The principle of a complex interval-valued Pythagorean fuzzy set (CIVPFS) is a valuable procedure to manage inconsistent and awkward information genuine life troubles. The principle of CIVPFS is a mixture of the two separated theories such as complex fuzzy set and interval-valued Pythagorean fuzzy set which covers the truth grade (TG) and falsity grade (FG) in the form of the complex number whose real and unreal parts are the sub-interval of the unit interval. The superiority of the CIVPFS is that the sum of the square of the upper grade of the real part (also for an unreal part) of the duplet is restricted to the unit interval. The goal of this article is to explore the new principle of CIVPFS and its algebraic operational laws. By using the CIVPFSs, certain Einstein operational laws by using the t-norm and t-conorm are also developed. Additionally, we explore the complex interval-valued Pythagorean fuzzy Einstein weighted geometric (CIVPFEWG), complex interval-valued Pythagorean fuzzy Einstein ordered weighted geometric (CIVPFEOWG) operators and utilized their special cases. Moreover, a multicriteria decision-making (MCDM) technique is explored based on the elaborated operators by using the complex interval-valued Pythagorean fuzzy (CIVPF) information. To determine the consistency and reliability of the elaborated operators, we illustrated certain examples by using the explored principles. Finally, to determine the supremacy and dominance of the explored theories, the comparative analysis and graphical expressions of the developed principles are also discussed.

BackgroundTraditional knowledge of indigenous plants is pivotal in developing strategies to feed livestock sustainably in low input systems. Likewise, in Pakistan the indigenous people of Central Punjab have been using their regional grasses as a ruminant fodder for centuries. This study evaluated the indigenous traditional knowledge to ascertain the value of various fodder grasses to optimise their use to feed livestock in Central Punjab.MethodsThe snowball technique was employed to identify key informants who had relevant knowledge about different grasses in the study area. Semi-structured questionnaires, face-to-face interviews and site visits were used for describing the fodder grasses. The data were then analysed by using relative frequency citation and pairwise comparison methods to determine the order of priority among the listed fodder grasses. Furthermore, SPSS 22 software was used for descriptive statistics and interpretation of associations among studied parameters. Microsoft Excel was used to present data as % values and graphs.ResultsOverall, 53 grasses were described with ethnobotanical information regarding their uses for fodder, ethnoveterinary and other purposes. All these grasses belonged to the family Poaceae where the subfamily Panicoideae had the maximum number of 30 grasses. We categorized these grasses into high (A), medium (B) and low priority (C) groups where the group A grasses were reported as not only the most abundant but also the most palatable forages to all ruminants. Their higher demand was reflected by the feeding systems of both ad libitum grazing and feeding after cutting and mixing with other feeds. The study also revealed 37 previously unreported ethnoveterinary uses of these grasses.ConclusionsThe results have reinforced the value of conserving ethnobotanical knowledge, being poorly documented previously, in developing strategies to feed livestock. It indicated the preferred fodder grasses as well as the possible reasons of their preference. The reported data need to be validated for nutritional and health benefits. This information could help the smallholder farmers in association with regional governments to propagate suitable fodder grasses for their use in sustainable livestock feeding to produce safe and healthy food for indigenous communities.

In this article, we combine the concept of a bipolar fuzzy set and a soft set. We introduce the notion of bipolar fuzzy soft set and study fundamental properties. We study basic operations on bipolar fuzzy soft set. We define extended union, intersection of two bipolar fuzzy soft set. We also give an application of bipolar fuzzy soft set into decision making problem. We give a general algorithm to solve decision making problems by using bipolar fuzzy soft set.

In this paper we propose a new three-step iteration process, called M iteration process, for approximation of fixed points. Some weak and strong convergence theorems are proved for Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Numerical example is given to show the efficiency of new iteration process. Our results are the extension, improvement and generalization of many known results in the literature of iterations in fixed point theory.

No abstract

No abstract

This study is reporting the biofuel synthesis and characterization from the novel nonedible feedstock cocklebur seeds oil. The Cocklebur crop seeds oil was studied as a potential source for biofuel production based on the chemical, structural and fuel properties analysis. The oil expression and FFAs content in cocklebur crop was reported 37.2% and 0.47 gram KOH/g, using soxhlet apparatus and acid base titration method, respectively. The maximum conversion and yield of the cocklebur crop seeds non-edible oil to biofuel was pursued 93.33%, using transesterification process. The optimum protocol for maximum conversion yield was adjusted: 1:7 oil-methanol molar ratios, ZnO nano-particle concentration 0.2 gm (w/w), reaction temperature 60 • C, and reaction time 45 min, respectively. ZnO nano-particle was prepared by a modified sol-gel method, using gelatin and the particle was XRD, TEM, XPS, and UV-vis spectroscopies. Qualitatively, the cocklebur crop synthesized biofuel was quantified and structurally characterized by GC/MS, FT-IR, NMR, and AAS spectroscopies. Quantitatively, the fuel properties of cocklebur crop biofuel was analyzed and compared with the international ASTM and EN standards.

No abstract