T-norm

In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection in a lattice and conjunction in logic. The name triangular norm refers to the fact that in the framework of probabilistic metric spaces t-norms are used to generalize triangle inequality of ordinary metric spaces.

Definition

A t-norm is a function T: [0, 1] × [0, 1] → [0, 1] which satisfies the following properties:

  • Commutativity: T(a, b) = T(b, a)
  • Monotonicity: T(a, b) ≤ T(c, d) if ac and bd
  • Associativity: T(a, T(b, c)) = T(T(a, b), c)
  • The number 1 acts as identity element: T(a, 1) = a
  • Since a t-norm is a binary algebraic operation on the interval [0, 1], infix algebraic notation is also common, with the t-norm usually denoted by *.

    The defining conditions of the t-norm are exactly those of the partially ordered Abelian monoid on the real unit interval [0, 1]. (Cf. ordered group.) The monoidal operation of any partially ordered Abelian monoid L is therefore by some authors called a triangular norm on L.

    Podcasts:

    PLAYLIST TIME:

    Latest News for: t-norm

    Edit

    Supporting the new norm of a marriage of convenience

    The Star 13 Apr 2025
    Since the General Election in 2022, non-Malay voters have become strategically more accepting of Umno, says this analyst. Read full story ... .
    Edit

    What RBI's proposed norms mean for co-lending, gold loans

    Live Mint 12 Apr 2025
    Two major frameworks proposed as part of the monetary policy statement on 9 April pertain to co-lending and lending against gold ornaments and jewellery—both popular loan segments for lenders and borrowers alike ....
    Edit

    Sebi for 'Optimal Regulation,' likely to Revamp Norms

    The Economic Times 12 Apr 2025
    ... overhaul to ease compliance burdens and modernize norms.
    Edit

    Sebi bats for ‘optimal regulation,’ likely to revamp norms

    The Times of India 12 Apr 2025
    ... overhaul to ease compliance burdens and modernize norms.
    Edit

    19-year-old 'tradwife' influencer goes viral for being a stay-at-home wife, defying societal norms

    Fox News 12 Apr 2025
    19-year-old social media influencer Savanna Stone is defying societal norms and ...
    Edit

    Gautam Budh Nagar: Admin cracks whip on private schools violating fee norms

    Hindustan Times 12 Apr 2025
    GREATER NOIDA ... 76 schools that failed to submit any details of fee revisions also came under scrutiny ... (HT File Photo) ... Strict action will be taken against any school found doing so ... Explore now! ... Admin cracks whip on private schools violating fee norms.
    Edit

    No longer married to traditional norms

    Deccan Herald 12 Apr 2025
    Education and career ambitions often took a backseat to the long-standing norm of early marriage. However, as social norms shift — particularly in urban centres — more women are asserting their right ...
    Edit

    Kerala eases dry-day norms, allows toddy in star hotels under new liquor policy

    India Today 11 Apr 2025
    Kerala eases dryday norms allows toddy in star hotels under new liquor policy ... .
    Edit

    Officiating Final Four games becoming the new norm for Pocatello native Tiffany Bird-Nelson

    Idaho State Journal 11 Apr 2025
    Being selected as one of the top officials in the country is becoming the new norm for Pocatello native Tiffany Bird-Nelson ... .
    Edit

    Appell Striping Disrupts Franchise Industry Norms with a Broker-Free Growth Model

    O'Colly 11 Apr 2025
    Industry leader in pavement maintenance and painting offers a direct path to franchise ownership with lower costs and strong national demand ... .
    Edit

    Mint Explainer: Why Sebi set up a committee to review conflict of interest norms

    Live Mint 11 Apr 2025
    Sebi has constituted a committee to strengthen its conflict of interest and disclosure frameworks for board members. We explain the need behind the markets regulator's decision and the challenges involved ....
    Edit

    Muthoot Finance Slips 14% In 2 Days On RBI's Draft Gold Loans Norms; Key Points ...

    News18 11 Apr 2025
    Shares of Muthoot Finance extended losses for the second consecutive session, falling as much as 8% to Rs 1,964.35 in intra-day trade on the BSE ... .
    ×