Abstract. Coloring of fuzzy graphs plays a vital role in theory and practical applications. The concept of chromatic number of fuzzy graphs was introduced by Munoz[6] et.al. Later Eslahchi and Onagh [7]defined fuzzy coloring of fuzzy graphs and defined fuzzy chromatic number χ (G). Incorporating the features of these two definitions, the definition of chromatic number of a fuzzy graph χ(G), is ...

this paper proposes a new mathematical model for the integrated procurement-production-distribution problem of a fuzzy mixed integer linear programming (fmilp) type. considering the uncertainty in real problems, a number of parameters such as demand, capacity, and cost where their values are not available or known precisely, have been considered as trapezoidal fuzzy numbers. to solve fuzzy mixe...

triangular intuitionistic fuzzy numbers (tifns) is a special case of intuitionistic fuzzy (if) set and the ranking of tifns is an important problem. the aim of this paper is to develop a new methodology for ranking tifns by using multiattribute decision making methods (madm). in this methodology, the value and ambiguity indices of tifns may be considered as the attributes and the tifns in compa...

in this paper, we deal with fuzzy random variables for inputs andoutputs in data envelopment analysis (dea). these variables are considered as fuzzyrandom flat lr numbers with known distribution. the problem is to find a method forconverting the imprecise chance-constrained dea model into a crisp one. this can bedone by first, defuzzification of imprecise probability by constructing a suitablem...

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{...

Fuzzy numbers are fuzzy subsets of the set of real numbers satisfying some additional conditions. Fuzzy numbers allow us to model very difficult uncertainties in a very easy way. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on the crucial Extension Principle. When operating with fuzzy numbers, the results of our calculations strongly depend on the shape ...

In this paper, considers the usage of intuitionistic fuzzy numbers in decision making. The values and ambiguities of the membership degree and the non-membership degree for trapezoidal intuitionistic fuzzy number are defined as well as the value-index and ambiguity-index. The proposed ranking method is easily implemented and has a natural interpretation. 2010 AMS Classification: 47S20, 03E72

The scale of fuzzy numbers have been used in the literature to measurement of many ratings/perceptions/valuations, expectations, and so on. Among the most common uses one can point out: the so-called ‘fuzzy rating’, which is based on a free fuzzy numbered response scheme, and the ‘fuzzy conversion’, which corresponds to the conversion of linguistic (often Likert-type) labels into fuzzy numbers....

The importance and difficulty of the problem of ranking fuzzy numbers is pointed out. Here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its valuation, and using this valuation to compare and order fuzzy numbers. Specifically we focus on expected value type valuations which are based upon the transformation of a fuz...

in this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{ax_n+x_{n-1}}{b+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $a, b$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.