A Novel Method of Ranking Intuitionistic Fuzzy Numbers using Value and θ Multiple of Ambiguity at Flexibility Parameters

In this paper a novel method of ordering intuitionistic fuzzy numbers, based on the notions of ‘value’ and θ-multiple of ‘ambiguity’ of an intuitionistic fuzzy number, is developed. Further, the flexibility parameters, of decision-making at (α, β)-levels, are used in the method. These parameters allow the decision-maker to take decisions at various (α, β)-levels of decision-making. Many a times, all the reasonable properties of ranking intuitionistic fuzzy numbers were never checked in the existing studies. However, in this study an utmost attempt is being made to study the reasonable properties thoroughly. Further, the existing methods are mostly based on intuition and the geometry of the intuitionistic fuzzy numbers. However, the proposed method completely complies with the reasonable properties of ranking intuitionistic fuzzy numbers as well as the coherent intuition and the geometry of the intuitionistic fuzzy numbers. Further, newer properties are also being developed in this study. These prove the novelty of the proposed method. Further, a few numerical examples are discussed that demonstrates the proposed method.

Comparing First Metatarsophalangeal Joint Flexibility in Hallux Rigidus Patients Pre- and Postcheilectomy Using a Novel Flexibility Device

Background: Hallux rigidus (HR) is a common pathology of the first metatarsophalangeal (MTP) joint causing pain and stiffness. However, severity of symptoms and radiographic findings are not always concordant. A novel flexibility device, which measures the mobility of the MTP joint through its arc of motion, has been validated. This study compares flexibility in patients before and after cheilectomy (with or without proximal phalanx osteotomy) for HR. Methods: This is a single-center study of adult patients with HR who were indicated for cheilectomy or cheilectomy and Moberg (dorsiflexion closing wedge) osteotomy of the proximal phalanx based on symptoms and radiographs from 2013 to 2015. Pre- and postoperatively, patients underwent testing with a validated flexibility protocol to generate flexibility curves. Parameters included early and late flexibility, laxity torque, and laxity angle. Patients completed Foot and Ankle Outcomes Scores (FAOS) pre- and postoperatively. Twelve operative patients underwent preoperative testing, with 9 completing postoperative testing (mean age, 53.0 years; 67% female; mean 2.8-year follow-up). Results: Patients had significant improvements in early sitting and standing flexibility, sitting and standing laxity angles, standing laxity torque, and both sitting and standing maximum dorsiflexion after surgery (all P < .05). While preoperative early flexibility, laxity angle, and maximum dorsiflexion all differed significantly between patients and controls ( P < .015), postoperative early flexibility was similar to controls ( P > .279). FAOS scores for pain, symptoms, sport, and quality improved significantly after surgery. Conclusion: Surgical treatment with cheilectomy was associated with significant improvements in nearly all flexibility parameters for sitting and standing positions. However, most postoperative flexibility parameters did not improve to the level of normal controls. Regardless, patients still experienced significant improvements in outcomes. This study demonstrated that surgical correction is associated with significant biomechanical and clinical results. The flexibility device can be used in further studies to assess outcomes after other HR procedures. Level of Evidence: Level II, prospective comparative study.

On the effect of the flexibility parameter on thermody­namic properties of acrylonitrile and methylvinylpyridine copolymers

We used thermal analysis to investigate the effects of temperature (20--300 °C) on the behaviour of acrylonitrile and methylvinylpyridine copolymers and determine the temperature ranges in which segmental mobility develops in them, as well as their glass transition temperatures. Data obtained via differential thermal analysis allowed us to compute activation energies for vitrification processes in copolymers of the series specified and to plot vitrification temperature as a function of copolymer composition. We used the method of increments to compute flexibility parameters for acrylonitrile and 2-methyl-5-vinylpyridine and analyse the effects of flexibility parameters on the manifestation of relaxation processes. The data obtained may be used to amend manufacturing parameters when developing chemisorptive filter materials based on the specified copolymer series.

The Effects of Specific Stretching Exercises on Flexibility and Balance Parameters in Gymnastics

This study was planned to examine the effect of Gymnastics-specific stretching exercises on flexibility and balance parameters. A total of 28 (16 males, 12 females) volunteer students were involved in the study, who were educated at the School of Physical Education and Sports. For 12 Weeks, 2 days a week and 90 min. stretching exercises specific to the gymnastics branch were applied and flexibility (sit-lie down) and Y balance tests were applied before the study. Anova test analysis was used to determine the difference between pre-test and post-test. Although the SA (right foot anterior), SPL (right foot posterolateral), SPM (right foot posteromedial), SLA (left foot anterior), SLPL (left foot posterolateral), SLPM (left foot posteromedial) scores of male and female students in the study showed a positive increase compared to the preliminary test scores, there was no statistically significant difference (p &gt; .05). As a result, gymnastic branch-specific stretching exercises increase the balance and flexibility parameters in a positive way; it is thought that the longer duration of training programs will have a positive effect on the athlete&rsquo;s performance.

Computing flexibility parameters and modelling the structure of poly(4-methylpentene-1)

We used the method of increments to compute thermodynamic characteristics of poly(4-methylpentene-1), specifically the Kuhn segment as a parameter of flexibility and packing density. In order to carry out the computations, we composed equations that take into account every atom in the repeat unit and the chemical bond types found in the macromolecule. The values obtained made it possible to classify poly(4-methylpentene-1) as a flexible polymer featuring high free volume. We consider possible structural transformation models for the polymer when the temperature varies in the 293...773 K range. Comparing model representations to structural transformations investigated experimentally explains a wide scope of experimentally detected relaxation and phase transitions.

Evaluation of Flexibility Optimization for Thermal Power Plants

The increasing share of fluctuating renewable energy sources leads to changing requirements for conventional power plants. The changing characteristics of the residual load requires the conventional fleet to operate with higher load gradients, lower minimum load at improved efficiency levels as well as faster start-ups and provision of ancillary services. Despite the requirements from the electricity market, the value of improving those flexibility parameters is hard to evaluate for power plant operators. In order to quantify the additional benefit that can be achieved by improving flexibility parameters on a certain power plant in a changing market environment, an adjustable load dispatch model has developed for that purpose. Using past electricity market data, the model is validated for typical coal and a typical gas fired power plants by reproducing their operational schedule. In the next step, the model is used to apply parameter changes to the power plants specifications and economic effects are demonstrated. General statements are derived on which flexibility parameter needs to be improved on each power plant type. Furthermore, specific economic evaluations are shown for the reference power plants in order to present the ability of the developed tool to support investment decisions for modernization projects of existing power plants.