The commonly accepted theory of fuzzy numbers (Czogała and Pedrycz, 1985) is that set up by Dubois and Prade (1978), who proposed a restricted class of membership functions, called (L,R)–numbers with shape functions L and R. However, approximations of fuzzy functions and operations are needed if one wants to follow Zadeh’s (Zadeh 1975; 1983) extension principle. It leads to some drawbacks that ...

This paper extends the author’s earlier work on the Law of Large Numbers for fuzzy numbers [2] to the case where the fuzzy numbers are of type L-R. Namely, we shall define a class of Archimedean triangular norms in which the equality lim n→∞ Nes(mn − ≤ ηn ≤ mn + = 1, for any > 0, holds for all sequences of fuzzy numbers, ξi = (Mi, α, β)LR, i ∈ N, with twice differentiable and concave shape func...

Estimation of the origin-destination trip demand matrix (O-D) plays a key role in travel analysis and transportation planning and operations. Many researchers have developed different O-D matrix estimation methods using traffic counts, which allow simple data collection as opposed to the costly traditional direct estimation methods based on home and roadside interviews. In this paper, a new fuz...

Wafer quolify munagemenf of0 river sysrem is addressed i n n fizzy andprobobilisric framework. Two ryper of uneerfoinry, namely randomness and vagueness. ore rreared simrrlfonmii.dy in the monogemmf problem. A.fuzzy-ser-bo.~ed dqfinifion rhaf is a more general case offhe existing crisp-set-based dqfmirion of low w l e r qualify is infroduced. The evenr of low wafer qu01it)i af r? check-poinr in...

is also a fuzzy lattice. Throughout this paper, if {λj : j ∈ J} is a collection of L-sets in X , then (∨λj)(x) = ∨{λj(x) : j ∈ J}, x ∈ X ; and (∧λj)(x)=∧{λj(x) : j ∈ J}, x ∈ X . If r ∈ L, then rX denotes the fuzzy set given by rX(x) = r for all x ∈ X ; that is, rX denotes the “constant” L-set of level r, that is, the smallest and the largest elements of LX are denoted, respectively, by 0X and 1...

The starting point of the paper is the (well-known)observation that the “classical” Rough Set Theory as introduced by PAWLAK is equivalent to the S5 Propositional Modal Logic where the reachability relation is an equivalence relation. By replacing this equivalence relation by an arbitrary binary relation (satisfying certain properties, for instance, reflexivity and transitivity) we shall obtain...

In crisp transportation, trying to fuzzify the amount of supply of the ith origin ai and the amount of demand of the jth destination bj, we use level l fuzzy numbers and level (l, r) interval-valued fuzzy numbers to fuzzify ai and bj in the constraints. We get transportation problem in the fuzzy sense. We also cooperate some statistical concepts and corresponding to (1 α) × 100% statistical con...

Defuzzification is the process of converting a fuzzy quantity to precise quantity, just as fuzzification is the conversion of a precise quantity to a fuzzy quantity. Various types of defuzzification methods, are available for conversion of fuzzy to non-fuzzy. In this paper, defuzzification functions in intuitionistic fuzzy environment such as triangular, trapezoidal, L-trapezoidal, R-trapezoida...