The notion of fuzziness as defined in this paper relates to situations in which the source of imprecision is not a random variable or a stochastic process, but rather a class or classes which do not possess sharply defined boundaries, e.g., the “class of bald men,” or the “class of numbers which are much greater than 10,” or the “class of adaptive systems,” etc. A basic concept which makes it possible to treat fuzziness in a quantitative manner is that of a fuzzy set, that is, a class in which there may be grades of membership intermediate between full membership and non-membership. Thus, a fuzzy set is characterized by a membership function which assigns to each object its grade of membership (a number lying between 0 and 1) in the fuzzy set. After a review of some of the relevant properties of fuzzy sets, the notions of a fuzzy system and a fuzzy class of systems are introduced and briefly analyzed. The paper closes with a section dealing with optimization under fuzzy constraints in which an approach to...

Fuzzy sets and systems

The rise in fuel and oil prices has driven the hunt for alternative renewable resources for production of chemical intermediates or biofuels since they provide a sustainable solution to an increasing demand. Levulinic acid (LA), one of the platform chemicals, can be produced chemically using renewable resources such as starch waste and lignocellulosic biomass which sounds to be an attractive alternative owing to its abundance and environmentally benign nature. The presence of acidic carboxyl and ketone carbonyl groups in LA impart a remarkable pattern of reactivity to levulinic acid and allow it to form several derivatives having significant applications in various fields, thereby making it a versatile green chemical. The present review deals with the current status of the technologies available for levulinic acid production, its recovery and the array of applications in several areas along with the gridlocks involved at each step of conversion process and suggest some possible remedies. Further, it not only throws light on the recent advancements in LA production approaches along with the avant-garde biotechnological approach for its biosynthesis but also depicts the current market scenario of commercial LA industry. The review also discusses the future R&D scope with an aim to enhance the yield of levulinic acid production and to make the process energy-efficient and cost-effective.

Levulinic acid production from renewable waste resources: Bottlenecks, potential remedies, advancements and applications

Recently, bipolar fuzzy sets have been studied and applied a bit enthusiastically and a bit increasingly. In this paper we prove that bipolar fuzzy sets and [0,1](2)-sets (which have been deeply studied) are actually cryptomorphic mathematical notions. Since researches or modelings on real world problems often involve multi-agent, multi-attribute, multi-object, multi-index, multi-polar information, uncertainty, or/and limit process, we put forward (or highlight) the notion of m-polar fuzzy set (actually, [0,1] (m)-set which can be seen as a generalization of bipolar fuzzy set, where m is an arbitrary ordinal number) and illustrate how many concepts have been defined based on bipolar fuzzy sets and many results which are related to these concepts can be generalized to the case of m-polar fuzzy sets. We also give examples to show how to apply m-polar fuzzy sets in real world problems.

/pdf/m-polar-fuzzy-sets-an-extension-of-bipolar-fuzzy-sets-5dbik37z3l.pdf

m-Polar fuzzy sets: an extension of bipolar fuzzy sets.

Production of 5-hydroxymethylfurfural and levulinic acid from lignocellulosic biomass and catalytic upgradation

Levulinic acid (LA) is one of the top bio-based platform molecules that can be converted into many valuable chemicals. It can be produced by acid catalysis from renewable resources, such as sugars, lignocellulosic biomass and waste materials, attractive candidates due to their abundance and environmentally benign nature. The LA transition from niche product to mass-produced chemical, however, requires its production from sustainable biomass feedstocks at low costs, adopting environment-friendly techniques. This review is an up-to-date discussion of the literature on the several catalytic systems that have been developed to produce LA from the different substrates. Special attention has been paid to the recent advancements on starting materials, moving from simple sugars to raw and waste biomasses. This aspect is of paramount importance from a sustainability point of view, transforming wastes needing to be disposed into starting materials for value-added products. This review also discusses the strategies to exploit the solid residues always obtained in the LA production processes, in order to attain a circular economy approach.

https://www.mdpi.com/2073-4344/6/12/196/pdf

New Frontiers in the Catalytic Synthesis of Levulinic Acid: From Sugars to Raw and Waste Biomass as Starting Feedstock

The notions of cubic a-ideals and cubic p-ideals are introduced, and several related properties are investigated. Characterizations of a cubic a-ideal are established. Relations between cubic p-ideals, cubic a-ideals and cubic q-ideals are discussed. The cubic extension property of a cubic a-ideal is discussed.

Cubic structures applied to ideals of BCI-algebras

Optimization of levulinic acid production from Gelidium amansii.

On the basis of the theory of a falling shadow, the notion of a falling fuzzy positive implicative ideal of a BCK-algebra is introduced. Relations between falling fuzzy positive implicative ideals and falling fuzzy ideals are given. Relations between fuzzy positive implicative ideals and falling fuzzy positive implicative ideals are provided.

Fuzzy positive implicative ideals of BCK-algebras based on the theory of falling shadows

The notions of (weak) hyper MV-deductive systems and (weak) implicative hyper MV-deductive systems are introduced, and several properties are investigated. Relations among hyper MV-deductive systems, weak hyper MV-deductive systems, implicative hyper MV-deductive systems and weak implicative hyper MV-deductive systems are discussed. A characterization of a hyper MV-deductive system is provided. A condition for a weak hyper MV-deductive system to be a weak implicative hyper MV-deductive system is given.

/pdf/hyper-mv-deductive-systems-of-hyper-mv-algebras-2sx0ccb0za.pdf

Hyper mv-deductive systems of hyper mv-algebras

The notion of intersectional soft sets is introduced, and several examples are given. The application of intersectional soft sets to BCK/BCI-algebras is discussed.

Min Su Kang

Papers

Cubic structures applied to ideals of BCI-algebras

Optimization of levulinic acid production from Gelidium amansii.

Fuzzy positive implicative ideals of BCK-algebras based on the theory of falling shadows

Hyper mv-deductive systems of hyper mv-algebras

Intersectional soft sets and applications to bck/bci-algebras