Impact of Normalization on Entropy-Based Weights in Hellwig's Method: A Case Study on Evaluating Sustainable Development in the Education Area.

Determining criteria weights plays a crucial role in multi-criteria decision analyses. Entropy is a significant measure in information science, and several multi-criteria decision-making methods utilize the entropy weight method (EWM). In the literature, two approaches for determining the entropy weight method can be found. One involves normalization before calculating the entropy values, while the second does not. This paper investigates the normalization effect for entropy-based weights and Hellwig's method. To compare the influence of various normalization methods in both the EWM and Hellwig's method, a study evaluating the sustainable development of EU countries in the education area in the year 2021 was analyzed. The study used data from Eurostat related to European countries' realization of the SDG 4 goal. It is observed that vector normalization and sum normalization did not change the entropy-based weights. In the case study, the max-min normalization influenced EWM weights. At the same time, these weights had only a very weak impact on the final rankings of countries with respect to achieving the SDG 4 goal, as determined by Hellwig's method. The results are compared with the outcome obtained by Hellwig's method with equal weights. The simulation study was conducted by modifying Eurostat data to investigate how the different normalization relationships discovered among the criteria affect entropy-based weights and Hellwig's method results.

Extended Hellwig's Method Utilizing Entropy-Based Weights and Mahalanobis Distance: Applications in Evaluating Sustainable Development in the Education Area.

One of the crucial steps in the multi-criteria decision analysis involves establishing the importance of criteria and determining the relationship between them. This paper proposes an extended Hellwig's method (H_EM) that utilizes entropy-based weights and Mahalanobis distance to address this issue. By incorporating the concept of entropy, weights are determined based on their information content represented by the matrix data. The Mahalanobis distance is employed to address interdependencies among criteria, contributing to the improved performance of the proposed framework. To illustrate the relevance and effectiveness of the extended H_EM method, this study utilizes it to assess the progress toward achieving Sustainable Development Goal 4 of the 2030 Agenda within the European Union countries for education in the year 2021. Performance comparison is conducted between results obtained by the extended Hellwig's method and its other variants. The results reveal a significant impact on the ranking of the EU countries in the education area, depending on the choice of distance measure (Euclidean or Mahalanobis) and the system of weights (equal or entropy-based). Overall, this study highlights the potential of the proposed method in addressing complex decision-making scenarios with interdependent criteria.

Treatment of Complications After Minimally Invasive Breast Augmentation with Aquafilling Gel.

INTRODUCTION: Recent studies have revealed that Aquafilling gel used for breast augmentation causes complications. In this study, we investigated which surgical approach should be used to treat these complications. MATERIALS AND METHODS: This observational cohort study analysed the data of 31 women suffering from complications after breast enlargement with Aquafilling injection who were treated at our department in 2016-2021. Patients underwent either conservative or radical surgery. GraphPad Prism 9 (GraphPad Software, La Jolla, CA, USA) was used for data processing. RESULTS: Approximately 88.89% of patients after conservative surgery required reoperation, while only 22.73% of patients treated radically needed revision surgery. Every patient who underwent an attempt to remove the gel via needle prior to admission required surgery. Seventy-five per cent of them had positive culture swabs, whereas only 26.09% of patients who did not undergo needle aspiration had positive cultures. A positive correlation between the volume of injected filler and the number of symptoms was observed. CONCLUSIONS: In addition to irrigation and drainage, Aquafilling removal should include infiltrated tissue excision during primary surgery. Moreover, needle aspiration of the filler is ineffective, and it may lead to a gel infection. Furthermore, the more filler is injected, the higher the number of complications observed. Level of Evidence IV This journal requires that authors assign a level of evidence to each article. For a full description of these Evidence-Based Medicine ratings, please refer to the Table of Contents or the online Instructions to Authors www.springer.com/00266 .

The Impact of the Intuitionistic Fuzzy Entropy-Based Weights on the Results of Subjective Quality of Life Measurement Using Intuitionistic Fuzzy Synthetic Measure.

In this paper, an extended Intuitionistic Fuzzy Synthetic Measure (IFSM) with intuitionistic fuzzy (IF) entropy-based weights is presented. This method can be implemented in a ranking problem where the assessments of the criteria are expressed in the form of intuitionistic fuzzy values and the information about the importance criteria is unknown. One example of such a problem is measuring the subjective quality of life in cities. We join the debate on the determination of weights for the analysis of the quality of life problem using multi-criteria methods. To handle this problem, four different IF entropy-based weight methods were applied. Their performances were compared and analyzed based on the questionnaires from the survey concerning the quality of life in European cities. The studies show very similar weighting systems obtained by different IF entropy-based approaches, resulting in almost the same city rankings acquired through IFSM by using those weights. The differences in rankings obtained through the IFSM measure (and only by one position) concern the six cities included in the analysis. Our results support the assumption of the equal importance of the criteria in measuring this complex phenomenon.

