the differences in human cognitive processes associated with understanding the principal's preferences. This work is the first approach to fuzzification of the preferences in the Inspire negotiation support system. [ABSTRACT FROM AUTHOR]

The study of the assessment and reflection of biological assets in the economic processes of agricultural enterprises can be represented as a chain of phenomena in which scientists and practitioners try to study and understand the nature and essence of biological assets in various aspects. This article discusses the principles of accounting for biological assets in the agricultural enterprises' economic life of the Republic of Tajikistan and identifies the reasons and mechanisms for their reflection based on the principles of the International Financial Reporting System (IFRS) in refraction to the specifics and national features of accounting. The author gives his own interpretation of these approaches and constructs the architecture of the information module for accounting for biological assets and the results of biotransformation, based on the web services architecture (WSA) within the framework of the development trend of these and new accounting models in connection with the transition of the world economy to a digital format. The article provides specific authors' approaches to implementing this architecture in PHP (Hypertext Preprocessor) and also implements one of the approaches to assessing the value of biological assets, based on the theory of fuzzy sets, taking into account the risk of investment inefficiency. [ABSTRACT FROM AUTHOR]

This study analyzes business performance through efficiency score estimation in two sustainable tourism models: cultural tourism and rural tourism. The study uses microeconomic data (microdata) of Spanish firms with different characteristics in terms of size, region, location and financial variables. Using multistage modeling (Data envelopment analysis, DEA, non-parametric frontier and non-parametric tests), the main results show that the average efficiency is higher for rural tourism destinations than for cultural tourism destinations. Similar to other tourism industries, efficiency results by geographical and regional destination confirm that location is a driver of the efficiency levels in rural and cultural tourism destinations. Furthermore, the results do not support the scale economies hypothesis: the average efficiency is higher for very small firms compared to other firm sizes, although the average efficiency for large firms is higher than that for medium-size firms. Regarding dynamic efficiency, the results reveal slight variations among the years examined, but the differences are not statistically significant. Finally, the study sheds light on the link between the efficiency of rural tourism and sustainable practices as the investment in environmental protection developed by regions during the period. [ABSTRACT FROM AUTHOR]

Over the years, banks have faced many difficulties, related mainly to lax credit standards for borrowers and counterparties. The goal of credit risk management is to maintain the volume of credit risk at acceptable level as it is a vital feature in risk management. Credit analysts take into consideration factors of a wider spectrum, e.g., the prospects of the line of business, the experience of board members, credibility of suppliers, etc. Those factors are often considered on the linguistic scale, which includes such imprecise and inaccurate phrases, for instance, such as: more/less experienced, better/worse prospects, etc., which, for the experts and decision makers, are justified and result from their personal experience, preferences and human nature. The paper presents the approach of supporting methods in the credit risk decision-making process. It presents evaluation scales of imprecise phrases commonly used during the process of credit risk assessment based on experts' preferences. Due to the imprecision, the oriented fuzzy numbers are a useful tool. For such described evaluation scales, we use a scoring function determined with the use of an adapted Simple Additive Weighting (SAW) method. [ABSTRACT FROM AUTHOR]

A formal model of an imprecise number can be given as, inter alia, a fuzzy number or oriented fuzzy numbers. Are they formally equivalent models? Our main goal is to seek formal differences between fuzzy numbers and oriented fuzzy numbers. For this purpose, we examine algebraic structures composed of numerical spaces equipped with addition, dot multiplication, and subtraction determined in a usual way. We show that these structures are not isomorphic. It proves that oriented fuzzy numbers and fuzzy numbers are not equivalent models of an imprecise number. This is the first original study of a problem of a dissimilarity between oriented fuzzy numbers and fuzzy numbers. Therefore, any theorems on fuzzy numbers cannot automatically be extended to the case of oriented fuzzy numbers. In the second part of the article, we study the purposefulness of a replacement of fuzzy numbers by oriented fuzzy numbers. We show that for a portfolio analysis, oriented fuzzy numbers are more useful than fuzzy numbers. Therefore, we conclude that oriented fuzzy numbers are an original and useful tool for modelling a real-world problems. [ABSTRACT FROM AUTHOR]

