Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of generalised interval-valued fuzzy soft set are proposed and their basic properties are studied. The lattice structures of generalised interval-valued fuzzy soft set are also discussed. Furthermore, an application o...

In this paper, we propose new methods to represent interdependence among alternative attributes and experts’ opinions by constructing Choquet integral using interval-valued intuitionistic fuzzy numbers. In the sequel, we apply these methods to solve the multiple attribute group decision-making (MAGDM) problems under interval-valued intuitionistic fuzzy environment. First, the concept of interva...

Decision making is one of the most complex administrative processes in management. In circumstances where the members of the decision making team are uncertain in determining and defining the decision making criteria, fuzzy theory provides a proper tool to encounter with such uncertainties. However, if decision makers cannot reach an agreement on the method of defining linguistic variables base...

In this paper, we examine and compare De Morgan-, Kleene-, and Booleandisjunctive and conjunctive normal forms and consider their role in fuzzy settings. In particular, we describe normal forms and truth tables for classical fuzzy propositional logic and interval-valued fuzzy propositional logic that are completely analogous to those for Boolean propositional logic. Thus, determining logical eq...

Matrices play important roles in various areas in science and engineering. The classical matrix theory can not solve the problems involving various types of uncertainties. That type of problems are solved by using fuzzy matrix [14]. Later much works have been done by many researchers. Fuzzy matrix deals with only membership values. These matrices can not deal non membership values. Intuitionist...

In this work, we introduce the concept of fuzzy parameterized intervalvalued fuzzy soft set theory (fpivfss) and study their operations. We then define fpivfss-aggregation operator to form fpivfss-decision making method that allows constructing more efficient decision processes. Finally, some numerical examples are employed to substantiate the conceptual arguments.

The last few decades have witnessed rapid progress in the field of type-2 fuzzy systems and in particular interval type-2 fuzzy systems. Encouraged by this progress, we present in this paper some theoretical foundations and applications of interval-valued fuzzy morphological associative memories (IV-FMAMs) as a rule-based system. We perform simulations concerning the application of IV-FMAMs to ...

In this paper, the notions of $(T,S)$-composition matrix and$(T,S)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(T,S)$ is a dual pair of triangular module. Theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. Furthermore, theirproperties and characterizations are presented. Then a new methodbased on $tilde{...

The generalization of two-valued (crisp) sets to fuzzy sets gave us a rich and powerful representation scheme within the domain of semantic uncertainty. A parallel generalization of conjunctions and disjunction is needed from tnorms and t-conorms to what we might appropriately call linguistic (fuzzy) connectives, “AND," “OR," etc. In fact a closer look at the canonical forms of the combination ...