Evaluation of outcomes of lower eyelid entropion and ectropion surgical repair.

<b><br>Introduction:</b> The imbalance of external and internal forces acting on the lower eyelid can result in entropion and ectropion, both of which cause ocular irritation and loss of proper eye protection. Potential complications of untreated cases include recurrent inflammation of the conjunctiva and cornea, conjunctival neovascularization, corneal abrasion or perforation, and ultimately even loss of vision. Although various surgical techniques are used to address this problem, their long-term outcome and effectiveness are still under discussion. </br> <b><br>Aim:</b> To evaluate outcomes of surgery for entropion and ectropion, including a modified Wheeler's method for entropion correction.</br> <b><br>Methods:</b> A non-comparative study (prospective and retrospective groups) included 100 patients operated on in two university hospitals' plastic surgery departments for lower eyelid entropion or ectropion, following formal ethics approval. The prospective group included 50 patients assessed preoperatively and at 3 and 12 months postoperatively. The retrospective group was comprised of 50 patients (2012-2018), whose preoperative documentation and clinical examinations were analyzed. The main outcome measures were change between pre- and postoperative patient-reported symptoms (VAS scale), ectropion/entropion grading scale (EGS/EnGS), quality of life (WHOQOL-BREF), and occurrence of complications.</br> <b><br>Results:</b> The differences in the severity of all symptoms before and after surgery evaluated with the VAS scale were statistically significant in both groups (p <0.05). We observed 6 recurrences (12%) in the prospective group and 9 (18%) in the retrospective group, with minor complications. Very good functional and esthetic postoperative results were confirmed in 70% (79) of the whole group and in 13 patients (81.3%) treated with the modified Wheeler's method. In the prospective group, the Mann- Whitney U test for dependent variables revealed significant improvement in the somatic, psychological, and environmental domains, with no significant change in the social relationships domain.</br> <b><br>Conclusions:</b> The results following entropion/ectropion surgery prove the effectiveness of the methods used. Complementing them with the modified Wheeler's method brought an increase in the number of very good outcomes. Surgery of lower eyelid malposition contributed to reduced symptoms and improved quality of life. The rates of postoperative sequelae were low.</br>.

Immunoexpression of Bmi-1, CK15, Bcl-2 in different types of basal cell carcinomas.

Introduction: Basal cell carcinoma (BCC) occurs in aggressive and non-aggressive forms. The expression of immunohistochemical markers varies in different types of BCC. Aim: Immunohistochemical analysis of selected proteins in BCCs. Material and methods: The immunohistochemical method was used to examine the immunoexpression of Bmi-1, CK15 and Bcl-2 in 56 cases of BCC divided into four groups. Results: Positive Bmi-1 staining 3-4+ level (nodular type) was seen in 91.3% of samples, 4+ (infiltrative) in 92.3%, 4+ (nodular/infiltrative) - 69.2%, 3+ - 30.8%, in BSC 3+ - 42.8%, and 28.6% each for 2+ and 4+. Low grade positivity (0-1+) in CK15 staining was present in 52.1% of nodular BCC, 46.2% - nodular/infiltrative, 92.3% - infiltrative, and 100% - BSC, but levels 2-3+ in nodular BCC in 47.8%, nodular/infiltrative BCC - 53.8%, infiltrative - 7.7%. Bcl-2 positivity (3-4+) was revealed in nodular BCC in 95.6%, (1-2+) in 100% of BSC, infiltrative and infiltrative/nodular BCC, but the lowest (0-1+) in 76.9% of nodular/infiltrative BCC, 71.4% of BSC, and in 38.4% of infiltrative BCC. Conclusions: Positive Bmi-1 staining was the highest in the aggressive infiltrative subtype of BCCs, whereas the lowest in basosquamous cell carcinomas (BSC). Infiltrative BCC was characterized by a lower level of CK15 expression than nodular BCC and nodular/infiltrative BCC. Differentiation of Bcl-2 expression depended on the type of tumour; the highest level was found in nodular BCC, low grade in nodular/infiltrative and infiltrative BCCs, and BSC.

The Extended Linguistic Hellwig's Methods Based on Oriented Fuzzy Numbers and Their Application to the Evaluation of Negotiation Offers.