In general, the present value (PV) concept is ambiguous. Therefore, behavioural factors may influence on the PV evaluation. The main aim of our paper is to propose some method of soft computing PV evaluated under the impact of behavioural factors. The starting point for our discussion is the notion of the Behavioural PV (BPV) defined as an imprecisely real-valued function of distinguished variables which can be evaluated using objective financial knowledge or subjective behavioural premises. In our paper, a BPV is supplemented with a forecast of the asset price closest to changes. Such BPV is called the oriented BPV (O-BPV). We propose to evaluate an O-BPV by oriented fuzzy numbers which are more useful for portfolio analysis than fuzzy numbers. This fact determines the significance of the research described in this article. O-BPV may be applied as input signal for systems supporting invest-making. We consider here six cases of O-BPV: overvalued asset with the prediction of a rise in its price, overvalued asset with the prediction of a fall in its price, undervalued asset with the prediction of a rise in its price, undervalued asset with the prediction of a fall in its price, fully valued asset with the prediction of a rise in its rice and fully valued asset with the prediction of a fall in its rice. All our considerations are illustrated by numerical examples. Presented examples show the way in which we transform superposition of objective market knowledge and subjective investment opinion into simple return rate. [ABSTRACT FROM AUTHOR]

The unit return is determined as the return in the quotation currency (QCR) per the unit of base exchange medium (BEM). The main purpose is to examine the applicability of a trading system with a constant modulus of unit return (CMUR). The CMUR system supports speculative operations related to the exchange rate, given as the BEM quotation per the QCR. Premises for investment decisions are based on knowledge about the quotation dynamics described by its binary representation. This knowledge is described by a prediction table containing the conditional probability distributions of exchange rate increments. Any prediction table depends on observation range. Financial effectiveness of any CMUR system is assessed in the usual way by interest rate and risk index based on Shannon entropy. The main aim of our paper is to present algorithms which may be used for selecting effective CMUR systems. Required unit return modulus and observation range are control parameters applied for management of CMUR systems. Optimal values of these parameters are obtained by implementation of the proposed algorithm. All formal considerations are illustrated by an extensive case study linked to gold trading. [ABSTRACT FROM AUTHOR]

The Japanese candlesticks' technique is one of the well-known graphic methods of dynamic analysis of securities. If we apply Japanese candlesticks for the analysis of high-frequency financial data, then we need a numerical representation of any Japanese candlestick. Kacprzak et al. have proposed to represent Japanese candlesticks by ordered fuzzy numbers introduced by Kosiński and his cooperators. For some formal reasons, Kosiński's theory of ordered fuzzy numbers has been revised. The main goal of our paper is to propose a universal method of representation of Japanese candlesticks by revised ordered fuzzy numbers. The discussion also justifies the need for such revision of a numerical model of the Japanese candlesticks. There are considered the following main kinds of Japanese candlestick: White Candle (White Spinning), Black Candle (Black Spinning), Doji Star, Dragonfly Doji, Gravestone Doji, and Four Price Doji. For example, we apply numerical model of Japanese candlesticks for financial portfolio analysis. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to investigate a speculative trading system with a constant magnitude of return rate. We consider speculative operations related to the exchange rate given as the quotient of the base exchange medium by the quoted currency. An exchange medium is understood as any currency or any precious metal. The unit return is defined as the return expressed in the quoted currency by the amount of base exchange medium. All possible states of the exchange market form a finite elemental space. All knowledge about the dynamics of this market is presented as a prediction table describing the conditional probability distributions of incoming exchange rate changes. On the other hand, in the proposed trading system each speculative operation is concluded in such a way that the gross payment is determined by the given magnitude of unit return. The paper contains an analysis of the following evaluation criteria: annual number of transaction, success probability, expected unit payment, expected unit profit, risk index, unit risk premium, return rate, interest rate, and interest risk premium. Both of these indices can be used to select the effective trading systems. Effectiveness is considered in the local sense and in the global sense. [ABSTRACT FROM AUTHOR]

