Multi-fuzzy set theory is an extension of fuzzy set theory, L-fuzzy set theory and Atanassov intuitionistic fuzzy set theory. In this paper we study the relation between Atanassov intuitionistic fuzzy and the proposed extension called Multi-fuzzy. Also we present the notion of Multi-fuzzy mappings and Atanassov Intuitionistic Fuzzy Sets Generating Maps. Mathematics Subject Classification: MSC: ...

the present paper introduces the notion of the complete fuzzy norm on a linear space. and, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. some characterizations of their properties are obtained.

In this paper, we introduce a stationary M∞-fuzzy metric on the set C B(X), where M∞-fuzzy metric can be thought of as the degree of nearness between two fuzzy sets with respect to any positive real number and C B(X) is the class of fuzzy sets with nonempty bounded closed α-cut sets. Under the φ-contraction conditions, we give some common fixed point theorems for self-mappings in the space C B(X).

An orthogonal approach to the fuzzification of both multisets and hybridsets is presented. In particular, we introduce $L$-multi-fuzzy and$L$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. In addition, we study the properties ofthese structures. Also, the usefulness of these structures is examined inthe framework of mechanical multiset proc...

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.Based on the ${L}$ukasiewicz triangular norm, we first p...

1.1.1. Definitions 1. Bounded Above (for a set): Let S ⊂ R. S is bounded above if ∃L ∈ R such that x ≤ L for all x ∈ S. L is called an upper bound for S. (Similar definition for bounded below and lower bound) 2. Bounded (for a set): Let S be a set. S is bounded if S is bounded above and bounded below. 3. Least Upper Bound (LUB) Axiom for R (for a set): Let S ⊂ R be bounded above. Then !∃L ∈ R s...

In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

in this paper, we consider the production possibility set with n production units such that the following four principles that governs: inclusion observations, conceivability, immensity and convexity. our goal is to estimate the output of a same and new production unit with existing production possibility and amount of input is specified. so, initially we find the interval changes of each input...

This paper deals with the simplest fuzzy PID controllers which employ two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. Mathematical model for a fuzzy PID controller is derived by using asymmetric Γ-function type and L-function type membership functions for each input, asymmetric trapezoidal membership functions for output, algebraic product trian...