This paper demonstrates twometa-mathematical propositions concerning the increasingly popular “intuitionistic” (= vague) approaches to fuzzy sets and fuzzy topology, as well as the closely related interval-valued (= grey) sets and interval-valued “intuitionistic” sets: (1) the term “intuitionistic” in these contexts is historically inappropriate given the standard mathematical usage of “intuiti...

Hesitant fuzzy evaluation strategy related to the interval-valued membership and nonmembership degrees should be an appropriate choice due lack of experience, ability knowledge some decision experts. In addition, it is important reasonably model interrelationship these this work, firstly, generalized q-rung orthopair hesitant sets (GIVqROHFSs) are defined, operational rules with respect GIVqROF...

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in amedical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised...

Dubois. D. , Prade. H. 1980. Fuzzy Sets and Systems. Mathematics in Science and Engineering, Academic Press, New York, 144. Jun. Y. B. , Kavikumar. J. 2011. Bipolar Fuzzy Finite State Machines. Bull. Malays. Sci. Soc. 34 no. 1: 181-188. Kandel. A. , Lee. S. C. Fuzzy Switching and Automata Theory Applications. Edward Arnold Publishers Ltd, London. Lee. K. J. 2000. Bipolar-valued fuzzy sets and t...

It is known that interval-valued fuzzy sets provide a more adequate description of expert uncertainty than the more traditional “type-1” (number-valued) fuzzy techniques. In the current approaches for using interval-valued fuzzy techniques, it is usually assumed that all fuzzy sets m(x) ∈ [m(x), m(x)] are possible. In this paper, we show that it is reasonable to restrict ourselves only to fuzzy...

Dubois. D. , Prade. H. 1980. Fuzzy Sets and Systems. Mathematics in Science and Engineering, Academic Press, New York, 144. Jun. Y. B. , Kavikumar. J. 2011. Bipolar Fuzzy Finite State Machines. Bull. Malays. Sci. Soc. 34 no. 1: 181-188. Kandel. A. , Lee. S. C. Fuzzy Switching and Automata Theory Applications. Edward Arnold Publishers Ltd, London. Lee. K. J. 2000. Bipolar-valued fuzzy sets and t...

Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decision-making preference. Hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (G-GIVIFSS) which conta...

The hesitant fuzzy soft set (HFSS), as a combination of hesitant fuzzy and soft sets, is regarded as a useful tool for dealing with the uncertainty and ambiguity of real-world problems. In HFSSs, each element is defined in terms of several parameters with arbitrary membership degrees. In addition, distance and similarity measures are considered as the important tools in different areas such as ...

The starting point of this paper is the introduction of a new measure of inclusion of fuzzy set A in fuzzy set B. Previously used inclusion measures take values in the interval [0,1]; the inclusion measure proposed here takes values in a Boolean lattice. In other words, inclusion is viewed as an Lfuzzy valued relation between fuzzy sets. This relation is reflexive, antisymmetric and transitive,...