This study proposes a novel fuzzy framework for eliciting and organizing the preference information of the negotiator to allow for the evaluation of negotiation offers. The approach is based on verbal evaluation of negotiation options that operates with linguistic variables to handle vague preferences and operationalizes them through oriented trapezoidal fuzzy numbers. Two variants of the linguistic method based on Hellwig's approach and oriented fuzzy numbers are proposed, which can be applied to building a scoring system for the negotiation template. Then, an example of determining such a scoring system and using it to evaluate the negotiation offers in typical multi-issue negotiation is shown. The results are discussed and compared with other methods known from the literature, in which the preference information is organized similarly but processed differently. The comparison shows that the presented methods can be an alternative to Simple Additive Weighting or TOPSIS methods that may also operate with oriented fuzzy numbers, but some of their characteristics may be problematic from the viewpoint of data interpretation. The former requires defuzzification of the global scores determined, while the latter requires the compulsory use of two reference points derived mechanically out of the negotiation space. By applying modified Hellwig's approaches, the former and the latter may be easily avoided.

On Some Extension of Intuitionistic Fuzzy Synthetic Measures for Two Reference Points and Entropy Weights.

In this paper, a novel Double Intuitionistic Fuzzy Synthetic Measure (DIFSM), based on intuitionistic fuzzy values for handling multi-criteria decision-making problems used to rank alternatives, is presented. In the studies, intuitionistic fuzzy sets (IFSs) represented uncertain, imprecise information or human judgment. The intuitionistic fuzzy sets can also reflect the approval, rejection, and hesitation of decision-makers. The degrees of satisfiability and non-satisfiability and uncertainty of each alternative with respect to a set of criteria are described by membership functions, non-membership functions, and hesitancy indexes, respectively. The aggregation algorithm DIFSM is inspired by Hellwig's method based on two reference points: ideal point (pattern) and anti-ideal point (anti-pattern), measuring distances between the alternative and ideal point and distance between the ideal and anti-ideal point. The proposed methods take into consideration the entropy-based weights of criteria. An illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach. Additionally, the comparative analysis results, using the DIFSM and the Intuitionistic Fuzzy TOPSIS-based framework, are presented.

Intuitionistic Fuzzy Synthetic Measure on the Basis of Survey Responses and Aggregated Ordinal Data.

The paper addresses the problem of complex socio-economic phenomena assessment using questionnaire surveys. The data are represented on an ordinal scale; the object assessments may contain positive, negative, no answers, a "difficult to say" or "no opinion" answers. The general framework for Intuitionistic Fuzzy Synthetic Measure (IFSM) based on distances to the pattern object (ideal solution) is used to analyze the survey data. First, Euclidean and Hamming distances are applied in the procedure. Second, two pattern object constructions are proposed in the procedure: one based on maximum values from the survey data, and the second on maximum intuitionistic values. Third, the method for criteria comparison with the Intuitionistic Fuzzy Synthetic Measure is presented. Finally, a case study solving the problem of rank-ordering of the cities in terms of satisfaction from local public administration obtained using different variants of the proposed method is discussed. Additionally, the comparative analysis results using the Intuitionistic Fuzzy Synthetic Measure and the Intuitionistic Fuzzy TOPSIS (IFT) framework are presented.

Fuzzy Representation of Principal's Preferences in Inspire Negotiation Support System.

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.

A Pharyngoplasty with a Dorsal Palatal Flap Expansion: The Evaluation of a Modified Surgical Treatment Method for Obstructive Sleep Apnea Syndrome-A Preliminary Report.

Surgical techniques for obstructive sleep apnea syndrome (OSAS) constantly evolve. This study aims to assess the effectiveness and safety of a new surgical approach for an OSAS pharyngoplasty with a dorsal palatal flap expansion (PDPFEx). A total of 21 participants (mean age 49.9; mean BMI 32.5) underwent a type III sleep study, an endoscopy of the upper airways, a filled medical history, a visual analog scale for snoring loudness, an Epworth Sleepiness Scale, and a Short Form Health Survey-36 questionnaire. A follow-up re-evaluation was performed 11 ± 4.9 months post-operatively. The study group (4 with moderate, 17 with severe OSAS) showed an improvement in all measured sleep study characteristics (p < 0.05), apnea-hypopnea index (pre-median 45.7 to 29.3 post-operatively, p = 0.009, r = 0.394), oxygen desaturation index (pre-median 47.7 and 23.3 post-operatively, p = 0.0005, r = 0.812), mean oxygen saturation (median 92% pre-operatively and median 94% post-operatively, p = 0.0002, r = 0.812), lowest oxygen saturation (p = 0.0001, r = 0.540) and time of sleep spent with blood oxygen saturation less than 90% (p = 0.0001, r = 0.485). The most commonly reported complications were throat dryness (11 patients) and minor difficulties in swallowing (5 patients transient, 3 patients constant). We conclude that a PDPFEx is a promising new surgical method; however, further controlled studies are needed to demonstrate its safety and efficacy for OSAS treatment in adults.