From the perspective of each evaluation criterion, any decision alternative is evaluated by means of trapezoidal ordered fuzzy numbers (TrOFN). This approach is justified in the way that some criteria are linguistically evaluated. In this paper, decision alternatives are evaluated using oriented fuzzy Simple Additive Weighting (OF-SAW) scoring function. The ranking of alternatives may be defined by means of a nonincreasing sequence of defuzzified values of a scoring function. Any defuzzification procedure distorts ordered fuzzy numbers in a way that information on imprecision and orientation is lost. This undermines the credibility of the determined alternatives' ranking. The main purpose of this paper is to avoid the defuzzification stage in the OF-SAW method. Thus, the OF-SAW method is equipped with fuzzy scoring order. This OF-SAW method is described as a negotiation scoring system. We study an empirical example of the OF-SAW application and rank some negotiation offers. Here, we focus on the effects of replacing the defuzzified scoring function by a fuzzy one. The obtained conclusions are generalized for the case of any decision alternatives. [ABSTRACT FROM AUTHOR]

In this paper, the model of imprecise quantity information is an ordered fuzzy number. The purpose of our study is to propose some methods of approximating any ordered fuzzy number using a trapezoidal ordered fuzzy number. The information ambiguity is evaluated by means of an energy measure. The information indistinctness is evaluated by Kosko's entropy measure. We discuss the problem of approximation of an arbitrary ordered fuzzy number by the nearest trapezoidal ordered fuzzy number. This way, we can simplify arithmetical operations on the linear space of ordered fuzzy numbers. The set of feasible trapezoidal ordered numbers is limited by the combination of the following conditions: invariance of energy measure, invariance of entropy measure, and invariance of information support. Evaluating the influence of individual limits combinations on the utility of given approximations, two combinations of those restraints, recommended for use, were chosen. It was also indicated that one of the recommended approximation problems can be used only for ordered fuzzy numbers characterized by a low level of entropy. The obtained results are currently used in such multi-criterial decision making models as financial portfolio management, evaluation of negotiations offers, the fuzzy TOPSIS model, and the fuzzy SAW model. [ABSTRACT FROM AUTHOR]

Bilateral agenesis of the long head of the biceps brachial tendon (LHB) is a very rare variation of the anatomy. We report a case of an 18-year-old man with bilateral agenesis of the long head of the biceps brachii tendon. We present initial findings, radiographical examinations and the follow-up of an unusual entity. Diagnosis of agenesis of the LHB can be challenging especially in cases of traumatic shoulder pain. It is not a very known entity because of its rareness. However, it could be associated with other congenital anomalies. The absence of the LHB is easily ignored in the diagnostic process. Clinical examination should be a pitfall, radiological examination is helpful to confirm the suspicion of LHB absence. MRI is often the first choice, although ultrasonography is cheaper and much easier to access and it is an excellent tool to visualise this anatomic variation with empty or shallow intertubercular groove., Competing Interests: Competing interests: None declared., (© BMJ Publishing Group Limited 2020. No commercial re-use. See rights and permissions. Published by BMJ.)

Background: To analyse the relation between immediate intraoperative neurophysiological changes during decompression and clinical outcome in a series of patients with lumbar spinal stenosis (LSS) undergoing surgery., Methods: Twenty-four patients with neurogenic intermittent claudication (NIC) due to LSS undergoing decompressive surgery were prospectively studied. Intra operative trans-cranial motor evoked potentials (tcMEPs) were recorded before and immediately after surgical decompression. Lower limb normalised tcMEP improvement was used as primary neurophysiological outcome. Clinical outcome was assessed using the Zurich Claudication Questionnaire (ZCQ) self-assessment score, before surgery (baseline) and at an average of 8 and 29 months post-operatively., Results: We found a moderate positive correlation between tcMEP changes and ZCQ at early follow-up (R=0.36). At late follow-up no correlation was found between intra-operative tcMEP and ZCQ changes. Dichotomizing the data showed a statistically significant relationship between tcMEP improvement and better functional outcome at early follow-up (P=0.013) but not at later follow-up (P=1)., Conclusions: Our findings suggest that intra-operative neurophysiological improvement during decompressive surgery may predict a better clinical outcome at early follow-up although this is not applicable to late follow-up possibly due to the observed erosion of functional improvement with time., Competing Interests: Conflicts of Interest: The authors have no conflicts of interest to declare.