Application of Fuzzy Logic in Investment-Intensive Decision Making

Fuzzy logic has been serving the industry for decades by resolving the ambiguities that appear as a result of imprecise environment. High-stake decision-making processes require inputs from various stakeholders to incorporate. If the risk is high, as in the case of high investment decision making, a robust system of incorporating opinions from multiple stakeholders must be set in place in order to avoid any inconsistency or bad decisions. Fuzzy matrices and arithmetic can play a rescuer in such situations. In this chapter, the authors demonstrate a decision-making framework incorporating the use of fuzzy numbers and arithmetic to make critical decisions in strategic marketing and new product development. Forecasting in the domains of new products is an utmost complex and critical process because no relevant history is available owing to the product's ‘one-of-its-kind' nature. In such cases, computation via analogy is an interesting paradigm, which is also discussed in the chapter.

Fuzzy Similarity Relations in Decision Making

Similarity is an ambiguous term that can be interpreted differently depending on the context of use. In this chapter, the authors review some of its uses before focusing on decision making. Ignoring the uncertainty of human knowledge would be denying a major attribute. Thus, they linked it to the fuzzy context. However, even taking this aspect into consideration, the opinion itself must be relevant. Therefore, the more a decision is similar to other opinions, the more it is coherent. Hence, there is a need to measure the similarity between each couple of expressed opinions.

Interval-Valued Fuzzy H-Ideals on ß-Algebra

The notion of interval valued fuzzy set was first introduced by Zadeh as a generalization of fuzzy sets. Using interval valued fuzzy set, various algebraic structures and related topics were discussed. This chapter extends fuzzy H-ideal into interval valued fuzzy H-ideals of β-algebra and deals some related results. It also provides the study on homomorphic images of an interval valued fuzzy H-ideals of β-algebra and the idea of Cartesian product of interval valued fuzzy H-ideals of β-algebra.

Intuitionistic Fuzzy Soft Ideals

The basic notions of soft sets theory are introduced by Molodtsov to deal with uncertainties when solving problems in practice as in engineering, social science, environment, and economics. This notion is convenient and easy to apply as it is free from the difficulties that appear when using other mathematical tools as theory of theory of fuzzy sets, rough sets, and theory of vague sets. The soft set theory has recently gaining significance for finding rational and logical solutions to various real-life problems, which involve uncertainty, impreciseness, and vagueness. The concepts of intuitionistic fuzzy soft left almost semigroups and the intuitionistic fuzzy soft ideal are introduced in this chapter, and some of their basic properties are studied.

Some Types of Ideals in QI-Algebras

In this chapter, ideals of QI-algebra are considered. Given a subset of a right distributive QI-algebra, the smallest ideal containing it is constructed. Also, the notions of implicative ideal, fantastic ideal, and normal ideal in a right distributive QI-algebra are introduced, and the authors proved that these notions are equivalent.

Bipolar Fuzzy Structure of H-Ideals in BCI-Algebras

In this chapter, the concepts of bipolar fuzzy H-ideals of BCI-algebras are introduced and their natures are investigated. Relations between bipolar fuzzy subalgebras, bipolar fuzzy ideals, and bipolar fuzzy H-ideals are discussed. Conditions for a bipolar fuzzy ideal to be a bipolar fuzzy H-ideal are provided. Some characterization theorems of bipolar fuzzy H-ideals are established. A bipolar fuzzy H-ideal is established by using a finite collection of H-ideals. The authors have shown that if every bipolar fuzzy H-ideal has the finite image, then every descending chain of H-ideals terminates at finite step.

Characterizations of Fuzzy Sublattices Based on Fuzzy Point

In a lattice 𝔏, the authors used the concept of belongingness and quasi-coincidence of fuzzy point to a fuzzy set, and by this notion, (∈,∈∨q)-fuzzy sublattice, (∈,∈∨q)-fuzzy ideal, cartesian product of (∈,∈∨q)-fuzzy sublattice, (∈,∈∨q)-fuzzy complemented sublattice, and cartesian product of (∈,∈∨q)-fuzzy complemented sublattice are introduced, and their properties are briefly studied. The relationship between fuzzy sublattice and (∈,∈∨q)-fuzzy sublattice, fuzzy ideal and (∈,∈∨q)-fuzzy ideal of L are established. The authors prove that the cartesian product of two (∈,∈∨q)-fuzzy ideals of a lattice is not necessarily a fuzzy ideal of a lattice. The theory of image and inverse image of an (∈,∈∨q)-fuzzy sublattice and (∈,∈∨q)-fuzzy ideal, an (∈,∈∨q)-fuzzy complemented sublattice, and (∈,∈∨q)-fuzzy complemented ideal of 𝔏 on the basis of homomorphism of lattices are also significantly established.

Solutions of Fuzzy System of Linear Equations

This chapter deals with solution methodology of fuzzy system of linear equations (FSLEs). In fuzzy set theory, finding solutions of FLSEs has long been a well-known problem to the researchers. In this chapter, the fuzzy number has been converted into interval number, and the authors have solved the interval system of linear equation for finding the fuzzy valued solution. Here, a fuzzy valued linear system has been introduced and a numerical example has been solved and presented for illustration of purpose.

Interval-Valued Intuitionistic Fuzzy Subnear Rings

The theory of interval-valued intuitionistic fuzzy sets is a generalization of both interval-valued fuzzy sets and intuitionistic fuzzy sets. In this chapter, the notion of interval-valued intuitionistic fuzzy subnear-ring is introduced, and some interesting properties are discussed. Some relations on the family of all interval-valued intuitionistic fuzzy subnear-ring are presented, and some related properties are investigated. Also, the authors represent upper and lower level set of interval-valued intuitionistic fuzzy set.

Fuzzy Bi-Interior Ideals of Semirings

In this chapter, the authors introduce the notion of a fuzzy bi-interior ideal of semiring and they characterize the regular semiring in terms of fuzzy bi-interior ideal of semiring. And also they proved Let I be a non-empty subset of a semiring M and χ_I be the characteristic function of I. Then I is a bi interior ideal of semiring if and only if χ_I is a fuzzy bi-interior ideal of semiring M.