Reducing Cognitive Effort in Scoring Negotiation Space Using the Fuzzy Clustering Model.

Negotiation scoring systems are fundamental tools used in negotiation support to facilitate parties searching for negotiation agreement and analyzing its efficiency and fairness. Such a scoring system is obtained in prenegotiation by implementing selected multiple criteria decision-aiding methods to elicit the negotiator's preferences precisely and ensure that the support is reliable. However, the methods classically used in the preference elicitation require much cognitive effort from the negotiators, and hence, do not prevent them from using heuristics and making simple errors that result in inaccurate scoring systems. This paper aims to develop an alternative tool that allows scoring the negotiation offers by implementing a sorting approach and the reference set of limiting profiles defined individually by the negotiators in the form of complete packages. These limiting profiles are evaluated holistically and verbally by the negotiator. Then the fuzzy decision model is built that uses the notion of increasing the preference granularity by introducing a series of limiting sub-profiles for corresponding sub-categories of offers. This process is performed automatically by the support algorithm and does not require any additional preferential information from the negotiator. A new method of generating reference fuzzy scores to allow a detailed assignment of any negotiation offer from feasible negotiation space to clusters and sub-clusters is proposed. Finally, the efficient frontier and Nash's fair division are used to identify the recommended packages for negotiation in the bargaining phase. This new approach allows negotiators to obtain economically efficient, fair, balanced, and reciprocated agreements while minimizing information needs and effort.

Intuitionistic Fuzzy TOPSIS as a Method for Assessing Socioeconomic Phenomena on the Basis of Survey Data.

In the assessment of most complex socioeconomic phenomena with the use of multicriteria methods, continuous data are used, the source of which are most often public statistics. However, there are complex phenomena such as quality of life and quality of services in the assessment, for which questionnaire surveys and ordinal measurement scales are used. In this case, the use of classic multicriteria methods is very difficult, taking into account the way of presenting this type of data by official statistics, as well as their permissible transformations and arithmetic operations. Therefore, the main purpose of this study was the presentation of a novel framework which can be applied for assessing socioeconomic phenomena on the basis of survey data. It was assumed that the object assessments may contain positive or negative opinions and an element of uncertainty expressed in the form a "no", "difficult to say", or "no opinion" answers. For this reason, the intuitionistic fuzzy TOPSIS (IF-TOPSIS) method is proposed. To demonstrate the potential of this solution, the results of measuring the subjective quality of life of the inhabitants of 83 cities in EU countries, EFTA countries, the UK, the Western Balkans, and Turkey are presented. For most cities, a high level of subjective quality of life was observed using the proposed approach. The highest level of quality of life was observed in Zurich, whereas the lowest was observed in Palermo.

Autoimmune syndrome induced by adjuvants after breast enhancement with polyacrylamide hydrogel: a study in Poland.

Autoimmune syndrome induced by adjuvants (ASIA) is the spectrum of diseases in which the substances considered inert to the body induce autoimmune reactions and inflammation. Some of the biomaterials recently used in plastic surgery, such as silicone or polyacrylamide hydrogel (PAAG) seem to trigger clinical features of ASIA. The aim of this study was to assess the incidence of these features within a group of women after breast augmentation with PAAG. As many as 30 consecutive patients (26-59 years, mean age 39.5) referred to the Clinic of Plastic Surgery after breast enhancement with PAAG were examined. The validated criteria of ASIA syndrome were employed. Descriptive statistics were chosen based on the distribution of variables. The research was approved by the Bioethical Committee of the Centre of Postgraduate Medical Education in Warsaw, Poland. Within the studied group, 50% of patients (n = 15) fulfilled ASIA diagnostic criteria. Apart from local complications, we encountered various general symptoms, among which fever (n = 13, 43.3%), tingling and numbness of upper extremities (n = 10, 33.3%) and chronic fatigue (n = 9, 30%) were the most common. These symptoms were present on an ambulatory visit, before qualification to the operation of hydrogel removal. All patients undergoing surgical PAAG removal (n = 8) declared alleviation or complete resolution of the symptoms. Polyacrylamide hydrogel breast filling, although limiting the invasiveness of the procedure in relation to silicone breast implants, also carries the risk of developing ASIA symptoms. The removal of PAAG may bring improvement in some cases.